essay on great mathematician

15 Famous Mathematicians and Their Contributions

Table of Contents

Introduction

Being a mathematician is hard. Only a few people have mastered this subject and achieved fame. Of those, there have been some famous Indian mathematicians . In this article, we will discuss some of the famous mathematicians and their contributions to Mathematics.

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Euclid was one among the famous mathematicians, and he was known as the ‘Father of Geometry.’ His famous Geometry contribution is referred to as the Euclidean geometry, which is there in the Geometry chapter of class IX. He spent all his life working for mathematics and set a revolutionary contribution to Geometry. 

2. Pythagoras

‘Pythagoras theorem’ is very popular and an important mathematical formula to solve mathematical problems. Since childhood, all of us have struggled to solve mathematical problems applying the Pythagoras theorem. Pythagoras discovered this prominent theorem and he became the father of ‘Pythagoras theorem.’ Pythagoras was from Greece, but he fled off to India in the latter part of his life.

3. Archimedes

Archimedes was a Greek Scientist, a great mathematician, and a Physician. He also worked his entire life in search of discovering mathematical formulas that are related to Physics. The best contribution of Archimedes in mathematics is known as the invention of compound pulleys, antiquity, and screw pump. Students of class X have to study these chapters of compound pulleys and antiquity.

4. Thales of Miletus

Thales of Miletus was one of the most famous mathematicians from Greece. He was very skilled in Geometry and used Geometry as a means to calculate the heights of pyramids and measure the distance of a ship from the shore. As he was also a philosopher, in the ‘Thales’ theorem’ he tries to apply Geometry by using deductive reasoning and derives the conclusion of four corollaries. You can learn more about Thales of Miletus here .

5. Aristotle

Aristotle was a great scholar and he had vast knowledge in various areas, including Physics, mathematics, geology, metaphysics, medicine, biology, and psychology. He was a student of Plato, and both of them together discovered many philosophical theories and contributed to mathematics and Platonism. He combines mathematics and philosophy and in his treaties, and uses mathematical science in three principal ways.

6. Diophantus

His algebraic equations are quite easy and unique, so he was popularly known as the ‘Father of Algebra.’ He wrote a series of books on Algebra. He later gained popularity for his book Arithmetica, where a brief description with examples was given on the best solution for all the algebraic equations and the theory related to the number. 

7. Eratosthenes 

Eratosthenes was a world-famous mathematician known for his unbelievable and exact calculation. He was the only mathematician who put efforts to calculate the earth’s circumference and calculated the Earth’s axis tilt. Both his calculations are exact, and so he became famous worldwide.

8. Hipparchus

Like Geometry, trigonometry chapters are also important for class IX and X students. The founder of trigonometry was an intelligent mathematician and mythologist Hipparchus. He discovered the first trigonometric table in mathematics. He was the first person to develop a well-grounded process by which people can predict solar eclipses.

9. Hero of Alexandria

Heron’s formula in mathematics is applied by students from class VI onwards. Yes, he was the one who discovered the square root of numbers. In today’s mathematics, his formula is known as Heron’s formula. So, he gained popularity and became known as the ‘Hero of Alexandria.’

10. Ptolemy

Ptolemy was a mathematician; he was also a geographer, musician, writer, and astronomer. His contributions to mathematics were incredible. He wrote about mathematics, and among them, his best treaty was called Almagest. He also believed that in the Universe, the position of the Earth was in the center.

11. Xenocrates

Xenocrates was a famous mathematician from Greek. He had written a series of books on mathematics. He emphasizes the theory of numbers in mathematics, and all his written books were based on the theory of numbers, and geometry. He could easily calculate the syllables from an alphabet. 

12. Anaxagoras

He was a great mathematician and an astronomer. Because of his outstanding knowledge of mathematics and cosmology, he discovered the exact clarification of eclipses and stated that the Sun is larger than Peloponnese. 

13. Hypatia

She was a famous mathematician and a philosopher. She was the first woman to give importance to mathematics. She was a genius, and for many young women, she became an inspiration and encouraged them to pursue their dreams. In Alexandria's history, she was the last famous mathematician.

14. Antiphon

Antiphon discovered the value of Pi. This renowned mathematician was the first one who calculated the upper bound and lowers bound values of Pi by inscribing and circumscribing around a circle, the polygon, and processed finally to calculate the areas of the polygon. His idea of calculating a polygon area became very famous, and it changed mathematics for the world. 

