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How challenging experiences led me to pursue a PhD in Mathematics by Shanise Walker

As a student graduating high school, I was convinced of one thing: I was going to be a high school mathematics teacher. Everything I had done in high school and the inspiration and encouragement I received from teachers, family, and friends helped me feel reassured that my decision was the right one. As a high school student, I excelled in every subject, but doing mathematics was a passion. My love for mathematics led me to tutoring both middle school and high school students in mathematics, participating in mathematics competitions, and learning about other areas of mathematics outside of the curriculum. I had even earned the highest achievement award every year for mathematics in my grade level, so being a high school mathematics teacher seemed like the perfect choice for me.

As an undergraduate student, I immediately declared that I wanted to be a mathematics education major. Although I would have to be accepted into the program, I was sure of my choice in major. Completing the requirements to get into the program were easy because I was eager to be a math teacher. For the first few years of undergrad, things were going well. I added the mathematics major to my degree program and became a double major in mathematics and mathematics education. I was accepted into the mathematics education program and was set on my goals; everything was going well.

Fast forward to the spring semester of junior year, something changed. While taking a math education course focused on technology in the classroom, I found myself in a situation that I could not explain and one that could not be explained to me at the time. One of the first assignments in the course was to write an argumentative essay on technology in the classroom and its benefits or hindrances. When I wrote my essay, I focused my attention on the hindrances and how too much technology could lead students to rely heavily on devices and not enough on understanding the concepts. In the end, I received a low score on this assignment and when I inquired about the low score, the teaching assistant responded, “It’s just wrong.” This was just the beginning of a long battle of receiving low grades because “it’s just wrong.” Those words haunted me, so I stopped inquiring and just accepted the grades. I received lower grades than my peers, even on assignments where we had the same answers. I really disliked going to that class, but I knew I needed to finish the course because it was a requirement for my mathematics education degree. The real test came during the group final project. The project consisted of a group paper and a class demonstration on teaching a math topic to students. For the group paper, my group scored near perfect, but on the class demonstration, I scored significantly lower than my classmates. My group members and I did not understand it since I had written over half of the group paper and the project idea was one that I had brought to the group. I spent countless hours working on this project only to get near perfect or perfect grades on the group graded portion of the project but a low grade on my individual portion.

After receiving the group project grade, I had had enough. I decided to meet with the instructor of the course about my grades and my displeasure with the course. During our meeting, I asked the instructor to explain to me why my grades were much lower than classmates, especially on assignments where we had the same answers. It was then that I learned that this was not about my work, but about who I am. The professor outright admitted that the teaching assistant had given me lower scores because I was Black. The professor was already aware of the situation and had been for semesters before I became a student in his course. It had happened to other Black students who had taken the course before me. I was given assurance that while my grades were low, my final grade would not be. When I left that meeting, I cried. I was angry. While I knew that the particular teaching assistant would not be a grader for any other courses I would take in the major, I felt that I no longer had a place of belonging in that major. Despite feeling like I didn’t belong, I still had a passion for teaching high school mathematics, so I was determined to complete the degree.

The determination to continue with my mathematics education degree would change while I was a participant in an 8-week summer REU mathematics program. When I arrived at the REU program, I had no knowledge of how to conduct mathematics research and I was also unsure of what exactly I would be researching. However, with good mentorship from my research mentor and a postdoctoral student (now a tenured faculty member), I found myself interested in mathematics beyond teaching it. I was interested in solving math problems and I found that sense of community during the REU program that was lacking in my home department. Within the first few weeks of the REU program, I had decided that I wanted to get a PhD in mathematics–a thought I had not had before. My research mentor gave me advice on preparing and applying to graduate school. I took the advice and applied for PhD mathematics programs.

When I returned to my university the fall after the REU program, I was still pursuing a double major in mathematics and mathematics education. I knew that I had only one semester of coursework before I would be student teaching, but there was some unrest in me in continuing my mathematics education degree. I had just come from spending an entire summer doing math research, and I had this motivation in me to pursue a PhD. A week before classes started, I dropped my remaining mathematics education courses. After dropping the courses, I found myself in the position of being able to graduate at the end of the semester since I needed only one mathematics course and one elective course in a certain area to graduate. However, I decided I wanted to stay the entire senior year, so I enrolled in two mathematics courses and other electives.

While I dropped my mathematics education courses, I did not immediately drop my mathematics education major because I was still a bit torn about the idea of perhaps not being able to teach high school mathematics. However, before the fall semester ended, I went for it. I dropped the major and pursued my newfound interest of getting a PhD in mathematics. I started on a research project with a faculty member in the mathematics department and began submitting applications for graduate school. I submitted a number of applications for PhD in mathematics programs before the Thanksgiving break, so everything was going well.

In the spring of my senior year, I had another incident that solidified my pursuit of a mathematics PhD. I attended a graduate school fair at my institution to learn about other graduate programs at other institutions. While doing so, I stumbled upon a master’s program in mathematics education and thought to myself: “Well, maybe I could get my teaching certification while in this program because after all, I still had a passion to teach high school mathematics.” The program was at an institution close to my hometown, so that also meant that I would be able to spend more time with my family. The deadline to apply to the master’s program had not yet passed, so I thought to myself I would give it a shot. I spoke with the program’s representative, and we discussed the program and my GRE scores. She told me that I would likely get into the program with probationary status due to my GRE composite score. When I told her I had already been accepted into PhD programs in mathematics, there was a bit of shock on her face (and I am sure on mine as well). What I knew to be true was that my GRE Verbal Reasoning score was not as high, but I had done well on the GRE Mathematics portion. The composite score missed the mark for their institution to be granted full admission, so with this information in mind, I did not apply to the program. I continued with my plan to get a PhD in mathematics and finally decided that teaching high school mathematics was not the best fit for me. The following fall, I went off to graduate school, pursuing a mathematics PhD program at the same institution I had done the REU. Six years later, I completed the program and earned a PhD in mathematics.

Now, as I write about this experience almost ten years later, for the first time I ask myself, “How can eight weeks change the whole course of your life?” This is exactly what the REU program did for me. It changed the course of my life. It gave me a mathematical experience that I had not encountered before. It provided me with the mentorship I needed to succeed and gave me a sense of belonging in the mathematics community that I had not felt before. It also provided me with motivation to pursue something different–a doctoral degree. For this, I am grateful.

Two years ago, I had an opportunity to fulfill my passion of teaching high school mathematics. I taught calculus to a group of underrepresented minority students at a STEM summer program for high school students. This experience was just as joyful as I thought it would be, and I will always cherish it.

1 Response to How challenging experiences led me to pursue a PhD in Mathematics by Shanise Walker

Hi, I’m really inspired by your passion ,persistence and clarity to stick on to take up mathematics at research level. Currently I’m doing my ph. D program in management in India. But having graduated in bachelor’s degree in maths, I now have ardent desire to continue my masters and then proceed to do ph. d in maths. Though it’s 30 years since I lost touch, your life story is still furthering my passion. Thanks and a nice flow of narrative. Regards, Soundra

Comments are closed.

Opinions expressed on these pages were the views of the writers and did not necessarily reflect the views and opinions of the American Mathematical Society.

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• Doing a PhD in Mathematics
• Doing a PhD

What Does a PhD in Maths Involve?

Maths is a vast subject, both in breadth and in depth. As such, there’s a significant number of different areas you can research as a math student. These areas usually fall into one of three categories: pure mathematics, applied mathematics or statistics. Some examples of topics you can research are:

• Number theory
• Numerical analysis
• String theory
• Random matrix theory
• Graph theory
• Quantum mechanics
• Statistical forecasting
• Matroid theory
• Control theory

Besides this, because maths focuses on addressing interdisciplinary real-world problems, you may work and collaborate with other STEM researchers. For example, your research topic may relate to:

• Biomechanics and transport processes
• Evidence-based medicine
• Fluid dynamics
• Financial mathematics
• Machine learning
• Theoretical and Computational Optimisation

What you do day-to-day will largely depend on your specific research topic. However, you’ll likely:

• Continually read literature – This will be to help develop your knowledge and identify current gaps in the overall body of knowledge surrounding your research topic.
• Undertake research specific to your topic – This can include defining ideas, proving theorems and identifying relationships between models.
• Collect and analyse data – This could comprise developing computational models, running simulations and interpreting forecasts etc.
• Liaise with others – This could take many forms. For example, you may work shoulder-to-shoulder with individuals from different disciplines supporting your research, e.g. Computer scientists for machine learning-based projects. Alternatively, you may need frequent input from those who supplied the data for your research, e.g. Financial institutions or biological research colleagues.
• Attend a wide range of lectures, seminars and events.

Browse PhD Opportunities in Mathematics

Application of artificial intelligence to multiphysics problems in materials design, study of the human-vehicle interactions by a high-end dynamic driving simulator, physical layer algorithm design in 6g non-terrestrial communications, machine learning for autonomous robot exploration, detecting subtle but clinically significant cognitive change in an ageing population, how long does it take to get a phd in maths.

The average programme duration for a mathematics PhD in the UK is 3 to 4 years for a full-time studying. Although not all universities offer part-time maths PhD programmes, those that do have a typical programme duration of 5 to 7 years.

Again, although the exact arrangement will depend on the university, most maths doctorates will require you to first register for an MPhil . At the end of your first year, your supervisor will assess your progress to decide whether you should be registered for a PhD.

Additional Learning Modules

Some Mathematics departments will require you to enrol on to taught modules as part of your programme. These are to help improve your knowledge and understanding of broader subjects within your field, for example, Fourier Analysis, Differential Geometry and Riemann Surfaces. Even if taught modules aren’t compulsory in several universities, your supervisor will still encourage you to attend them for your development.

Most UK universities will also have access to specialised mathematical training courses. The most common of these include Pure Mathematics courses hosted by Mathematics Access Grid Conferencing ( MAGIC ) and London Taught Course Centre ( LTCC ) and Statistics courses hosted by Academy for PhD Training in Statistics ( APTS ).

What Are the Typical Entry Requirements for A PhD in Maths?

In the UK, the typical entry requirements for a Maths PhD is an upper second-class (2:1) Master’s degree (or international equivalent) in Mathematics or Statistics [1] .

However, there is some variation on this. From writing, the lowest entry requirement is an upper second-class (2:1) Bachelor’s degree in any math-related subject. The highest entry requirement is a first-class (1st) honours Master’s degree in a Mathematics or Statistics degree only.

It’s worth noting if you’re applying to a position which comes with funding provided directly by the Department, the entry requirements will usually be on the higher side because of their competitiveness.

In terms of English Language requirements, most mathematics departments require at least an overall IELTS (International English Language Testing System) score of 6.5, with no less than 6.0 in each individual subtest.

Tips to Consider when Making Your Application

When applying to any mathematics PhD, you’ll be expected to have a good understanding of both your subject field and the specific research topic you are applying to. To help show this, it’s advisable that you demonstrate recent engagement in your research topic. This could be by describing the significance of a research paper you recently read and outlining which parts interested you the most, and why. Additionally, you can discuss a recent mathematics event you attended and suggest ways in how what you learnt might apply to your research topic.

As with most STEM PhDs, most maths PhD professors prefer you to discuss your application with them directly before putting in a formal application. The benefits of this is two folds. First, you’ll get more information on what their department has to offer. Second, the supervisor can better discover your interest in the project and gauge whether you’d be a suitable candidate. Therefore, we encourage you to contact potential supervisors for positions you’re interested in before making any formal applications.

How Much Does a Maths PhD Typically Cost?

The typical tuition fee for a PhD in Maths in the UK is £4,407 per year for UK/EU students and £20,230 per year for international students. This, alongside the range in tuition fees you can expect, is summarised below:

Note: The above tuition fees are based on 12 UK Universities [1]  for 2020/21 Mathematic PhD positions. The typical fee has been taken as the median value.

In addition to the above, it’s not unheard of for research students to be charged a bench fee. In case you’re unfamiliar with a bench fee, it’s an annual fee additional to your tuition, which covers the cost of specialist equipment or resources associated with your research. This can include the upkeep of supercomputers you may use, training in specialist analysis software, or travelling to conferences. The exact fee will depend on your specific research topic; however, it should be minimal for most mathematic projects.

What Specific Funding Opportunities Are There for A PhD in Mathematics?

Alongside the usual funding opportunities available to all PhD Research students such as doctoral loans, departmental scholarships, there are a few other sources of funding available to math PhD students. Examples of these include:

You can find more information on these funding sources here: DiscoverPhDs funding guide .

What Specific Skills Do You Gain from Doing a PhD in Mathematics?

A doctorate in Mathematics not only demonstrates your commitment to continuous learning, but it also provides you with highly marketable skills. Besides subject-specific skills, you’ll also gain many transferable skills which will prove useful in almost all industries. A sample of these skills is listed below.

• Logical ability to consider and analyse complex issues,
• Commitment and persistence towards reaching research goals,
• Outstanding verbal and written skills,
• Strong attention to detail,
• The ability to liaise with others from unique disciple backgrounds and work as part of a team
• Holistic deduction and reasoning skills,
• Forming and explaining mathematical and logical solutions to a wide range of real-world problems,
• Exceptional numeracy skills.

What Jobs Can You Get with A Maths PhD?

One of the greatest benefits maths PostDocs will have is the ability to pursue a wide range of career paths. This is because all sciences are built on core principles which, to varying extents, are supported by the core principles of mathematics. As a result, it’s not uncommon to ask students what path they intend to follow after completing their degree and receive entirely different answers. Although not extensive by any means, the most common career paths Math PostDocs take are listed below:

• Academia – Many individuals teach undergraduate students at the university they studied at or ones they gained ties to during their research. This path is usually the preferred among students who want to continue focusing on mathematical theories and concepts as part of their career.
• Postdoctoral Researcher – Others continue researching with their University or with an independent organisation. This can be a popular path because of the opportunities it provides in collaborative working, supervising others, undertaking research and attending conferences etc.
• Finance – Because of their deepened analytical skills, it’s no surprise that many PostDocs choose a career in finance. This involves working for some of the most significant players in the financial district in prime locations including London, Frankfurt and Hong Kong. Specific job titles can include Actuarial, Investment Analyst or Risk Modeller.
• Computer Programming – Some students whose research involves computational mathematics launch their career as a computer programmer. Due to their background, they’ll typically work on specialised projects which require high levels of understanding on the problem at hand. For example, they may work with physicists and biomedical engineers to develop a software package that supports their more complex research.
• Data Analyst – Those who enjoy number crunching and developing complex models often go into data analytics. This can involve various niches such as forecasting or optimisation, across various fields such as marketing and weather.

What Are Some of The Typical Employers Who Hire Maths PostDocs?

As mentioned above, there’s a high demand for skilled mathematicians and statisticians across a broad range of sectors. Some typical employers are:

• Education – All UK and international universities
• Governments – STFC and Department for Transport
• Healthcare & Pharmaceuticals – NHS, GSK, Pfizer
• Finance & Banking – e.g. Barclays Capital, PwC and J. P. Morgan
• Computing – IBM, Microsoft and Facebook
• Engineering – Boeing, Shell and Dyson

The above is only a small selection of employers. In reality, mathematic PostDocs can work in almost any industry, assuming the role is numerical-based or data-driven.

How Much Can You Earn with A PhD in Maths?

As a mathematics PhD PostDoc, your earning potential will mostly depend on your chosen career path. Due to the wide range of options, it’s impossible to provide an arbitrary value for the typical salary you can expect.

However, if you pursue one of the below paths or enter their respective industry, you can roughly expect to earn [3] :

Academic Lecturer

• Approximately £30,000 – £35,000 starting salary
• Approximately £40,000 with a few years experience
• Approximately £45,000 – £55,000 with 10 years experience
• Approximately £60,000 and over with significant experience and a leadership role. Certain academic positions can earn over £80,000 depending on the management duties.

Actuary or Finance

• Approximately £35,000 starting salary
• Approximately £45,000 – £55,000 with a few years experience
• Approximately £70,000 and over with 10 years experience
• Approximately £180,000 and above with significant experience and a leadership role.

Aerospace or Mechanical Engineering

• Approximately £28,000 starting salary
• Approximately £35,000 – £40,000 with a few years experience
• Approximately £60,000 and over with 10 years experience

Data Analyst

• Approximately £45,000 – £50,000 with a few years experience
• Approximately £90,000 and above with significant experience and a leadership role.

Again, we stress that the above are indicative values only. Actual salaries will depend on the specific organisation and position and responsibilities of the individual.

Facts and Statistics About Maths PhD Holders

The below chart provides useful insight into the destination of Math PostDocs after completing their PhD. The most popular career paths from other of highest to lowest is education, information and communication, finance and scientific research, manufacturing and government.

Note: The above chart is based on ‘UK Higher Education Leavers’ data [2] between 2012/13 and 2016/17 and contains a data size of 200 PostDocs. The data was obtained from the Higher Education Statistics Agency ( HESA ).

Which Noteworthy People Hold a PhD in Maths?

Alan turing.

Alan Turing was a British Mathematician, WW2 code-breaker and arguably the father of computer science. Alongside his lengthy list of achievements, Turning achieved a PhD in Mathematics at Princeton University, New Jersey. His thesis titled ‘Systems of Logic Based on Ordinals’ focused on the concepts of ordinal logic and relative computing; you can read it online here . To this day, Turning pioneering works continues to play a fundamental role in shaping the development of artificial intelligence (AI).

Ruth Lawrence

Ruth Lawrence is a famous British–Israeli Mathematician well known within the academic community. Lawrence earned her PhD in Mathematics from Oxford University at the young age of 17! Her work focused on algebraic topology and knot theory; you can read her interesting collection of research papers here . Among her many contributions to Maths, her most notable include the representation of the braid groups, more formally known as Lawrence–Krammer representations.

Emmy Noether

Emmy Noether was a German mathematician who received her PhD from the University of Erlangen, Germany. Her research has significantly contributed to both abstract algebra and theoretical physics. Additionally, she proved a groundbreaking theorem important to Albert Einstein’s general theory of relativity. In doing so, her theorem, Noether’s theorem , is regarded as one of the most influential developments in physics.

Other Useful Resources

Institute of Mathematics and its Applications (IMA) – IMA is the UK’s professional body for mathematicians. It contains a wide range of useful information, from the benefits of further education in Maths to details on grants and upcoming events.

Maths Careers – Math Careers is a site associated with IMA that provides a wide range of advice to mathematicians of all ages. It has a section dedicated to undergraduates and graduates and contains a handful of information about progressing into research.

Resources for Graduate Students – Produced by Dr Mak Tomford, this webpage contains an extensive collection of detailed advice for Mathematic PhD students. Although the site uses US terminology in places, don’t let that put you off as this resource will prove incredibly helpful in both applying to and undertaking your PhD.

Student Interviews – Still wondering whether a PhD is for you? If so, our collection of PhD interviews would be a great place to get an insider perspective. We’ve interviewed a wide range of PhD students across the UK to find out what doing a PhD is like, how it’s helped them and what advice they have for other prospective students who may be thinking of applying to one. You can read our insightful collection of interviews here .

[1] Universities used to determine the typical (median) and range of entry requirements and tuition fees for 2020/21 Mathematics PhD positions.

• http://www.lse.ac.uk/study-at-lse/Graduate/Degree-programmes-2020/MPhilPhD-Mathematics
• https://www.ox.ac.uk/admissions/graduate/courses/dphil-mathematics?wssl=1
• https://www.graduate.study.cam.ac.uk/courses/directory/mapmpdpms
• https://www.ucl.ac.uk/prospective-students/graduate/research-degrees/mathematics-mphil-phd
• http://www.bristol.ac.uk/study/postgraduate/2020/sci/phd-mathematics/
• https://www.surrey.ac.uk/postgraduate/mathematics-phd
• https://www.maths.ed.ac.uk/school-of-mathematics/studying-here/pgr/phd-application
• https://www.lancaster.ac.uk/study/postgraduate/postgraduate-courses/mathematics-phd/
• https://www.sussex.ac.uk/study/phd/degrees/mathematics-phd
• https://www.manchester.ac.uk/study/postgraduate-research/programmes/list/05325/phd-pure-mathematics/
• https://warwick.ac.uk/study/postgraduate/research/courses-2020/mathematicsphd/
• https://www.exeter.ac.uk/pg-research/degrees/mathematics/

[2] Higher Education Leavers Statistics: UK, 2016/17 – Outcomes by subject studied – https://www.hesa.ac.uk/news/28-06-2018/sfr250-higher-education-leaver-statistics-subjects

[3] Typical salaries have been extracted from a combination of the below resources. It should be noted that although every effort has been made to keep the reported salaries as relevant to Math PostDocs as possible (i.e. filtering for positions which specify a PhD qualification as one of their requirements/preferences), small inaccuracies may exist due to data availability.

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Best Doctorates in Mathematics: Top PhD Programs, Career Paths, and Salaries

Given that only a small proportion of the general population holds a PhD in Mathematics, there aren’t many people pursuing doctoral studies in the math field. It requires a high level of intelligence and mathematical ability which a typical person doesn’t possess. It also requires a decent work ethic and the ability to commit five to seven years to research and study.

However, PhD in Mathematics salaries are high. If you’re interested in pursuing a PhD in Mathematics, check out our article to find the best mathematics PhDs and what mathematics jobs you can get. First, let’s find out what a PhD in Mathematics is.

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What is a phd in mathematics.

A PhD in Mathematics is a doctoral degree obtained by a graduate student in mathematics. This kind of mathematics graduate program allows students to develop their research capabilities in mathematics and its potential applications.

PhD in Mathematics can be a Doctor of Philosophy, Doctor of Science, or Doctor of Applied Mathematics degree. Students need to submit their PhD thesis in order to complete the math degree program they are pursuing. Math doctorate programs can take between three and six years to complete, depending on how much time is dedicated to the thesis and its required research.

How to Get Into a Mathematics PhD Program: Admission Requirements

The requirements to get into a mathematics PhD program typically include application fees, school transcripts, a professional resume, three letters of recommendation, and a statement of academic purpose. The admission process for most mathematical PhD programs is similar.

Some schools also require that students have mastered the material roughly equivalent to the undergraduate mathematics major, such as several semesters of calculus and experience with differential equations. Other doctoral math programs require applicants to submit essays or a minimum GPA score as entrance requirements.

PhD in Mathematics Admission Requirements

• Professional CV or resume
• Statement of academic purpose
• Application fee
• At least three recommendation letters
• Undergraduate and graduate school transcripts

Mathematics PhD Acceptance Rates: How Hard Is It to Get Into a PhD Program in Mathematics?

It is extremely hard to get into a PhD program in Mathematics. For example, the Harvard PhD acceptance rate is 4.59 percent and the University of Wisconsin has a zero percent PhD acceptance rate over a five-year median. Doctoral studies in mathematics are rigorous and have a low acceptance rate, making it difficult to get into and obtain a Doctorate in Mathematics.

How to Get Into the Best Universities

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Best PhDs in Mathematics: In Brief

Best Universities for Mathematics PhDs: Where to Get a PhD in Mathematics

The best universities for mathematics PhDs are Harvard University, Massachusetts Institute of Technology, Princeton University, Stanford University, University of California, Berkeley, and Yale University.

Other universities also have excellent PhD in Mathematics programs that we haven’t mentioned in our list, like Johns Hopkins University, Colorado State University, University of California, Los Angeles, and University of Chicago.

Columbia University is a private Ivy League research university founded in 1754 as King's College. It is among the top five national universities and is known as the oldest institution of higher education in New York. At Columbia University, students can find doctoral studies in biological sciences, astronomy, chemistry, economics, music, psychology, and religion.

Mathematics PhD

The PhD mathematics program is designed for full-time students interested in research and teaching at the university level. It is an intense course also meant for students that seek careers in quantitative research and development in business or government. It covers subjects like analysis and probability, Riemann surfaces, cumulative algebra, and modern geometry.

Mathematics PhD Overview

• Program Length: 4 years
• Acceptance Rate: 6%
• Tuition and Fees: $25,248/semester
• PhD Funding Opportunities: Department of Defense Funding, NIH Fellowship Parent Funding 

Mathematics PhD Admission Requirements

• A completed online application form at the Online Application System
• $120 application fee
• Statement of purpose
• A video essay (to be completed in the Online Application System)
• A current resume or CV
• Official transcripts from each university you attended
• Two letters of reference

Harvard University was established in 1636 by the Puritan clergyman John Harvard. It is known as the oldest institution of higher learning in the US and as one of the most prestigious universities in the world. It offers many PhD programs in subjects such as anthropology, statistics, virology, physics, neuroscience, mathematics, immunology, and history of science.

This doctoral program is intended for students who aspire to be research mathematicians and have demonstrated a strong interest in this field. The math graduate courses cover topics like commutative algebra, advanced real analysis, differential geometry evolution dynamics, Riemann surfaces, and Hodge theory.

• Program Length: 4-5 years
• Acceptance Rate: 7%
• Tuition and Fees: $50,928/first two years of study; $13,240/second two years of study
• PhD Funding Opportunities: Hertz Foundation, National Defense Science and Engineering Graduate Fellowship Program, National Physical Science Consortium for Minorities and Women, National Science Foundation
• Application
• $105 application fee 
• Transcripts
• Letters of recommendation
• Demonstration of English proficiency (for non-native speakers)

Massachusetts Institute of Technology (MIT) is a land-grant research university in Cambridge. Founded in 1861, MIT is best known for its programs in physical science and engineering. It offers a wide array of doctoral studies in aeronautics and astronautics, physics, political science, economics, chemical engineering, biology, brain, and cognitive sciences.

Doctor of Philosophy or Doctor of Science Mathematics Degree

In addition to choosing between a Doctor of Philosophy and a Doctor of Science program, students can choose to apply to the Pure or Applied Mathematics programs. Geometry, number theory, algebra, logic, statistics, topology, astrophysics, combinatorics, analysis, probability, numerical analysis, and theoretical physics, are covered in the Pure and Applied Mathematics curricula.