15. Diocles

Diocles was a profound geometer and mathematician. He was renowned for his discovery in the subdivision of geometry. In the books of Mathematics, the ‘Geometry curve’ is known by his name as the ‘Cissoid of Diocles.’ To find out a solution to doubling the cube, the method of Cissoid of Diocles was used.

We have discussed above the list of famous mathematicians and their contributions to mathematics. However, they all are from Greek. There are famous Indian mathematicians also like Srinivasa Ramanujan, Aryabhata, Shakuntala Devi, and many more.

If you wish to know more about famous Indian mathematicians and their mathematics contributions, then comment in this section. For any question related to this article about ‘famous mathematicians and their contributions, ’ feel free to ask.

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The 10 best mathematicians

Pythagoras (circa 570-495bc).

Vegetarian mystical leader and number-obsessive, he owes his standing as the most famous name in maths due to a theorem about right-angled triangles, although it now appears it probably predated him. He lived in a community where numbers were venerated as much for their spiritual qualities as for their mathematical ones. His elevation of numbers as the essence of the world made him the towering primogenitor of Greek mathematics, essentially the beginning of mathematics as we know it now. And, famously, he didn't eat beans.

Hypatia (cAD360-415)

Women are under-represented in mathematics, yet the history of the subject is not exclusively male. Hypatia was a scholar at the library in Alexandria in the 4th century CE. Her most valuable scientific legacy was her edited version of Euclid's The Elements , the most important Greek mathematical text, and one of the standard versions for centuries after her particularly horrific death: she was murdered by a Christian mob who stripped her naked, peeled away her flesh with broken pottery and ripped apart her limbs.

Girolamo Cardano (1501 -1576)

Italian polymath for whom the term Renaissance man could have been invented. A doctor by profession, he was the author of 131 books. He was also a compulsive gambler. It was this last habit that led him to the first scientific analysis of probability. He realised he could win more on the dicing table if he expressed the likelihood of chance events using numbers. This was a revolutionary idea, and it led to probability theory, which in turn led to the birth of statistics, marketing, the insurance industry and the weather forecast.

Leonhard Euler (1707- 1783)

The most prolific mathematician of all time, publishing close to 900 books. When he went blind in his late 50s his productivity in many areas increased. His famous formula ei π + 1 = 0, where e is the mathematical constant sometimes known as Euler's number and i is the square root of minus one, is widely considered the most beautiful in mathematics. He later took an interest in Latin squares – grids where each row and column contains each member of a set of numbers or objects once. Without this work, we might not have had sudoku.

Carl Friedrich Gauss (1777-1855)

Known as the prince of mathematicians, Gauss made significant contributions to most fields of 19th century mathematics. An obsessive perfectionist, he didn't publish much of his work, preferring to rework and improve theorems first. His revolutionary discovery of non-Euclidean space (that it is mathematically consistent that parallel lines may diverge) was found in his notes after his death. During his analysis of astronomical data, he realised that measurement error produced a bell curve – and that shape is now known as a Gaussian distribution.

Georg Cantor (1845-1918)

Of all the great mathematicians, Cantor most perfectly fulfils the (Hollywood) stereotype that a genius for maths and mental illness are somehow inextricable. Cantor's most brilliant insight was to develop a way to talk about mathematical infinity. His set theory lead to the counter-intuitive discovery that some infinities were larger than others. The result was mind-blowing. Unfortunately he suffered mental breakdowns and was frequently hospitalised. He also became fixated on proving that the works of Shakespeare were in fact written by Francis Bacon.

Paul Erdös (1913-1996)

Erdös lived a nomadic, possession-less life, moving from university to university, from colleague's spare room to conference hotel. He rarely published alone, preferring to collaborate – writing about 1,500 papers, with 511 collaborators, making him the second-most prolific mathematician after Euler. As a humorous tribute, an "Erdös number" is given to mathematicians according to their collaborative proximity to him: No 1 for those who have authored papers with him; No 2 for those who have authored with mathematicians with an Erdös No 1, and so on.

John Horton Conway (b1937)

The Liverpudlian is best known for the serious maths that has come from his analyses of games and puzzles. In 1970, he came up with the rules for the Game of Life, a game in which you see how patterns of cells evolve in a grid. Early computer scientists adored playing Life, earning Conway star status. He has made important contributions to many branches of pure maths, such as group theory, number theory and geometry and, with collaborators, has also come up with wonderful-sounding concepts like surreal numbers, the grand antiprism and monstrous moonshine.

Grigori Perelman (b1966)

Perelman was awarded $1m last month for proving one of the most famous open questions in maths, the Poincaré Conjecture. But the Russian recluse has refused to accept the cash. He had already turned down maths' most prestigious honour, the Fields Medal in 2006. "If the proof is correct then no other recognition is needed," he reportedly said. The Poincaré Conjecture was first stated in 1904 by Henri Poincaré and concerns the behaviour of shapes in three dimensions. Perelman is currently unemployed and lives a frugal life with his mother in St Petersburg.

Terry Tao (b1975)

An Australian of Chinese heritage who lives in the US, Tao also won (and accepted) the Fields Medal in 2006. Together with Ben Green, he proved an amazing result about prime numbers – that you can find sequences of primes of any length in which every number in the sequence is a fixed distance apart. For example, the sequence 3, 7, 11 has three primes spaced 4 apart. The sequence 11, 17, 23, 29 has four primes that are 6 apart. While sequences like this of any length exist, no one has found one of more than 25 primes, since the primes by then are more than 18 digits long.

Alex Bellos is the author of Alex's Adventures in Numberland

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Essay on Srinivasa Ramanujan for Students | 500+ Words Essay

December 10, 2020 by Sandeep

Essay on Srinivasa Ramanujan: Srinivasa Ramanujan was a renowned mathematician of India. He was born on 22nd December 1887 in Madras during the British Raj. Since childhood, he was drawn towards maths and took a particular interest in learning the subject. He did not receive formal education in mathematics but had mastered maths in various sections. During his time in Cambridge, he grew close to the great mathematician named Hardy. Together they invented the Hardy-Ramanujan number 1729. He got married at the age of 22 to Janakiammal on 14th July 1904. Several books were written by him based on his theories and formulas. He even received the K. Ranganatha Rao prize for mathematics. On 26th April 1920, he departed at the age of 32.

Below we have provided an essay on Srinivasa Ramanujan in English, written in easy and simple words for class 4, 5, 6, 7, 8, 9 and 10 school students.

Essay on Srinivasa Ramanujan 500 Words in English

Below we have provided extended essay on Srinivasa Ramanujan, suitable for classes 7, 8, 9 and 10 students.

Ramanujan was the maths genius who said that “An equation for me has no meaning unless it expresses a thought of God.” He always had a vision of scrolls of complicated maths unfolding before him. He is referred to as an Indian Mathematician who lived during the British period and who contributed substantially to mathematics analysis, number theory, infinite series and continued fractions. He has been described by many as a simple person with pleasant manners.

Ramanujan was born on 22nd December 1887 into a Tamil Brahmin family in Erode, Madras. His father, Kuppuswamy Srinivasa Iyengar hailed from Thanjavur district and worked as a clerk in a saree shop. His mother, Komalatammal, was a housewife and used to sing at a local temple. They lived in a small traditional home. When Ramanujan was only a year and a half old, his mother was blessed with a son named Sadagopan but unfortunately died less than three months later.

In 1889, Ramanujan contracted smallpox but recovered, unlike many others who faced the death. Then, in 1891 and 1894, his mother again gave birth to two more children, but both of them died before their first birthdays. Since his father was at work most of the day, his mother took care of him, and their bond grew stronger. From his mother he learnt about the tradition and Puranas, to sing religious songs and to attend puja at a temple.

He became well versed with the Brahmin culture and followed particular eating habits. Just before turning ten, he passed his primary education in English, Tamil, geography and arithmetic. His scores were the best in the district. In the same year, he encountered formal mathematics for the first time. At the age of sixteen, he acquired a library copy of A Synopsis of Elementary Results in Pure and Applied Mathematics from a friend.

He studied the contents of the book thoroughly. The next year, he developed and investigated the Bernoulli numbers and calculate Euler’s constant up to 15 decimals. His peers could hardly understand his nature, and we’re always in awe because of his brilliance. Due to his extraordinary mind, he received a scholarship to study at Government Arts College, Kumbakonam. But he lost this scholarship because of his firm determination towards studying only maths and ignoring other subjects.

Later, too he failed in subjects like English, Sanskrit and physiology. In 1906, he flunked in his Fellow of Arts exam in December. Without a FA degree, he left college and decided to study independently in mathematics through research and referring books. Such a condition caused him extreme poverty, and he reached on the brink of starvation. He married Janakiammal on 14th July 1909 and took a job as a tutor at Presidency College.