Doctor of Philosophy or Doctor of Science Mathematics Degree Overview

• Acceptance Rate: N/A
• Tuition and Fees: $27,755/term
• PhD Funding Opportunities: Postdoctoral and Senior Research Awards, Faculty Early Career Development Program, Mathematical Sciences Postdoctoral Research Fellowships (MSPRF)

Doctor of Philosophy or Doctor of Science Mathematics Degree Admission Requirements

• Fill out the online application
• Transcripts including grades in math/science/engineering courses
• At least three names and email addresses of recommendation letter writers
• Educational and work history
• Statement of objectives
• Outside financial support and potential outside support
• Credit/debit card payment of the $75 application fee
• Self-reported grades
• Arrange for submission of official transcripts and letters of recommendation

Princeton University is a private Ivy League research university that was founded in 1746. It is known as the fourth-oldest institution of higher education in the US. Princeton University has many PhD programs in subjects like philosophy, mechanical and aerospace engineering, electrical and computer engineering, and neuroscience.

Applied and Computational Math PhD

In this program, students gain a thorough understanding of areas of mathematics critical to scientific and engineering applications, such as numerical analysis and other computational approaches. In the first year, students choose three topics from six applied mathematics categories. At the end of the first year, students need to take a preliminary exam. 

Before the third year, students need to pass the general examination which culminates in a seminar on a research topic. The final requirement for this program is the doctoral dissertation which can be a mathematical contribution to one field of science or engineering.

Applied and Computational Math PhD Overview

• Tuition and Fees : $58,790/year 
• PhD Funding Opportunities: University, departmental, and program fellowships, research and teaching assistantships, external financial support

Applied and Computational Math PhD Admission Requirements

• $75 application fee
• Recommendation letters
• Fall semester grades (for students currently enrolled in master’s degree programs)
• English language tests (for international students)

Established in 1829, Rochester Institute of Technology is known for its excellent technology, engineering, and computing programs. It offers PhDs in Astrophysical Sciences and Technology, Biomedical and Chemical Engineering, Color Science, Imaging Science Sustainability, and many more disciplines.

Mathematical Modeling PhD

Students in this program plan their own trajectory based on required coursework, research, and their selected concentration. They can select from concentrations in the areas of applied inverse problems, biomedical, and discrete mathematics, among others. Some of the program’s courses cover subjects like numerical analysis and computing for mathematical modeling. 

Mathematical Modeling PhD Overview

• Acceptance Rate: 74%
• Tuition: $54,176/year 
• PhD Funding Opportunities: Federal loans, Outside Scholarships, Yellow Ribbon Program, employment through co-ops, internships, or assistantships

Mathematical Modeling PhD Admission Requirements

• Online graduate application
• Copies of official transcripts of all previously completed undergraduate and graduate courses
• Bachelor’s degree from an accredited university or college
• Current resume/CV
• Two letters of recommendation
• Personal statement of educational objectives
• TOEFL, IELTS, or PTE score (international students)
• $65 application fee

Stanford University is well-known for its enterprising student population and high return on investment. Founded in 1885 by California senator Leland Stanford, Stanford University is consistently ranking in the top 10 national universities. Stanford offers many PhD programs in its Graduate School of Engineering, including programs in engineering, medicine, and education.

Mathematics PhD Program

Students in this PhD program take courses in algebraic topology, differential topology, differential geometry, algebraic geometry, theory of probability, real analysis, modern algebra, and mathematical methods of imaging. In the first year, the coursework prepares the students for the qualifying examinations which test them on their skills in algebra and real-world analysis. 

Students must have a dissertation advisor and seek candidacy in their second year. Students will take their Area Examination during their third year, which must be completed by the conclusion of the Winter Quarter. In the fourth and fifth years, students are expected to finish their dissertation research.

Mathematics PhD Program Overview

• Acceptance Rate: 5.7%
• Tuition and Fees: $56,487
• PhD Funding Opportunities: Federal programs, university fellowships, research assistantships, teaching assistantships

Mathematics PhD Program Admission Requirements

• Bachelor’s degree from a regionally accredited US college or university 
• Unofficial transcripts/academic records
• Names and contact information of those who can provide between three and six letters of recommendation
• Online application
• $125 application fee or fee waiver

University of California, Berkeley was founded in 1868. UC Berkeley is known for strict academic criteria for its undergraduate programs. The school has more than 130 academic departments and 80 multidisciplinary research areas. UC Berkeley is among the top universities in the world.

PhD Program in Applied Mathematics

The applied mathematics program requires doctoral students with previous graduate study in mathematics must demonstrate exceptional mathematical research skills. Students in this course can learn about linear algebra and differential equations, multivariable calculus, and discrete mathematics. There are also major electives like mathematical biology and statistics.

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PhD Program in Applied Mathematics Overview

• Program Length: 5-6 years
• Acceptance Rate: 18%
• Tuition and Fees: $10,248.75/semester (resident); $17,799.75/semester (non-resident)
• PhD Funding Opportunities : Berkeley Fellowships, Chancellor’s Fellowships, Cota-Robles Fellowships, Mentored Research Awards, UC Dissertation-Year Fellowships, Conference Travel Grants, Parent and Caregiver Grants

PhD Program in Applied Mathematics Admission Requirements

• A bachelor’s degree or equivalent from an accredited institution
• A minimum GPA of 3.0
• Enough experience in your undergraduate program to complete the program
• At least three letters of recommendation
• $120 application fee (California residents); $140 application fee (all other applicants)

The University of Michigan - Ann Arbor is among the top 30 national universities. It was founded in 1817 in Ann Arbor. Some of the most popular majors from this university are business administration, experimental psychology, and economics. It also has good PhD level programs in education, electrical and computer engineering, and computer and information science.

Applied & Interdisciplinary Mathematics PhD

This PhD degree's purpose is to create graduates who are well-prepared to pursue successful careers in the mathematical sciences, whether in government or academia. Students in the applied and interdisciplinary mathematics course can learn about risk management and modeling of financial losses, mathematical theory of probability, and modern mathematics.

Applied & Interdisciplinary Mathematics PhD Overview

• Program Length: 5-6 years 
• Acceptance Rate: 26%
• Tuition and Fees: $25,230.38 (in state); $50,646.38 (out of state)
• PhD Funding Opportunities: Graduate Student Instructorship (GSI): Mathematics Graduate Student Instructor Teacher Training Program, and Graduate Student Research Assistantship (GSRA)

Applied & Interdisciplinary Mathematics PhD Admission Requirements

• Three letters of recommendation
• Personal Statement (500-word limit)
• TOEFL or IELTS Exam (non-native English speakers)
• Three semesters of calculus
• One or two semesters of differential equation courses
• One semester course in modern algebra, linear algebra, geometry or topology
• Advanced calculus of one and several variables 
• $75 application fee (US citizens); $90 application fee (international applicants)

Nelson Dewey, the first governor of Wisconsin, founded the University of Wisconsin in 1848. It has one of the best engineering and business majors. It also has several good graduate degrees from its Department of Mathematics like Doctor of Philosophy, Master of Arts – Foundations of Advanced Studies, and Master of Arts – Foundations for Research.

Mathematics, PhD

The University of Wisconsin’s Doctor of Philosophy program offers a foundation in fundamental and advanced graduate mathematics. Students in this PhD program can learn about linear algebra, abstract algebra, differential equations, knot theory, and real analysis.

Mathematics, PhD Overview

• Program Length: 5 years
• Acceptance Rate: 16%
• Tuition and Fees: $12,176/year (in state); $25,504/year (out of state)
• PhD Funding Opportunities: Graduate assistantships, fellowships, traineeships, student loans, student jobs, research and travel grants

Mathematics, PhD Admission Requirements

• Application to the UW–Madison Graduate School
• Master’s degree in mathematics or a related field
• Official transcripts
• Supplementary information form
• Three academic letters of recommendation and one additional letter
• Proof of English proficiency (for non-native speakers)
• One-page statement of purpose

Yale University was founded in 1701 in New Haven, Connecticut. It is among the top 10 national universities and is known for its Ivy League reputation . Yale has many PhD programs like anthropology, applied physics, architecture, biomedical engineering, chemical, and environmental engineering. 

PhD in Applied Mathematics

The applied mathematics program entails the study and application of mathematics to issues prompted by a diverse set of application fields. Students study and apply mathematics concepts to questions driven by a variety of applicable fields.

It covers topics such as discrete algorithms, linear and nonlinear partial differential equations, statistical theory and applications, information theory, econometrics, and classical and modern applied harmonic analysis. This program also covers topics like financial statistics, financial mathematics, econometrics probability theory, and information theory. 

PhD in Applied Mathematics Overview

• Acceptance Rate: 6.2%
• Tuition and Fees: $45,700/year
• PhD Funding Opportunities: Financial aid, university fellowships, dissertation fellowships, teaching fellowships

PhD in Applied Mathematics Admission Requirements

• A list of all the prior colleges or universities you’ve attended 
• Unofficial transcripts from each school
• TOEFL scores (non-native English-speaking applicants)

Can You Get a PhD in Mathematics Online?

Yes, you can get a PhD in Mathematics online. However, there aren’t many online PhD math programs out there because of two reasons. The first reason is that there isn’t a big demand for PhDs in Mathematics, so online universities are not inclined to find ways to make those programs more accessible.

The second reason is that in traditional doctoral studies graduate students in mathematics are used as research and teaching assistants. Usually, math doctoral studies take place within a community in which PhD students are apprentices learning alongside instructors and one another.

Best Online PhD Programs in Mathematics

How Long Does It Take to Get a PhD in Mathematics?

It takes about five years to get a PhD in Mathematics. Depending on the academic institution and the specifications of the program, it can take between three and six years. Some students prefer to have a master’s degree before entering a doctoral program in mathematics, but most programs do not require students to have more than a bachelor’s degree .

Some doctoral mathematics academic programs offer two degrees called dual degree programs. You can begin pursuing a Master’s Degree in Mathematics and begin earning credits for a PhD at the same time.

Is a PhD in Mathematics Hard?

Yes, a PhD in Mathematics is hard. Doctoral studies that require advanced knowledge of mathematics would be extremely difficult for most people. Whether you choose to pursue a PhD in Applied Mathematics or Pure Mathematics, you will encounter complex theoretical concepts.

How Much Does It Cost to Get a PhD in Mathematics?

On average, it costs $12,171 per year to get a PhD in Mathematics . This data is based on the National Center for Educational Statistics’s (NCES) report for the average costs of postgraduate studies at public institutions from 2018 to 2019. According to this data, it would cost a total of $48,684 for four years of studies. The cost to get a PhD in Mathematics has likely risen since 2019.

How to Pay for a PhD in Mathematics: PhD Funding Options

The PhD funding options that students can use to pay for a PhD in Mathematics include research fellowships, teaching assistantships, and tuition waivers. In the previous section, we mentioned the cost of doctoral degrees , but this number is with a deduction in the tuition.

These funding options enable students to lower the cost of tuition. For example, domestic students receive lower tuitions. Without funding options or deductions, a PhD can cost from $20,000 to $30,000 per year.

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What Is the Difference Between a Mathematics Master’s Degree and PhD?

The difference between a Master’s Degree in Mathematics and a PhD is the career opportunities they provide graduates. People who pursue a PhD in Mathematics usually seek jobs in research and academia, while people who pursue master’s degrees are more interested in advancing their professional careers.

A PhD in Math is more research-intensive and focused on historical and current perspectives within the mathematics field. Master’s degrees are a bit broader. Master’s degrees can take up to three years to complete, while PhD can take up to six years. Math PhD students also teach and engage in departmental activities, while master’s students do not.

Master’s vs PhD in Mathematics Job Outlook

It is usually required for postsecondary teachers to have PhDs. According to the Bureau of Labor Statistics (BLS), these professionals have a job outlook of 12 percent , four percent higher than the average for all occupations.

Mathematics and statisticians are usually required to hold a master’s degree and they have a job outlook of 33 percent , nearly three times the average for all occupations. According to these numbers, the job outlook for Master’s Degrees in Mathematics is higher than for PhDs in Mathematics. However, these are just two examples of careers available to master’s and PhD holders.

Difference in Salary for Mathematics Master’s vs PhD

According to PayScale, mathematicians with a master’s degree earn $85,000 per year, and mathematicians with a PhD degree earn $110,000 a year. This is a difference of $25,000 per year for mathematics master’s vs PhD holders.

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Why You Should Get a PhD in Mathematics

You should get a PhD in Mathematics because it expands your academic career opportunities and salary options. With a PhD in Math, you can work for private businesses or government agencies. Many PhD grads work in engineering, medicine, and software development, where they apply the advanced mathematical knowledge they acquired from their doctoral programs.

Reasons for Getting a PhD in Mathematics

• Specialized skills. A PhD in Mathematics equips you with highly valuable and marketable skills. Aside from subject-specific abilities, you can obtain several transferable skills that will be beneficial in practically any industry, such as exceptional numeracy, logical ability, holistic deduction, and reasoning skills.
• Higher salary. A PhD is a terminal graduate degree, meaning it is the highest level of academic certification you can achieve in this field. So with a PhD you will gain the highest skills and knowledge in mathematics. High-level skills and knowledge often translate to a high salary.
• Career opportunities. One of the best advantages math PhDs have is the option of following a variety of employment pathways. To some extent, all sciences are built on basic mathematical principles, so there are many career opportunities with a PhD in Mathematics. With this kind of degree, you can work in finance, academia, or IT.
• Research opportunities. Doctoral Degrees in Mathematics cover theoretical mathematics which is one of the best areas for research and research methodology. During your doctoral studies in math, you will study and research with some of the smartest people in the world.

Getting a PhD in Mathematics: Mathematics PhD Coursework

Getting a PhD in Mathematics is not an easy task. Students need to learn different math courses, some of which require advanced knowledge of mathematics. There is some standard mathematics PhD coursework, like classes in mathematical analysis or mathematical logic. Find out more details on common mathematics PhD courses below.

Mathematical Analysis

These kinds of courses explain the principles of mathematical analysis, including differentiability, continuity, sequence and series convergence, the Riemann integral, function sequences, and series. Students can also learn real applications of real-world analysis, including the estimation of indeterminate integrals, Laurent series, WKB theory, Cauchy theorem, and residual theorem.

Differential Topology

Courses in differential topology are a part of the theory of differential forms and De Rham’s theory. Somer differential topology courses teach about multilinear algebra, Stokes’ theorem, and an introduction to cohomology. But, in most cases, these courses teach about winding numbers, vector fields, index, smooth maps, transversality, and differential manifolds.

Discrete Mathematics

Courses in discrete mathematics usually cover finite geometry, finite groups, finite topology, finite fields, fundamental algebraic topology, combinatorics, and graph theory. Students can learn about the symmetry group of the regular icosahedron because it is a reoccurring subject throughout the course.

Theory of Probability

Theory of probability courses introduce students to discrete and continuous random variables, independent random variables, conditional probability, distribution functions, Poisson distributions, Bayes theorem, and joint distribution. Students in this course will learn how to use math principles in the analysis of random phenomena.

Algebraic Geometry

In most cases, algebraic geometry courses teach students about complex algebraic varieties, cohomology, affine, and projective algebraic geometry. They also cover the fundamental concepts of complex analytic varieties, Bezout’s theorem, algebraic curves, and surfaces, the language of schemes, and properties of morphisms.

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How to Get a PhD in Mathematics: Doctoral Program Requirements

Some of the most common doctoral program requirements to get a PhD in Mathematics are coursework, qualifying exams, research, classroom teaching, and thesis defense. Some doctoral program requirements may vary, but there are a few common steps for most math programs. Keep reading to find out more.

PhD students must finish eight or nine-term courses at the graduate level, in most cases maintaining at least a C average grade. The time for completion of a PhD math coursework is four to five years.

The residency requirement can vary from university to university. For most math PhD candidates, the usual residency requirement is around three years. The whole point of residency is to continue the education and training of students in a specialized field of mathematics.

A committee of three faculty members administers the Qualifying Examination, which is an oral test. Each student selects three qualifying test subjects and discusses them with appropriate examiners. Subjects must be in separate, reasonably broad mathematical fields. 

Typically, the primary topic is decided in cooperation with the potential thesis advisor. After completing the qualifying test, students must choose a thesis advisor, who is usually the primary topic examiner.

In academic positions, teaching is important, especially in mathematical doctoral studies. Many people in math PhD programs aspire to academic positions, so teaching is one of the best ways to learn about the mathematics academic profession. It is an excellent way to learn public presentation skills by completing at least one semester of classroom teaching.

Writing and defending a thesis for a PhD in Mathematics is the culmination of this graduate program. Usually, a thesis is anticipated to contain original research of a high enough quality to be published in a high-level research journal. The defense is usually held in the classroom of the Institute and is presented to the Thesis Examination Committee.

Potential Careers With a Mathematics Degree

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PhD in Mathematics Salary and Job Outlook

People with a PhD in Mathematics earn above the average annual salaries and have careers with above the average job growth. For example, actuaries have a 24 percent job growth till 2030. According to the Bureau of Labor Statistics, the average job growth rate for all occupations is 7.7 percent .

Earning a mathematics PhD is difficult but you will graduate with a wide range of job opportunities. People with a PhD in Math earn between $82,360 to $108,660 per year. Overall, people with PhDs in Mathematics have a good salary and job outlook.

What Can You Do With a PhD in Mathematics?

With a PhD in Mathematics, you can work in education or IT and for private, corporate, or government corporations. You can work as a postdoctoral research associate, a math professor in postsecondary or higher education, a director of analytics, a research scientist, a principal software engineer, or an asset manager.

Best Jobs with a PhD in Mathematics

• Data Scientist
• Mathematicians and Statistician
• Operations Research Analyst

What Is the Average Salary for a PhD in Mathematics?

The average salary for a PhD in Mathematics is $110,000 , according to PayScale. The salary range for doctorate-level degree mathematics jobs ranges from $48,690 to $167,040 per year. Lower-earning operations research analysts make an average of $48,690 , while top-earning data scientists earn $167,040 annually, according to the Bureau of Labor Statistics.

Highest-Paying Mathematics Jobs for PhD Grads

Best Mathematics Jobs with a Doctorate

There are many jobs you can find with a math PhD. The skills you will gain are applicable to almost any field. Find out more about the best PhD in Mathematics jobs below.

Data scientists are specialists who know how to extract and interpret data. They know how to use models and algorithms to analyze massive data repositories. They use various strategies to determine the optimal methods for developing a data model for a business. Data scientist is one of the most in-demand and highest-paid jobs in 2022. 

• Salary with a Mathematics PhD: $108,660
• Job Outlook: 22% job growth from 2020 to 2030
• Number of Jobs: 105,980
• Highest-Paying States: Washington, California, Delaware, New York, New Jersey

Actuaries are more concerned with the financial implications of risk and uncertainty. Actuaries are financial analysts who analyze past and present financial data and forecast future risks. They assess risk using financial theory, statistics, and math and develop plans that reduce the cost of risk.

• Salary with a Mathematics PhD: $105,900
• Job Outlook: 24% job growth from 2020 to 2030
• Number of Jobs: 27,700
• Highest-Paying States: Georgia, New Hampshire, New York, Connecticut, Vermont

Some of the main responsibilities economists have are to predict the customer demand for the firm's products and the firm's product sales. They deal extensively with microeconomic issues while researching trends, collecting, evaluating, and analyzing data. Economists also investigate how to efficiently allocate resources like raw materials, labor, land, or machines.

• Salary with a Mathematics PhD: $105,630
• Job Outlook: 13% job growth from 2020 to 2030
• Number of Jobs: 18,600
• Highest-Paying States: New York, District of Columbia California, New Hampshire, Illinois

In most cases mathematicians and statisticians work in academia and government. Usually, both of the positions require the use of analyzing data or applying statistical and mathematical techniques that help solve problems. 

Statisticians are increasingly involved in statistics and research methodology. Mathematicians are more involved in researching mathematical models or abstractly measuring values and creating results. Mathematics and statistics are the best duos that understand the principles of probability.

• Salary with a Mathematics PhD: $96,280
• Job Outlook: 33% job growth from 2020 to 2030
• Number of Jobs: 44,800
• Highest-Paying States: District of Columbia, New York, New Jersey, Virginia, Maryland

Operations research analysts utilize mathematics and logic to assist businesses in making informed decisions and solving complex problems. They are high-level problem solvers that use sophisticated approaches such as mathematical modeling and statistical analysis to help companies operate more economically.

• Salary with a Mathematics PhD: $82,360
• Job Outlook: 25% job growth from 2020 to 2030
• Number of Jobs: 104,100
• Highest-Paying States: Virginia, Alabama, Maryland, Hawaii, New York

Is a PhD in Mathematics Worth It?

Yes, a PhD in Mathematics is worth it if you are interested in solving math problems and analytical thinking. You also have to be willing to commit to the long educational journey and research required to achieve this level of degree.

Exploring the mathematical fields is challenging and demanding but with time it provides excellent career opportunities. Math positions are respected and well-paid with positive job outlooks. Other than its academic difficulty, there aren’t many downsides when it comes to doctoral math degrees because you can go on to work in many fields.

Additional Reading About Mathematics

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PhD in Mathematics FAQ

Yes, a math PhD is useful because it will help you acquire some transferable skills that will be useful in virtually any industry. It is also useful for those interested in mathematics research or academia. If you wonder what you can do with a math degree , a PhD will equip you with many valuable skills.

Yes, a PhD in Mathematics is difficult to learn. It is difficult to be admitted to a doctoral program in mathematics, and it is also difficult and too abstract for most people to grasp advanced mathematical principles taught in PhD studies. Doctoral math studies are objectively difficult, even for those who are naturally strong at math and have excelled at it their whole life.

Mathematicians need several skills like active learning, complex problem-solving, critical thinking, and analytical skills. A good mathematician also needs information ordering and inductive and deductive reasoning abilities.

Mathematicians mainly explore mathematical principles or models and create their own mathematical theories and concepts. Most of the work they do is in the theoretical realm, that is why they mainly want to work in IT, social science, engineering, or financial fields.

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Doctorate and examples of difficult solved problems

Okay. My questions are: How do some people do doctorates in mathematics and spend so much time like three to six years trying to answer one or two open problems? How do they have the patience, psychological strength, perseverance to solve those problems for so much time?

Other questions: People like Perelman, Wiles who spend seven years each one of them for the Poincare conjecture, Fermat's last theorem to prove them respectively, how do they do it? Do they know beforehand some of the possible ways to solve those problems? What should someone study to ultimately solve problems like those? How will he know if he follows the correct paths to prove them?

Should i try to solve problems that do not take so many years or months to solve at the beginning at least? Perhaps they take like two weeks or a month to solve or less than that? How could i find those open problems?

I am an undergraduate student in math at university. I try to read some math and physics that are not included in the material covered in my undergraduate studies.

• self-learning
• problem-solving

• 8 $\begingroup$ Look up survival bias. You focus on examples of people who solved a famous problem without accounting for the many who tried and did not solve it. Consider also the role of being around at the right time. In the case of FLT, if Frey never observed that a counterexample to FLT should lead to a non-modular elliptic curve over $\mathbf Q$ then the path to FLT Wiles pursued would never have started. He would not have put aside everything for 7 years to try to prove modularity of elliptic curves over $\mathbf Q$ without having the motivation that it implies FLT (by the work of Serre and Ribet). $\endgroup$ –  KCd Commented Jan 1, 2022 at 15:54
• 7 $\begingroup$ Your question seems to be based on a misconception. Doing a PhD in math is, in most cases, not about "trying to answer one or two open problems". It is about diving into a particular (sub-)field of mathematics, understanding, exploring and developing (old and new) ideas. A specific open problem can sometimes be a useful guide to this end, but in many cases, the outcome of a PhD is a collection of various results and theorems in a particular field rather than the very solution to a specific single open problem. $\endgroup$ –  Jochen Glueck Commented Jan 1, 2022 at 17:17
• 4 $\begingroup$ If you'd like to try math research as an undergraduate, look into REUs (research experiences for undergraduates) or ask your math professors to see if they'd be willing (or know someone who'd be willing) to supervise a research project. $\endgroup$ –  TomKern Commented Jan 1, 2022 at 22:13
• 4 $\begingroup$ Just look up “survivor bias”. Maybe I should have called it “selection bias”. What I meant was focusing (in your examples) on results that were the highlight of someone’s career as if they just jumped right to working on that at some random time, when the broader truth is that lots of people had worked steadily on such problems and did not come up with a solution, and people don’t make a habit of reporting their failures (you singled out the two who “survived” to the end of solving very famous problems). What is more typical is to make just partial progress, and this is valuable too. $\endgroup$ –  KCd Commented Jan 2, 2022 at 16:14
• 4 $\begingroup$ In fact the solution to FLT depended on such partial progress: Frey’s offering was a new perspective on FLT, and he published it in the hope that others could build on it. Then Serre was motivated to make a further conjecture, Ribet proved Serre’s idea could work (that is, modularity of elliptic curves over $\mathbf Q$ really did imply FLT), and then Wiles proved enough of modularity to reach a solution of FLT. So the work of Wiles was itself a case of partial progress (on modularity, not FLT), and others built on his work over the next several years to fully settle modularity. $\endgroup$ –  KCd Commented Jan 2, 2022 at 16:24

4 Answers 4

There is one trick that often helps even if you are not Perelman or Wiles: try to solve several unrelated problems simultaneously rotating the amounts of time you spend on each of them so when you feel that you are completely stuck on one, you concentrate heavily on some other one and think of the first one in the background until you get some fresh idea about it that you think is worth trying in serious.

In addition to reducing the frustration, this approach often rewards you with revealing some unexpected connections when the techniques that you try on problem X without success suddenly turn out to be applicable to problem Y while you would never think of using them if you concentrated on Y alone. I usually make my living as a mathematician from spending about 50% of my time thinking (with various degrees of success) on random questions that come my way from my friends, colleagues, or just complete strangers on MathOverflow. True, that strategy may be 50% suboptimal if your goal is to prove the Riemann hypothesis and you care about nothing else, but if you just want to have fun and establish plenty of contacts in the process, it pays off handsomely.

As to the dissertation, in my case it just came naturally from several topics I was thinking of even as an undergraduate. I just hid the failures (which constituted the overwhelming majority) and brought a few remaining successes to the light. That turned out to be sufficient. I should also say that I was lucky with my adviser who had an amazing skill of finding a problem matching the graduate student abilities and inclinations without having any idea of how to approach that problem himself. How that could be done still remains a complete mystery to me.

At least at first (i.e. before completing your Ph.D.) it helps to have an advisor. She can "advise" you on this: When to stop working on that problem and try another; how to try first a simpler case; references to use to avoid repeating what others have done.