Ramanujan met deputy collector V. Ramaswamy Aiyer in 1910, who was the founder of Mathematical society and wished to work in the revenue department. When Ramanujan showed his mathematics book to him, he stated that- “I was struck by the extraordinary mathematical results contained in Ramanujan’s books.” As he advanced further in maths, he even wrote his formal paper on the properties of Bernoulli numbers.

A journal editor M.T. Narayana Iyengar noted that Mr Ramanujan’s methods and presentation was terse and lacked precision and clearness. An ordinary person could hardly follow him. In England, he was awarded a Bachelor of Arts by Research degree. He was also elected to the London Mathematical Society. Ramanujan was the first Indian to be elected a Fellow of Trinity College, Cambridge.

In 1994, he died due to Tuberculosis and left the world. In the words of Hardy, Ramanujan had produced groundbreaking theorems and defeated him many times. He had never seen such theories in his life before. In his obituary, it was written that his insight into the subject was terrific and what he did was outstanding and remarkable.

The government of India in 2011, declared his birthday as National Mathematics Day to commemorate his valuable contribution and efforts. The former President even proclaimed that 2012 would be celebrated as National Mathematics Year.

Also Read – Republic Day Speech 2022 in English

Short Essay on Srinivasa Ramanujan in 250 Words

Below we have provided a short essay on Srinivasa Ramanujan, suitable for class 3, 4, 5 & 6 students.

Srinivasa Ramanujan was a well-known Indian Mathematician who was born on 22nd December 1887 during the British rule. He was born in a poor Indian village, Erode belonging to a Tamil family. His father’s name was Kuppuswamy Srinivas Aiyangar who worked as a clerk in a saree shop, and his mother was a religious housewife. They lived in Erode only for a year and then moved to Kumbakonam.

In this small town, Ramanujan attended many primary schools and achieved a distinction in his primary education. At the age of thirteen, he focused his attention on the sum of geometric an arithmetic series and in 1902, he created a method to solve quadratic equations and even explored Euler’s Constant. In the same year, he received a scholarship for his outstanding performance in his studies, and therefore he got admission at Kumbakonam’s Government college.

His passion for mathematics grew more robust, and hence he excelled in maths but failed in other subjects. The failure caused him depression, and he fled to Vizagapatnam without telling his parents. One year later, he returned to study and pass at First Art’s examination but again failed in all and passed in maths. Ramanujan got married to his old distant relative Janaki Ammal.

Furthermore, he published his first paper based on Bernoulli numbers in Journal of the Indian Mathematical Society and received recognition and achievement. His hard work got paid off, and he was appointed as a clerk at Madras Port Trust. At this time, he became famous throughout Madras and caught the attention of C.L.T Griffith who helped Ramanujan. Later, Ramanujan graduated from London and held a degree of Science for research on highly composite numbers.

7 Brilliant Mathematicians and Their Impact on the Modern World

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• Sir Isaac Newton (1642-1727)
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Emmy Noether (1882-1935)

John von neumann (1903-1957).

• Alan Mathison Turing (1912-1954)
• Benoit B. Mandelbrot (1924-2010)

Maryam Mirzakhani (1977-2017)

Math. It's one of those things that is easy to either love or hate. Those who fall on the hate side of things might still have nightmares of showing up for a high school math test unprepared, even years after graduation. Math is, by nature, an abstract subject, and it can be hard to wrap your head around it if you don't have a good teacher to guide you.

But even if you don't count yourself a fan of mathematics, it's hard to argue that it hasn't been a vital factor in our rapid evolution as a society. We reached the moon because of math. Math allowed us to tease out the secrets of DNA, create and transmit electricity over hundreds of miles to power our homes and offices and gave rise to computers and all that they do for the world. Without math, we wouldn't be where we are today. (And yes, some may argue that that might not have been such a bad thing.)

Regardless, our history is rich with mathematicians who helped advance our collective understanding of math, but there are a few standouts whose work and intuition pushed progress in leaps and bounds. Their vision and discoveries continue to echo through the ages, reverberating today in our cell phones, satellites, hula hoops, and automobiles. We picked some of the most remarkable mathematicians whose work continues to help shape our modern world, sometimes hundreds of years after their death. Enjoy!

Isaac Newton (1642-1727)

We start our list with Sir Isaac Newton, considered by many to be the greatest scientist of all time. There aren't many subjects that Newton didn't have a significant impact on—he was one of the inventors of calculus, built the first reflecting telescope , and helped establish the field of classical mechanics with his seminal work, "Philosophiæ Naturalis Principia Mathematica." He was the first to decompose white light into its component colors and gave us the three laws of motion , now known as Newton's laws. (You might remember the first one from school: "Objects at rest tend to stay at rest and objects in motion tend to stay in motion unless acted upon by an external force.")