One of my fellow graduate students (1970s) wanted to solve the four color problem. His advisor said "no". Wait until after you have tenure to attempt that. If you really want to do graph theory, let's find a more reasonable problem for you to work on.

A story says someone once asked Hilbert why he never worked on the Riemann hypothesis. He replied that he would probably have to spend 5 years getting the background before he could attempt it, and he did not want to waste 5 years on a probable failure. [From memory, maybe the details are wrong?]

• $\begingroup$ In the versions of the quote I've seen, Hilbert's remark is in reference to Fermat's Last Theorem. These versions also say three years, not five. $\endgroup$ –  Will Orrick Commented Jul 9, 2022 at 3:11
• 1 $\begingroup$ Hilbert did, of course, have a great deal of interest in the Riemann Hypothesis--it was on his famous list of problems--and, although analytic number theory (according to Wikipedia ) was not one of his areas of expertise, there's even an approach to the problem with his name on it, the Hilbert–Pólya conjecture. Another famous quote of Hilbert's: "If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proved?" $\endgroup$ –  Will Orrick Commented Jul 9, 2022 at 3:11
• $\begingroup$ In hindsight, I think maybe that anecdote was actually about von Neumann, not Hilbert. $\endgroup$ –  Gerald Edgar Commented Aug 4, 2022 at 15:56

For my thesis I learned a certain collection of tools quite well (Hormander's machinery for solving $\bar{\partial}$ -problems in several complex variables with control of the norm of the solutions in some Hilbert space). I learned the kinds of problems people had solved with these tools. I choose one problem which seemed tractable with this technology but which no one had tackled yet (concerning approximation of holomorphic functions on a domain by holomorphic functions on a slightly enlarged domain). This problem was too hard, so I introduced additional constraints on the problem until it was tractable. I think this sort of pathway is fairly typical. You don't go chasing the Riemann hypothesis: you learn the tools of the trade, and then push the boundary just a little bit.

Take this answer with a grain of salt since my research career ended with my thesis. I am much more interested in teaching. A more seasoned researcher or dissertation advisor might have a more informed take.

This is the number one result on my Google search for survivor bias:

https://en.wikipedia.org/wiki/Survivorship_bias

If you want to do original work, some degree of initiative is required. "Message to Garcia". Of course this doesn't mean NEVER to ask a question. But to not even Google, shows extremely low initiative. You ain't solving FLT with that ethic.

Also, yes, psychological hardening--although having nothing to do with survivor bias--is a benefit to doing R1 research. There's a lot of discouragements (including people issues) along the way.

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Department of Mathematics

Mathematics phd program.

The Ph.D. program in the Department of Mathematics provides students with in-depth knowledge and rigorous training in all the subject areas of mathematics. A core feature is the first-year program, which helps bring students to the forefront of modern mathematics. Students work closely with faculty and each other and participate fully in both research and student-run seminars.

Questions? Email [email protected]

• The firm deadline for applications for Autumn 2025, is December 5, 2024.
• The (general and advanced) GRE tests are no longer accepted. Please do not submit these scores.

• How Hard is a PhD?

Written by Hannah Slack

Successfully completing a PhD can be a long and difficult process that requires years of intensive research, writing and rigorous assessment. It’s no surprise that only around 1% of people aged 25–64 who have been to university have completed a doctorate .

While it’s easy to understand that the degree is difficult, many prospective students don’t fully understand what’s actually hard about the PhD or why. This guide takes you through the main obstacles students struggle with and why they occur.

How hard is it to get a PhD?

Contrary to what many people think, the biggest risk to achieving a PhD is dropping out, not failure. You might hear that around 50% of people leave PhD study before completion. This number comes from a 2013 study in the US , where doctoral study is typically longer, sometimes reaching up to ten years.

Research in the UK has produced more optimistic numbers. A study of 26,000 PhD candidates across 14 universities found that only 16.2% of students dropped out , and 3.3% failed.

Overall, how hard it is to successfully complete a PhD degree depends on a number of factors including your project, institution, background, financial situation and even the state of research in your field. You’re also far more likely to drop out due to personal circumstances or changes in motivation than fail. A large factor determining whether you’ll achieve a PhD or not is commitment.

How hard is a PhD compared to Masters study?

The PhD and Masters are very different degrees that come with their own challenges. Many people find the intensity of a Masters difficult. Often, you’ll undertake a variety of modules and a dissertation within a year or two. Masters degrees are fast paced and require intensive research into existing scholarship. This type of study can sometimes feel overwhelming as many students juggle multiple deadlines and projects.

On the other hand, a PhD requires a significant original contribution to knowledge. Students dedicate many years of their time to slower and more consistent research, culminating in the creation of a thesis around 80,000 words. Dedication, maintaining motivation and ensuring useful research outcomes are all challenges faced during the PhD.

Many academics will refer to the Masters as a sprint and the PhD a marathon. Both have their own set of obstacles but how you overcome them can be quite different.

Why is PhD study so difficult?

The PhD is difficult because it’s a lengthy process that involves completing and writing up an advanced research project that must sustain rigorous peer review from academic experts. By the end, you will need to demonstrate that you’re a world-leading expert on your topic.

Here are some of the key obstacles many doctoral students struggle with:

• Maintaining motivation – Completing a PhD takes at least three years, often more. While your supervisor is there for support, you’re the person accountable for your progress. This is a significant length of time to stay motivated.
• Time pressure – While three years may seem like a long time, this includes conducting a thorough literature review, completing a research project with viable outcomes and writing everything up in a thesis. Handing in on time will often take precedence over perfectionism.
• Returning to university – Many PhD students come from employment and so need to readapt to the demands of academic education again. It can take time to find your feet with the different work style.
• Adaptability – Research will almost never go as planned. Processes can take longer than expected and results may not be as predicted. Throughout the degree you will experience many highs and lows so it’s important to take setbacks in your stride and adapt where necessary.
• Self-doubt – Your supervisor should regularly offer critical feedback on your work. Over the years this can instil doubt about your abilities as a researcher. As constructive review is an important part of the process, it’s important to learn how to handle and implement feedback effectively.

How hard is part-time PhD study?

Many people opt to study their PhD part-time as it allows greater flexibility around existing personal and work commitments. By the end, you will have completed the same amount of research as a full-time student. However, studying over a longer period can change the nature of the above common challenges.

It’s likely that maintaining motivation will be more difficult as you’ll be studying over a longer period. You may also face outside commitments which take priority over your thesis, making it harder to sustain a consistent level of progress.

On the other hand, you may face less time pressure. Part-time PhDs typically take between 5-8 years, allowing you more room to work at a pace that suits your lifestyle.

How hard is the PhD viva?

One of the key concerns many prospective and current students have is how difficult the viva will be. The viva is the final oral assessment where a student defends their research to a panel of academic examiners. Generally, how difficult the viva will be depends on the quality of the thesis you submit. It will also depend on how well you prepare and the examiners you’re assigned. Any negative comments are reflective of the work you submitted not you as a researcher. There are many reasons a thesis may receive criticism and not all of them will be in your control.

As mentioned at the beginning of this guide, very few people fail the PhD. So, while the viva can be difficult and intimidating it’s also highly unlikely to have a negative outcome.

Overall, a PhD is a long and often challenging learning process. While there are many obstacles to overcome you will have gained and refined invaluable skills and experience by the end.

Ready to apply for a PhD?

Find out what PhD opportunities are currently available with our FindAPhD listings .

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What happens during a typical PhD, and when? We've summarised the main milestones of a doctoral research journey.

The PhD thesis is the most important part of a doctoral degree. This page will introduce you to what you need to know about the PhD dissertation.

This page will give you an idea of what to expect from your routine as a PhD student, explaining how your daily life will look at you progress through a doctoral degree.

Our guide tells you everything about the application process for studying a PhD in the USA.

Is your supervisor moving universities? Or have you discovered another doctoral programme that better suits your goals? In this guide we take a look at how you can transfer a PhD to another university.

This guide covers the different types of research misconduct, their possible consequences and how you can avoid them!

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How difficult is it to get a PhD? The real doctorate struggles.

There is no doubt that getting a PhD is no small feat. It requires dedication, hard work, and plenty of motivation to stay on track.

Getting a PhD can be a very challenging process that requires several years of intensive research, coursework, and writing. However, the difficulty of obtaining a PhD can vary depending on factors such as the specific program and field of study.

Also, I have witnessed that the individual student’s background and preparation, and the level of commitment and effort they are willing to invest also highly influence how hard a PhD is for an individual candidate.

In order to complete in a timely fashion PhD candidates must also be prepared to invest a significant amount of time into their studies in order to complete the necessary coursework (US-based PhDs) and research.

The process can be especially difficult if the student is attempting to balance work or family life while completing their studies.

Quite often younger PhD students find it easier than mature age students due to the fact that they have fewer adult commitments and responsibilities in their private life – but this isn’t always the case.

However, with proper planning and perseverance, it is certainly possible for anyone to reach this educational achievement.

It was something I was very proud to have completed and it certainly opened doors to other opportunities.

Why is a PhD so difficult?

A PhD is an advanced academic degree that requires a huge amount of dedication and hard work.

Ask any PhD graduate and they are likely to say that it is one of the most challenging parts of their life in academia.

That is because it is a lengthy process that involves several years of research, writing, and, at the end, defending a dissertation in front of other experts in the field in order to be awarded the degree.

Typically, a PhD student will:

• have completed a Masters degree to a high standard for acceptance into the PhD program
• conduct a literature review of a field to find research gaps
• generate a research question and hypothesis
• work over multiple years to explore their research question and answer it fully
• fail multiple times and have their work critiqued continuously by experts in their field and that PhD supervisor.
• Write up their work in peer-reviewed journals and their thesis
• defend their peer-reviewed papers and their thesis
• continually stay up-to-date with the literature throughout their entire course
• some students may also have teaching and other administrative requirements at the University in which they are studying.

The entire process can be quite challenging and overwhelming, as students must stay up-to-date with new developments in their area of study while also meeting stringent academic standards.

They must also be able to effectively communicate complex concepts to their peers in things like peer-reviewed papers as well as at conferences and symposia.

All these factors make obtaining a PhD an incredibly difficult task but one that is ultimately rewarding for those who are successful.

It can be confronting when you look at a PhD in one whole chunk. However, by splitting down the tasks involved in a PhD it can become much more manageable and less detrimental on your mental health.

If you want to know more about how doing a PhD part-time you can check out my other articles:

• How long does it take to get a PhD part time? Complete a PhD on your own time.
• Is a PhD worth it now in 2023? [the data]  

What is the hardest part of getting a PhD?

One of the most challenging aspects of obtaining a PhD is that it takes a great deal of time and dedication.

You shouldn’t underestimate how easily your brain plays tricks on you over a multi-year project. Staying on course and ignoring your internal monologue is one of the most challenging parts again a PhD.

It can take anywhere from five to seven years of rigorous study and research to complete all the requirements for a PhD.

During this time, students must master complex topics in their field, conduct independent research projects, write lengthy dissertation papers, and navigate any number of other challenges along the way.

Working with your supervisor

Working with your PhD supervisor can, for some, be one of the most difficult aspects of doing a PhD.

Your PhD supervisor will dictate the outcome of your PhD and therefore it is worth spending a lot of time making sure you select the right PhD supervisor for you.

Some supervisors want to completely micromanage whilst others are happy to allow their students to explore freely.

Taking the time to make sure you can fully nurture this relationship will also ensure a less stressful PhD.

If you want to know more about great ways to build a relationship with your supervisor check out my YouTube video:

I also have a lot of content on my YouTube channel on choosing and working with academic supervisors.

Is it worth getting a PhD?

Whether or not it is worth getting a PhD depends on a few different factors.

For some people, having a PhD is important for career advancement and provides an opportunity to pursue higher-level positions in their field.

It may also be beneficial for those that wish to teach at the university level or conduct research in their field of interest.

On the other hand, pursuing a PhD can be time consuming and expensive, and the long years of study may not ultimately result in any tangible rewards.

I also have a YouTube video where I talk about whether getting a PhD is worth the effort:

There are a load of juicy secrets in this one.

Whether or not it is worth getting a PhD will depend on the individual’s goals and objectives. If they are looking for career advancement opportunities or want to pursue teaching or research opportunities, then getting a PhD may be worth the cost and effort involved.

How hard is it to manage the PhD workload?

You may have heard that a PhD is a massive task because of the workload.

If you are doing your PhD in the United States of America you may find that there are three years of coursework to complete before you start the research component of the degree. This workload can be huge.

No matter where you do your PhD the amount of work and effort it takes to complete a PhD is much greater than what was required for an undergraduate degree.

No longer do you have set deadlines and a structured course – you will need to figure out the pathway through your PhD on your own.

Furthermore, given that most U.S.-based PhD programs are structured like traditional college courses, it can be difficult to stay on top of all the readings and material without falling behind.

If you decide to pursue a doctoral degree you must make sure you are prepared for the increased workload and dedication required in order to be successful.

Speak to your support networks and your family to ensure that they will be able to support you when things get tough.

Is a PhD intellectually difficult?

You may be surprised to hear that PhD isn’t necessarily intellectually difficult. But it does require dedication and effort to work through some challenging intellectual problems.

I often say that a PhD is 80% dedication, 10% smarts and 10% luck.

A PhD can be an extremely intellectually challenging experience for any student because it requires a great deal of dedication and hard work to complete, and it is regarded as the highest level of education available.

The expectations of a PhD student are far greater than those of an undergraduate, and the research process can take years to complete.

Nonetheless, it is your ability to persevere through problems and stick to your research plan by improving on your research little by little day after day that will really dictate how successful your PhD is.

I have seen incredibly smart people fail a PhD whilst others, who have not done so well in undergraduate, have flourished in the research environment.

How long are PhD programs?

Research shows that the average amount of time to complete a PhD across disciplines is 4.4 years. Depending on the country, a PhD will take anywhere between two and seven years to complete depending on whether there is a coursework component (US universities).

The majority of students taking anywhere from five to seven years to complete their degree.

This is due to the nature of PhD programs, which require significant research and fieldwork experience in addition to coursework.

Depending on a student’s chosen field of study, some PhD programs may last longer than others.

Here is data from a study that looks at Australian university PhD completion  published in 1994 .

Some PhD programs may have requirements that must be met before graduation, such as publishing research or completing an internship. It is important for prospective students to understand what is expected of them in order to ensure they will be able to complete their program within the allotted timeframe.

If you want to know more about how long a PhD takes check out my other article:

• How long does it take to get a PhD? Complete a PhD quickly
• How long is a PhD dissertation? [Data by field]

How many hours do PhD students work?

Although PhD students often have to put in long hours of work to complete their degree is not necessary that a student puts in an insane number of hours as long as they were continuously and diligently towards the end goal of getting a PhD.

The amount of hours that a PhD student work will depend on the culture of the labs that they are currently researching in.

Some supervisors require students to be in the lab for many hours every day whilst others are happy from a 9-to-5 “work schedule”.

On average, PhD students work around 40-50 hours per week.

This includes time spent in:

• independent study
• researching
• and much more

Researching and writing a dissertation can require even more hours of work.

In addition to this, many PhD students also teach classes or take on other roles within the university that add to their workload.

All of this means that PhD students can often find themselves putting in long hours and having little free time outside of the academic demands of their program.

Wrapping up

This article has been through all of the difficult components that people may face if they decide to get a PhD.

I was able to complete my PhD in three years and I somewhat enjoyed the process. Of course it had its challenges but overall it was a worthwhile and rewarding experience for me.

However, some people’s experiences are also very different due to different pressures outside of academia and the culture in the research group in which they are working.

The ultimate difficulty depends very much on the individual circumstances and dedication of the PhD student but always involves dedicating yourself to the pursuit of knowledge over many years. This, in itself, can be a very challenging aspect to overcome.

Dr Andrew Stapleton has a Masters and PhD in Chemistry from the UK and Australia. He has many years of research experience and has worked as a Postdoctoral Fellow and Associate at a number of Universities. Although having secured funding for his own research, he left academia to help others with his YouTube channel all about the inner workings of academia and how to make it work for you.

Thank you for visiting Academia Insider.

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Scientists Created the Most Impossible Maze of All Time. And It Could Salvage Humanity.

This mind-bending labyrinth might revolutionize our approach to carbon capture.

Gear-obsessed editors choose every product we review. We may earn commission if you buy from a link. Why Trust Us?

• Using concepts from geometry, mathematicians from the U.K. and Switzerland have developed the world’s most difficult maze.
• This study suggests that quasicrystals could play a big role in adsorption—the process of an atom or molecule adhering to a surface—which is a technique often used in carbon capture technology.

Walk your way through a corn maze, and you can get turned around pretty quick—but just be thankful the researchers behind the world’s most devilishly difficult maze weren’t your labyrinthine designers. A new paper, published in the journal Physical Review X , details what is possibly the world’s most difficult maze, designed using geometric concepts like Hamiltonian cycles and Ammann-Beenker tilings. In other words, this maze is so dizzying that it’d make even David Bowie jealous .

But first, a brief refresher on some mathematical geometry . To even start to understand these complicated designs come to be, first picture a knight on a typical chess board. Now, move the knight piece around—two spots forward, one spot back—until it visits every spot on the board once and only once. This is what’s known as a “Knight’s Tour,” and it’s one example of potentially infinite Hamiltonian cycles (named for Irish mathematician William Rowan Hamilton), which is when a loop through map visits all stopping points.

Now, scientists from Britain and Switzerland have expanded this basic idea to create ever larger Hamiltonian cycles in irregular structures, such as Ammann-Beenker tilings—tiling patterns that never repeat. This kind of structure closely resembles exotic matter known as quasicrystals, which differ from crystals at the very atomic level. Where atoms and patterns in crystalline structures repeat in regular intervals, quasicrystals —as you might guess—also repeat in a pattern but the pattern doesn’t repeat exactly . According to these researchers, the quasicrystals can only be described mathematically as “slices through a crystal that live in six dimensions.”

“When we looked at the shapes of the lines we constructed, we noticed they formed incredibly intricate mazes,” University of Bristol’s Felix Flicker, the lead author of the study, said in a press statement . “The sizes of subsequent mazes grow exponentially—and there are an infinite number of them.”

Quasicrystals are incredibly rare. Three have only been found in one meteorite from Siberia , and the Trinity nuclear test in 1945 created the world’s first artificial quasicrystal . When employing Hamiltonian cycles on the surface of these quasicrystals so that every atom is visited once, the cycles create amazing intricate mazes known as “fractals” that could have the unintended side effect of improving the adsorption of materials—especially particularly troublesome ones like carbon dioxide .

Unlike absorption, which dissolves via liquid or solid, adsorption is when atoms, ions, or molecules instead adhere to a surface. This is a particularly important process in the world of carbon capture, which currently uses normal crystals . But mind-bendingly complex quasicrystals could be better fitted for the task—in more ways than one.

“Our work also shows quasicrystals may be better than crystals for some adsorption applications,” Cardiff University’s Shobhna Singh, a co-author of the study, said in a press statement. “For example, bendy molecules will find more ways to land on the irregularly arranged atoms of quasicrystals. Quasicrystals are also brittle, meaning they readily break into tiny grains. This maximizes their surface area for adsorption.”

Figuring out a way to remove large amounts of carbon dioxide in the atmosphere is itself a bit of a maze. Who knows—maybe a maze can be part of the solution.

Darren lives in Portland, has a cat, and writes/edits about sci-fi and how our world works. You can find his previous stuff at Gizmodo and Paste if you look hard enough. 

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Excessive Heat Hits Young Children Hard

• Posted July 8, 2024
• By Elizabeth M. Ross
• Climate Change and Education
• Cognitive Development
• Early Education
• Evidence-Based Intervention

Note: Back in January, we reported on a new paper that explained the risks of extreme heat for babies and young children. With much of the United States experiencing the hottest season of the year, we are republishing our article which includes practical tips for beating the heat at the local level. 

More frequent record-breaking world temperatures, such as the ones experienced in 2023, the warmest year ever recorded , can cause major health complications for the most vulnerable among us, including babies and toddlers whose bodies react differently to excessive heat than adults. Young children are not able to regulate their body temperatures in the same way as grown-ups and severe heat can lead to “muscle breakdown, kidney failure, seizure, coma, or even death in extreme cases,” according to a new working paper from the Center on the Developing Child at Harvard. It can create additional risks during pregnancy too. 

“High temperatures may result in reduced blood flow in the placenta, dehydration, and inflammation,” the authors explain, which can cause premature births and low birth weights for babies, and other research has found that extreme heat exposure increases the rate of stillbirths . 

The new paper highlights how rising temperatures, related to climate change, can impact the long-term development of all children and especially those from low-income communities of color and poorer countries through:

• Learning loss. Children’s cognitive functions slow down and their ability to concentrate. Overheated classrooms can cause students and teachers to become unmotivated, distracted, or irritable, the report says. The Environmental Protection Agency estimates that days that are just 7 degrees Fahrenheit warmer than current average temperatures cause more than a $13 billion loss in future earnings per year because of missed learning in schools. 
• Sleep. Hotter and more humid temps reduce the likelihood of a good night’s sleep. Children need plenty of rest for healthy growth and development and without it, problems can emerge such as obesity, emotional and behavioral challenges, language development concerns, and diminished problem-solving skills. 
• Mental health. The body’s stress response system can be activated and, if it happens too often, disturb the development of healthy emotional regulation circuits in children’s brain

Practical solutions at the community level: 

Efforts to address climate change nationally and globally can help children’s health and development, according to the paper, but its authors also stress the importance of engaging with local leaders and residents who best understand specific challenges and needs on the ground. 

The scientists offer the following strategies for policymakers and community and education leaders: 

• Evaluate all childcare, preK–12 schools, and after-school and summer programs for potential exposure to extreme heat and provide resources to help, including shade, cooling options, and access to clean drinking water. 
• Design new buildings and retrofit older ones to be energy efficient and reduce heat exposure. New building materials can be used for cooler pavements, roofs, and permeable surfaces. Consider planting more trees and vegetation to provide shade and reduce air temperatures outside.
• Put air conditioning and other cooling mechanisms into public schools. Districts can consider less expensive and less power-draining solutions than air conditioners, including evaporative coolers. 
• Consider more sustainable sources of energy, like solar power. Lower-income families may be eligible for help with energy bills through a federal cooling assistance program .
• Build up community resilience with “heat action plans” which can bring together local government agencies, community groups, and health care facilities to collaborate and identify areas and people at greatest risk during heat waves. 

Extreme Heat Affects Early Childhood Development and Health is a working paper produced by the Early Childhood Scientific Council on Equity and the Environment at the Center on the Developing Child.

Additional resources:

• Read the working paper, including resources for taking action.
• Ed. Magazine: Place Definitely Matters
• Harvard EdCast: Empowering Schools to Take Climate Action

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Applied Mathematics MS Program

This is a two-year professional degree program designed to prepare you for a career in contemporary industry or business. You'll receive thorough training in applied mathematics and scientific computing, exposure to mathematics-related subjects in science and engineering, and experience in a group project. Our graduates have been successful in securing desirable positions with companies ranging from small, local firms to large, international corporations.

Professor; Director, Applied Mathematics & Computation; Director, Applied Math MS Graduate Admissions

Program goals and structure

The Master's Degree Program in Applied Mathematics is specially designed to prepare graduates for a successful career in today's industrial/business world. Accordingly, the program is structured into the following three components:

• a core of graduate courses in applied subjects within the Department of Mathematics and Statistics;
• a selection of advanced courses in other departments;
• a group project in which an applied scientific problem is undertaken in a colloborative effort.

The graduate courses in the Department concentrate on Analytical Methods, Numerical Methods, and Probability/Statistics. These courses give the student a thorough background in advanced applied mathematics.

Given the interdisciplinary nature of Applied Math, students are encouraged to take courses outside the Department. These are determined depending on each student's interests and preparation. In recent years, they have been chosen from Computer Science, Engineering (Industrial, Mechanical, Electrical), Physics, and Management Science. These courses expose the student to the use of practical mathematical tools by scientists and engineers. Courses taken outside of the department require the director's approval in order to count towards the MS degree.

Students in the program are required to complete at least one course that includes a group project component. The group projects are intended to emulate industrial teamwork on a large, technical problem. Through the combined efforts and diverse talents of the group members, a mathematical model is developed, a computer code is implemented, and a final report is written. In the process, the students learn how to start solving a new and hard problem, how to make a professional presentation of their work, and how to collaborate effectively with their coworkers.

Applications and admissions

Those wishing to be considered for Fall admission should submit all application materials to the Graduate Admissions Office during the preceding Spring. Reviewing of applications will start after the application deadline  January 10 , with precedence given to those before that date. Later applications are considered provided that openings are available.

All applicants are expected to have a strong undergraduate preparation in mathematics, including advanced calculus, linear algebra, and differential equations. Some exposure to computer science and/or scientific computing is also desirable, as is some knowledge of another area of science or engineering. A Bachelor's Degree in Mathematics, however, is not necessary. Students with undergraduate majors in Physics or Engineering, for instance, and with sufficient mathematical background, are encourage to apply.

The program is able to offer a tuition waiver and a stipend to a limited number of students upon admission. This financial support takes the form of a teaching assistantship in the department. The duties of the students in the Master's Degree Program are usually restricted to grading or consulting for an undergraduate course, although instructing in an elementary course is also possible.

For additional information, contact the Program Director  Markos Katsoulakis .

Recent Applied Math MS Graduates

List under constant construction. Recent alumni of the Applied Math MS program may contact Graduate Program Manager Kaitlyn O'Konis ( @email ) to provide the department with their most recent employment information.

• Dvir Blander (Data Analyst, SmartSense by Digi)
• Nuha Futa (Senior Data Scientist, Citizens)
• Suzet Nkwaya (Data Scientist, MFS Investment Management)
• Linqi Meng (Holyoke Medical Center)
• Matheau Santana-Gijzen (Graduate Student, PhD, Johns Hopkins University)
• Renato Spacek (Graduate Student, PhD, École de Ponts ParisTech, France)
• Nicolas Malloy (System Engineer, Zoox)
• Brendan Shanahan (Senior Software Engineer, Intellia Therapeutics, Inc.)
• Program Overview
• Applied Mathematics MS
• Remote Statistics MS
• How to Apply
• Financial Aid
• Admissions FAQ
• Recent Courses
• Qualifying Exams
• Alumni Testimonials

Award-winning teaching, research opportunities, and interdisciplinary programs in a diverse, inclusive community of excellence.