We would live in a very different world had Newton not been born. Other scientists would probably have worked out most of his ideas eventually, but there is no telling how long it would have taken and how far behind we might have fallen from our current technological trajectory.

Carl Gauss (1777-1855)

Isaac Newton is a hard act to follow, but if anyone can pull it off, it's Carl Gauss. If Newton is considered the greatest scientist of all time, Gauss could easily be called the greatest mathematician ever. Carl Friedrich Gauss was born to a poor family in Germany in 1777 and quickly showed himself to be a brilliant mathematician. He published "Arithmetical Investigations," a foundational textbook that laid out the tenets of number theory (the study of whole numbers). Without number theory, you could kiss computers goodbye. Computers operate, on the most basic level, using just two digits—1 and 0, and many of the advancements that we've made in using computers to solve problems are solved using number theory. Gauss was prolific, and his work on number theory was just a small part of his contribution to math; you can find his influence throughout algebra, statistics, geometry, optics, astronomy, and many other subjects that underlie our modern world.

Mathematical Association of America / Wikimedia Commons / Public Domain

Born Amalie Emmy Noether, Emmy Noether was a German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics.

She is particularly known for Noether's Theorem, which establishes a fundamental connection between symmetries in physics and conserved quantities. This theorem has had a significant impact on the field of theoretical physics and is considered a cornerstone of modern theoretical physics.

Noether's work continues to influence both mathematics and physics. Her contributions are foundational in various branches of mathematics, such as abstract algebra, algebraic geometry, and topology. Her theorem remains a cornerstone in theoretical physics, providing deep insights into the conservation laws that govern physical systems.

Emmy Noether's legacy is a testament to her brilliance, perseverance, and the enduring impact of her ideas on multiple fields of study. Despite facing barriers as a woman in academia during a time when this wasn't the norm, Noether's work has left a lasting legacy and continues to inspire mathematicians and physicists to this day.

John von Neumann was born János Neumann in Budapest a few years after the start of the 20th century, a well-timed birth for all of us, for he went on to design the architecture underlying nearly every single computer built on the planet today. Right now, whatever device or computer that you are reading this on, be it a phone or computer, is cycling through a series of basic steps billions of times over each second, steps that allow it to do things like render internet articles and play videos and music, steps that were first thought up by von Neumann.

Von Neumann was a child prodigy who received his Ph.D. in mathematics at the age of 22 while also earning a degree in chemical engineering to appease his father, who was keen on his son having a good marketable skill. Thankfully for all of us, he stuck with math. In 1930, he went to work at Princeton University with Albert Einstein at the Institute of Advanced Study. Before his death in 1957, von Neumann made important discoveries in set theory, geometry, quantum mechanics, game theory, statistics, computer science and was a vital member of the Manhattan Project.

Remarkably, Von Neumann proposed a theory of global warming caused by human activity, noting that the Earth was only 6 degrees F (3.3 C) colder during the last glacial period. In 1955, he wrote : "Carbon dioxide released into the atmosphere by industry's burning of coal and oil—more than half of it during the last generation—may have changed the atmosphere's composition sufficiently to account for a general warming of the world by about one degree Fahrenheit."

Alan Turing (1912-1954)

Alan Turing was a British mathematician who has been called the father of computer science. During World War II, Turing bent his brain to the problem of breaking Nazi crypto-code and was the one to finally unravel messages protected by the infamous Enigma machine. Being able to break Nazi codes gave the Allies an enormous advantage and was later credited by some historians as one of the main reasons the Allies won the war.

Besides helping to stop Nazi Germany from achieving world domination, Turing was instrumental in the development of the modern computer. His design for a so-called "Turing machine" remains central to how computers operate today. The "Turing test" is an exercise in artificial intelligence that tests how well an AI program operates; a program passes the Turing test if it can have a text chat conversation with a human and fool that person into thinking that it, too, is a person.

Turing's career and life ended tragically when he was arrested and prosecuted for being gay. He was found guilty and sentenced to undergo hormone treatment to reduce his libido, losing his security clearance as well. On June 8, 1954, Turing was found dead of an apparent suicide.

Turing's contributions to computer science can be summed up by the fact that his name now adorns the field's top award. The Turing Award is to computer science what the Nobel Prize is to chemistry, or the Fields Medal is to mathematics. In 2009, then British Prime Minister Gordon Brown apologized for how his government treated Turing, but stopped short of issuing an official pardon.