Lederle Graduate Research Tower, 1654 University of Massachusetts Amherst 710 N. Pleasant Street Amherst, MA 01003-9305, USA

Department Phone: (413) 545-2762 Department Fax: (413) 545-1801 Department Office: LGRT 1622

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How hard is a Phd in Mathematics in mit?

• Thread starter OhNoYaDidn't
• Start date May 13, 2012
• Tags Hard Mathematics Mit Phd
• May 13, 2012
• Scientists develop new technique for bespoke optical tweezers
• New technique offers unprecedented control over light at terahertz frequencies
• Researchers realize time reversal through input-output indefiniteness

Getting any PhD from a decent math program, including MIT, is challenging. I don't think this is something that we can easily compare between two schools (as definition of "harder" differs from a person to another person). Getting INTO a PhD program in mathematics at MIT, on the other hand, is significantly harder than many math PhD programs in US.  

• May 17, 2012

PieceOfPi said: Getting INTO a PhD program in mathematics at MIT, on the other hand, is significantly harder than many math PhD programs in US.

I think the most important part of your application is your letter of recommendations. If you want to get into any particular graduate school, the best way to increase your odds is to have an excellent letter written by someone who is well known (and liked) by that institution. Most anything can be overlooked with strong enough letters. I have just been accepted into graduate school, so I'm no authority. In my defense I became very close to my advisor and learned a lot about the process from his experience.  

you are ignoring the gist of my comment about vetting. namely schools take people that seem likely to succeed. hence by making yourself more qualified, you increase the likelihood of admission.  

mathwonk said: you are ignoring the gist of my comment about vetting. namely schools take people that seem likely to succeed. hence by making yourself more qualified, you increase the likelihood of admission.

OhNoYaDidn't said: My question is pretty much what i wrote in the title, I'm wondering how hard a phd in mathematics from mit or an ivy league univ would be.

I think that you already know the answer. Notice how you didn't word the question, "How easy would a phd in mathematics from mit or an ivy league univ be?" but "how hard would it be?" I'm 16, but even I know that you're going to have to work your *** off, and that it could easily be the most difficult thing that you'll have to do in your life. Maybe not for everybody, but judging by the fact that you have self-doubt about your capabilities, then I doubt it will just be a breeze for you. In the end, you'll never know until you apply, either get rejected/accepted, and actually go through the program. Second-hand accounts will never be able to apply for you, because other people AREN'T you. Your abilities are different from theirs, as is your work ethic, etc. First hand experience is going to be the best answer to your question.  

• May 18, 2012

Timo said: Seven.

Sankaku said: It is over Nine Thousand...

Nano-Passion said: Lol. I do remember when my friend spammed that phrase every 5 minutes. >.< For people who don't know, it's from a parody of DBZ.

• May 19, 2012

I second the advice about letters of recommendation. Especially because there are extremely terrific applicants of very different shapes, the letters indicating a good fit for the program are the most crucial thing, once you have good coursework, grades, and scores. I have seen applicants of various resumes get rejected from universities like MIT. Aside from the very few true prodigies out there, I think aside from having spectacular awards or publications, most of us are in the same boat admissions-wise aside from the letters. Keep in mind it's not just how good your letters are, but how they are received by admissions (hence a lot of variables that you have no control over -- apply to a good number of schools that you could be happy at, and you'll probably be fine). However, simply maintaining a great record from a terrific undergraduate mathematics program with strong but not stellar letters can still get you into a great program for PhD.  

DeadOriginal said: Followed by Vegeta getting crapped on by Goku of course.

clope023 said: I remember it going the other way in that particular fight actually. Just saiyan.

Related to How hard is a Phd in Mathematics in mit?

1. how much time does it take to complete a phd in mathematics at mit.

The average time to complete a Phd in Mathematics at MIT is 5-6 years. However, this can vary depending on the individual's research progress and other factors.

2. What is the coursework like for a Phd in Mathematics at MIT?

The coursework for a Phd in Mathematics at MIT is rigorous and challenging. It typically involves advanced courses in pure and applied mathematics, as well as seminars and independent research projects.

3. Are there any specific entrance requirements for the Phd program in Mathematics at MIT?

Yes, in order to be accepted into the Phd program at MIT, applicants must have a strong background in mathematics, as well as a bachelor's and/or master's degree in a related field. They must also have excellent grades and letters of recommendation.

4. How much does it cost to pursue a Phd in Mathematics at MIT?

The cost of a Phd in Mathematics at MIT varies depending on the individual's financial situation. However, most Phd students receive full tuition waivers and stipends to cover living expenses through teaching or research assistantships.

5. What are the job prospects after completing a Phd in Mathematics at MIT?

Graduates from the Phd program in Mathematics at MIT have excellent job prospects. Many go on to become professors or researchers at top universities, while others pursue careers in industry or government agencies.

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How hard is it to find a job in pure mathematics research with a PhD?

Not necessarily a Professor but just any job that is purely research based, like say a Postdoctoral Researcher. I don't care about how much money I make, I just want to at least be able to get a job. Is aiming for a job in Pure Mathematics that's research-based as opposed to application-based reasonable?

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Is it possible to start a PhD in mathematics at the age of 29? [duplicate]

I graduated with a bachelor’s degree in mathematics. I was initially focused on branches in analysis like operator algebra. At the third year of my undergraduate study, I experienced a financial loss in my family. It was only a slight loss and would not influence the life and regular plans of my family. But at that time I was not mentally strong enough and I could not concentrate on study. I postponed two years to graduate, in 2020.

These days I am trying to apply for a master program in mathematics. My GPA is not top, but fair enough, and I also did my graduation thesis carefully. I applied for several programs in Europe and received the conditional admission of Uni of Göttingen, but my Toefl grade did not meet the requirements. This year I have prepared all the things and I am going to apply for several master’s programs in Germany.

I am currently interested in low-dimensional topology and want to select this area as my direction. But when I apply for a PhD, I am 29 years old, is it a huge disadvantage? I also referred to several persons working on geometric topology, and the time cost seems to be high. But I am still enthusiastic about mathematics and want to get a bread.

Anyone could give me some suggestions?

• gt.geometric-topology
• oa.operator-algebras
• 37 $\begingroup$ As far as I know it is not uncommon to start a PhD later in life, and 29 is not even that late. Age alone should not be much of a disadvantage. $\endgroup$ –  Wojowu Commented Feb 28, 2022 at 9:43
• 3 $\begingroup$ You may want to look at this thread. The "age gap" is somewhat smaller there but you should find some stories shared there encouraging! mathoverflow.net/q/59999/30186 $\endgroup$ –  Wojowu Commented Feb 28, 2022 at 9:44
• 5 $\begingroup$ This post is also tangentially related: Too old for advanced mathematics? And maybe you can find some related posts also on Academia . $\endgroup$ –  Martin Sleziak Commented Feb 28, 2022 at 9:46
• 5 $\begingroup$ Lefschetz started his PhD at age 33. So no age is too late. $\endgroup$ –  Kapil Commented Mar 1, 2022 at 12:03
• 4 $\begingroup$ @Brady, OK, but the question is whether it's possible to start a PhD in math at age 29. What's true for, say, sociology doesn't necessarily hold for Mathematics. $\endgroup$ –  Gerry Myerson Commented Mar 2, 2022 at 11:08

8 Answers 8

I don't think being 29 could ever be considered a disavantage on the intellectual or creative level to start a PhD. The comments below your question give you links to lists of famous mathematicians who were late starters. One famous example is Stephan Banach who wrote the equivalent of his master thesis at 28 and got the equivalent of what we call today a PhD at age 30.

I would nevertheless advise to be very careful on other aspects of a mathematician's carreer. Unfortunately, such a career is rarely based solely on talent and genius, unless you solve the equivalent of the Riemann hypothesis in your field. Financial and sociological issues are very important and might become more and more difficult to tolerate as you grow older.

If you plan to get a PhD and then move to industry and/or work for private companies, I guess (though I don't have a formal proof, only examples from friends and colleagues) that your professional life won't be any significantly different or harder than that of your colleagues who got their PhD a few years earlier than you. On the other hand, you have to know that there is an extremely fierce competition for jobs in academia.

It has now become standard to be on very unstable positions (called post-doc positions) for at least 3–4 years after the completion of your PhD. And sometimes up to 10 years! (I have seen that among younger colleagues.) During these years, you need to gain recognition from the bigwigs in your field, so that they can support your application for the next stage of your career: the tenure track position (which I will describe below). And that might be extremely difficult, even if you prove some big results.

I know someone who, as a PhD student, answered an implicit \footnote{added as per suggested by Dan Petersen} question of Serre (you might call it a conjecture ) on cohomological invariants of some finite groups. Instead of congratulating him for his results, Serre became mad at this guy, accused him of stealing his ideas, saying that "the main steps of the proof were already known to him, and that he was going to publish very soon a paper answering his own question." The guy was forced by Serre's affiliates to rewrite his paper and explicitly mention that his work contains no original contribution as "everything was already known to Serre" (but of course not published).

His career in abstact algebra, which should have certainly flourished in the best possible way, considering his brilliant debut, brutally stopped there. This guy was only 25 or 26 at the time, and was strong enough to start a new career in another field. I can't however imagine him doing the same if he was 36 (instead of 26).

But that is a single example, and obviously, most PhD don't end up like this. On the other hand, even if you succeed in having your peers acknowledge your work in a positive way and find some good post-doc positions, you still are in the middle of the jungle. Indeed, if you gain enough support from the bigwigs in your field, you can only upgrade from post-doc positions to a tenure track position.

While tenure track positions are certainly less insecure than post-doc positions, they still aren't permanent positions. They last between 5 to 10 years, and the same game has to be played again with the bigwigs: publish (a lot and frequently) on the subjects which they consider to be interesting, gain their recognition and ask them to support your application.

Then, finally, after 10 to 15 years of such a life (where you might have to move out places every 2 or 3 years), you may hope for a stable and permanent position. Which means that if you start your PhD at 29 and plan to work in the academia, you might secure a permanent position at 40 at the earliest. Granting the fact that you have been able to give plain satisfaction to the numerous bigwigs you will encounter during this 10 to 15 years period of time.

I do believe this is really an important issue to consider before getting bogged down in the academia. You really don't feel the same about those things whether you are in your late twenties or you come close to 40.

• 8 $\begingroup$ @Alex : I am certainly not tryng to discourage you from fulffilling your dreams. Mathematics is certainly worth devoting ones life to it. I am just trying to warn you that academia is far from being what it looks from this outside. It is a jungle! In my opinion, age only play a central role in some situations. When you are (very) young, you don't really care about job security and you recover very quickly from the humiliations the bigwigs may suject you to. I do believe that you become less and less able to tolerate such things when you get older. $\endgroup$ –  Libli Commented Feb 28, 2022 at 19:28
• 24 $\begingroup$ For those curious, this seems to be the paper referred to: arxiv.org/pdf/1112.6283.pdf . I do not understand why people like Serre do not understand that forcing (explicitly or implicitly) someone to write that makes you look like an enormous jerk. $\endgroup$ –  user2520938 Commented Mar 1, 2022 at 8:34
• 6 $\begingroup$ Regarding taking a PhD to industry: Be aware of the opportunity cost. Years invested in earning a PhD are years not spent building connections and industry-specific skillsets. (This is not to say a PhD-->industry is not worthwhile, but rather to be cognizant of the tradeoff.) $\endgroup$ –  Neal Commented Mar 1, 2022 at 14:31
• 10 $\begingroup$ I think the anecdote about Serre in this answer is inappropriate for many reasons: 1) It is a disparaging accusation against a person identified by his real name, made by an anonymous user. 2) It is based only on second-hand information about an incident which happened 10 years ago. 3) The student is easily identifiable from your description (see the comment of @user2520938), who would perhaps not like the affair to be dragged out in public, either. 4) It is not relevant to the question of whether it is a good idea to start a PhD at age 29. $\endgroup$ –  Dan Petersen Commented Mar 2, 2022 at 4:42
• 9 $\begingroup$ @DanPetersen : Life is full of unlikely events, sometimes very disappointing. I am sorry if this event involving Serre may shed some shadows on the naive picture of him you may have created for yourself. But the story happened exactly as I tell it. I was almost in first lines when it occured. $\endgroup$ –  Libli Commented Mar 2, 2022 at 10:04

I completed my PhD at the age of 32 which is not uncommon to Israelis. We often lose several years due to military service. So starting at 29 might be a bit late, but it is not a disaster. It is more about talent and commitment. Good luck.

• 12 $\begingroup$ Starting later in life, after having some life experiences can be a huge advantage. I witnessed many Israeli students doing their Ph.D thesis at Cornell, after completing their IDF time. They cut through their Ph.D work like a hot knife through butter. People going to grad school, straight out of the high school -> undergrad degree cycle, often get dizzy from the array of discussion and research topics, math's tangled history. $\endgroup$ –  Ryan Budney Commented Feb 28, 2022 at 18:31

This is/was certainly possible.

Proof : Reuben Hersh started a PhD after 30 (born in 1927, he defended his thesis in 1962 at the age of 35) after having been working a decade as a machinist. He eventually became a successful professor at the University of New Mexico. His scientific work ranges from hyperbolic PDEs to Probability and Philosophy.

• 5 $\begingroup$ Hersh’s experience 60 years ago shouldn’t count for much here. At the time, American academia was expanding, the academic job market was plentiful, and PhDs were quicker. That’s no longer true in the US, and I doubt it’s true in Germany. $\endgroup$ –  user44143 Commented Mar 1, 2022 at 15:41
• $\begingroup$ @MattF. The OP did not address the question of job market, but only that of feasibility of a PhD at the age of 29. Hersh's example shows that the answer is positive. $\endgroup$ –  Denis Serre Commented Mar 1, 2022 at 16:21
• $\begingroup$ Check out Hersh's published dissertation, esp. p. 321: jstor.org/stable/24900768 . Do you think someone today could get a PhD with a dissertation that "is virtually identical to" a paper only 18 pages long and described as "nothing but a straightforward use of Laplace and Fourier transformations"? I doubt it -- and that matters for someone today. $\endgroup$ –  user44143 Commented Mar 1, 2022 at 18:09
• 2 $\begingroup$ @MattF. Half (?) of the PhD theses in maths are either not cited, or forgotten after five years. That of R. Hersh is still a fundamental step in the theory of hyperbolic Initial Boundary Value Problem. Today, an advisor would ask the student (say R. Hersh grandchild) to elaborate around the 18 pages fundamental paper. It would extend to 100 pages, but the core of the thesis would remain about the same. $\endgroup$ –  Denis Serre Commented Mar 1, 2022 at 19:29
• $\begingroup$ Maybe the math would be no better! But adding another 80 pages would add another 6 months or year to the PhD. $\endgroup$ –  user44143 Commented Mar 2, 2022 at 16:38

Just another example: I graduated late, then worked 2 years outside university, then started my PhD, defended my thesis at 37, and at 47 I became associate professor. Since you ask this frequently: my field is dynamical systems.

It wasn't easy to catch up. I had to accept a few things which look cool in your 20s but uncomfortable in your 40s.

• $\begingroup$ Do your parents support this career? Is it not easy to overcome some anxiety of peer pressure in this process? $\endgroup$ –  Alex Commented Mar 1, 2022 at 14:16
• 2 $\begingroup$ I was lucky enough to work in very good and supportive teams. The difficult part was to move every 2 years or less and to wait my mid 40s to start building my own family. $\endgroup$ –  Paul Commented Mar 1, 2022 at 14:39

As a yes or no question, then certainly yes.

You are at a tiny disadvantage though, which you obviously know to be posing the question. And tiny disadvantages sometimes gradually get bigger, but sometimes they feeble into non-importance. Ultimately, it probably won't be the deciding factor. But it will manifest itself: on the professional level, it might mean you get judged negatively by some (short-sighted, and hopefully not many) professors/panel members; and on the personal level, it might mean you'll attach more importance to your family and financial status than you would have done a few years ago. No one knows how it will play out, but those will be the issues. That's all it is.

I don't know much but I can assure you that no one will be walking about thinking "omg they're just starting their phd". But you're right that (referring to one of your comments) it isn't that easy to overcome the social/peer pressure, but what should be easy anyway. Just make sure you're aware of it and have your approach to cope with it (and not just ignore it - I've seen too many people fail their Ph.D.'s not because they're mathematically incapable but because they don't know how to deal with the pressures involved). Anyway, pretty soon you'll talk to enough people to realise few people care about your age, they just care what maths you do.

Also, as a small personal supporting note cause no one likes getting rejected and it was that bit that made me catch your post: good that you avoided Goettingen, my supervisor there literally told me I was too old to go for a postdoc (at 28). So look at it as a bullet dodged, if it helps. (By the way, Mihailescu is at Goettingen and he didn't start his Ph.D. until he was aroud 40! (He's great by the way, incase this last paragraph is otherwise too negative.))

• $\begingroup$ 28 is common even if this is only the first post-doc…what I have realized is that being admitted to a master program is not difficult, it is a challenge whether I can find a supervisor afterwards. $\endgroup$ –  Alex Commented Mar 1, 2022 at 15:25
• $\begingroup$ it will be more difficult, but not terribly so (at all). there are plenty of posts here, on stackexchange, or on quora, about how to correctly approach a professor - learn about their research and if you find it interesting then tell them. you can't really fake this. and at that point they won't care about your age. (usually, but ye unfortunately there will be some cases where "at a tie" you could get marked down.) it's good to acknowledge that you're starting older, but that's where it ends - don't let it worry you. after that just focus on your mathematics. $\endgroup$ –  tomos Commented Mar 1, 2022 at 16:14
• $\begingroup$ Given what you say, why do you describe the disadvantage as tiny? Having less family time and less money are not tiny things for someone who has the values you suggest. $\endgroup$ –  user44143 Commented Mar 1, 2022 at 18:35
• $\begingroup$ i agree, i think i was just trying to say that the gap starts smaller and either gets bigger (if you miss out on things because you're judged too old, but you would have been fine and it would have been a chance to "catch up", or because as you say your family means you have less time for maths so your output decreases but that of your "competitors" doesn't) or gets neutralised early on (either through luck or being particularly good or particularly hard-working). but at the "beginning" there might not actually be that much difference between the candidates. $\endgroup$ –  tomos Commented Mar 1, 2022 at 19:23
• $\begingroup$ @tomos Thanks for your suggestions. Are you familiar with pure mathematics in Germany? I mean if there are comparatively abundant positions of phd there… $\endgroup$ –  Alex Commented Mar 1, 2022 at 19:53

I started my PhD at age 30, and don't feel my age was a significant obstacle. However, I believe almost no one should do a PhD, regardless of age.

• $\begingroup$ how come? if i may ask $\endgroup$ –  tomos Commented Mar 2, 2022 at 14:40
• $\begingroup$ There's nothing about an academic career that makes it worth staying extra years in school, taking one or more temporary positions, having little control over the city one lives in, just in the (possibly unlikely) hope that one will eventually find a tenure track position. Not to mention the fact that anyone capable of doing a PhD in a technical field could likely get a job in industry making 2x or 3x as much as a professor. $\endgroup$ –  Michael Benfield Commented Mar 2, 2022 at 17:15
• $\begingroup$ @tomos What he said is not comparatively unrealistic, if one has not set up a family or other burdens…No doubt pure maths requires strong brain muscle, and people are definitely the strongest in their young 20s, I acknowledge that…Different persons also have different stamina, and certain physical exercise could help maintain better. $\endgroup$ –  Alex Commented Mar 2, 2022 at 19:01

May be I live in another part of the world? I never asked this question to myself when I started my PhD from Mathematics Department and I was 29 at that time :)

I thought I was too young to do a PhD :D

• 1 $\begingroup$ Which field are you working in? $\endgroup$ –  Alex Commented Mar 1, 2022 at 12:18

I think the bottom line is that some things are easier if you start earlier, but that talent and quality will ultimately find a way and that these things are not determined by your physical age. If you have something original to say, you should still be able to say it regardless of your age.

Note that obtaining a PhD at a relatively old age is quite common for Israeli mathematicians and physicists. For example, if you need inspiration, Yuval Ne'eman started his PhD in physics aged 33. His main contribution (age 36) was his discovery of the classification of hadrons using $SU(3)$ flavour symmetry (known colloquially as the ''eightfold way''). This is a major achievement in twentieth-century physics.

• $\begingroup$ It's worth noting that Ne'eman's achievement was over sixty years ago: he was born in 1925, with the eight-fold way in 1961, and his related dissertation in 1962 ( proquest.com/docview/1812968444 ). $\endgroup$ –  user44143 Commented Mar 1, 2022 at 18:47
• 1 $\begingroup$ You are right. However, this does not contradict the fact that it is an interesting example of someone who started doing formal research relatively late in life but still made great advances. $\endgroup$ –  Hollis Williams Commented Mar 1, 2022 at 20:41

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Finding Post-PhD employment in Mathematics - How difficult?

I have completed a 4 year bachelor of Mathematics at a decent university, and a comment was made by Pete L. Clark , on this website, here : "post-PhD academic job market is one step shy of airtight at the moment."

I was intending to study a PhD in america, and am wondering if his statement rings true in the most part. Is it truly difficult to find a post-PhD academic job, specifically in Mathematics, and if so, are there relevant statistics backing this up?

• mathematics

• 5 I applied to over 100 jobs one year and heard back from 3. You can draw what conclusions you want from that. –  Jessica B Commented Jan 18, 2016 at 7:53
• 5 It depends heavily on whether you are looking at R1 schools or others, how famous your advisor is, and how amazing your thesis is. –  David Ketcheson Commented Jan 18, 2016 at 8:37
• 2 @ProspectiveTimidStudent I got a job, so I didn't do too badly. Unless you're pretty amazing, you don't decide on 'the job you want', you hope to get an offer in a country you're ok with living in. –  Jessica B Commented Jan 18, 2016 at 9:59
• 1 @Jessica B: congrats on the job. Did you apply broadly in several countries? I was never sure how common that was, although I suspected it was more common for students who were not from the U.S. originally. I do think that, even in the U.S., choosing which state you want to live in is asking a lot, and even choosing a particular region of the country can be challenging. –  Oswald Veblen Commented Jan 18, 2016 at 14:50
• 2 I'm a fan of @PeteLClark, but I think that statement was a bit of an exaggeration. Having seen what fields with actually airtight job markets look like in the humanities, math looks great in comparison: there is a triple digit number of jobs to apply for! –  Ben Webster Commented Jan 18, 2016 at 18:23

2 Answers 2

The American Mathematical Society publishes detailed data about mathematics employment in the United States. In particular, the Report on New Doctoral Recipients has

"... information about the fall employment plans of doctoral recipients, a demographic profile summarizing characteristics of citizenship status, gender, and racial/ethnic group, the starting salaries, and other employment information about new doctoral recipients"

The data is always delayed by a year because of response and processing time. The most recent report as I write this is 2013-2014 . My own take is as follows.

First, the statistics show that the overall unemployment rate is low: a new math PhD recipient is likely to be able to find a job of some sort immediately after graduation. In 2013-14, 85% of math PhD recipients were known to be employed immediately after graduation, and only 5% were known to still be looking (9% were unknown). This is partially due to the ability of mathematics PhDs to look for jobs in business, industry, and government, although the majority work in academia.

Second, based on my personal opinion and experience, the job market for postdocs and research-intensive tenure track positions is very competitive (this is true both in the U.S. and Europe, as well as some other countries and regions). You will need to be one of the very strongest candidates in your area to have a reasonable chance at such jobs.

Third, the market for tenure-track positions at non-research-intensive colleges is also competitive, but in a different way. For these, you want to have a strong vita showing teaching skill and research ability in line with the institution where you are applying. Simply having a PhD and teaching a handful of classes as an graduate student is unlikely to make you stand out from the other applicants.

Overall, because the job market is competitive, if you do enter a PhD program, you need to plan early for the career path you wish to follow. Simply "getting a PhD", and only worrying about the job market in your last semester, is not a good strategy. You want to begin shaping your vita early in your graduate program so that you are in a good position when you graduate.

• 3 I also summarized some of the data from the previous survey here: academia.stackexchange.com/a/44187/19607 where I was trying to say the picture isn't so bleak for math PhDs. –  Kimball Commented Jan 18, 2016 at 16:09
• 1 Postdocs and research-oriented TT jobs are very competitive, but if we restrict our attention to people who get their PhDs from top programs (say top 15), the situation is quite a bit better. I graduated from such a program two years ago, and every graduating student from my department who wanted a postdoc got a respectable one that year. That's anecdotal, but far from anomalous, I feel. And once you have a respectable postdoc, a research-oriented TT job isn't a lock by any means, but (again anecdotally) the odds don't seem terrible. Point being: pedigree matters a lot. –  user37208 Commented Jan 18, 2016 at 18:42
• 2 @user37208: I agree that it helps to go to a good school, but (sub)field also matters quite a bit. In my field, there have been several highly qualified people in the last decade who have been unable to find postdocs and/or research tenure track positions. –  Oswald Veblen Commented Jan 18, 2016 at 18:55
• @OswaldVeblen Could you elaborate a bit on how can one make oneself competitive to get a job at a non-research intensive college? What should one be doing except for teaching a handful of classes? Suggestions? –  user82261 Commented May 10, 2019 at 21:24

This varies wildly depending on many factors, from what type of job you want, where you get your PhD, number of publications you obtain, quality of PhD, who your advisor is, and what field you're working in. Any or all of these can and will drastically change the answer to this question and decide if the job market is airtight or swung right open for you.

The academic job market is very difficult, but not impossible. You end up at the end applying to a number of jobs somewhere in the triple digits and you can end up with something from a >10% rate in getting shortlists to none at all. A good way to view this is to ask at the beginning of your PhD for the placement records for their recently graduated PhD students. The graduate secretary should have a list and be able to tell you how students have done in the past. This can be a guideline and tell you how well you need to perform to get the type of job you want. It's also important to note who their advisor is and what field they studied. Look at the placement of the students who graduated with who you may want to work with, in the case that you know that.

One thing to be clear about is that post PhD, even if you do not get an academic job, there is a ton of industry options out there. I applied for three industry jobs when I graduated and got one campus interview that I cancelled when I got an academic offer. There is headhunting for math PhDs to join industry (from both the finance and tech industry). Even if you get unlucky with the market or in grad school, then there are plenty of other options.

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