Benoit Mandelbrot (1924-2010)

Benoit Mandelbrot landed on this list thanks to his discovery of fractal geometry . Fractals, often-fantastical and complex shapes built on simple, self-replicable formulas, are fundamental to computer graphics and animation. Without fractals, it's safe to say that we would be decades behind where we are now in the field of computer-generated images. Fractal formulas are also used to design cellphone antennas and computer chips, which takes advantage of the fractal's natural ability to minimize wasted space.

Mandelbrot was born in Poland in 1924 and had to flee to France with his family in 1936 to avoid Nazi persecution. After studying in Paris, he moved to the U.S. where he found a home as an IBM Fellow. Working at IBM meant that he had access to cutting-edge technology, which allowed him to apply the number-crunching abilities of electrical computer to his projects and problems. In 1979, Mandelbrot discovered a set of numbers, now called the Mandelbrot set . In a documentary titled "The Colours of Infinity," science-fiction writer Arthur C. Clarke described it as "one of the most beautiful and astonishing discoveries in the entire history of mathematics." Learn more about the technical steps behind drawing the Mandelbrot set.

Mandelbrot died of pancreatic cancer in 2010.

Maryeraud9  / Wikimedia Commons / CC BY-SA 4.0

Maryam Mirzakhani was an Iranian mathematician known for her visionary work in the field of complex geometry and particularly for her contributions to the study of moduli spaces of Riemann surfaces.

She made history in 2014 when she became the first Iranian and first woman to be awarded the prestigious Fields Medal, generally considered the highest honor in mathematics. Her work combined insights from various areas of mathematics, including hyperbolic geometry, topology, and dynamics, and had implications not only in pure mathematics but also in theoretical physics and other fields.

Her work was notable for its singular creativity and elegance and for the way in which she developed innovative techniques to study geometry. Tragically, she passed away in 2017 at the age of 40, but her contributions continue to inspire the mathematical community, particularly those interested in the intersections of geometry, topology, and complex analysis.

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21 Famous and Greatest Mathematicians | 2024 Edition

Who are the most famous and greatest mathematicians to have ever lived? Well, answering this question is not easy, considering that mathematics has been known to humanity since prehistoric times, long before the birth of Christ.

From the timeless brilliance of Euclid and Pythagoras to the revolutionary insights of Alan Turning and Maryam Mirzakhani, mathematicians across the world have left an indelible mark on the pages of history. They transformed our understanding of the world, solved age-old mysteries, and paved the way for numerous scientific and technological breakthroughs.

The role of mathematics in our lives is immense. Math has made it possible to transmit electricity over thousands of kilometers, aided in the exploration of the concept of DNA, given rise to computers, and is essential in our quest to deepen our understanding of the universe.

“Mathematics is the alphabet with which God has written the universe” — Galileo Galilei

Without math, scientists can’t develop better medicines, researchers can’t explore new technologies, architects can’t design innovative structures, economists can’t make accurate predictions, and our world would be missing the solutions to many important challenges. 

Similar to many other fields, the mathematics we know today didn’t just randomly come into existence. The development of new, groundbreaking theorems and equations is a process that spans decades. Now, let’s explore the individuals behind these advancements. 

Table of Contents

16. Srinivasa Ramanujan

Known For : Ramanujan–Petersson conjecture, Ramanujan’s master theorem

Srinivasa Ramanujan was perhaps the most remarkable mathematician in modern India. Although Ramanujan had no formal training, his advanced mathematical knowledge at a very young age left many completely awestruck.

By the age of 16, he had independently developed and studied Bernoulli numbers, as well as calculated the Euler–Mascheroni constant. Before his untimely death at the age of 32, Ramanujan had successfully formulated nearly 4,000 different mathematical identities.

He gained international fame after G. H Hardy, a prominent British mathematician, recognized his work and compared him with the likes of Euler and Jacobi .

15. Joseph-Louis Lagrange

Known For : Lagrangian mechanics, Celestial Mechanics, Number Theory

Joseph Lagrange was one of the most notable students of the great Leonhard Euler. Lagrange started his mathematical career with variational calculus (in 1754), which led to the formulation of the Euler–Lagrange equation.

Lagrange later reformulated classical mechanics, introducing Lagrangian Mechanics . His renowned work on analytical mechanics, titled “Mécanique analytique,” played a crucial role in advancing the field of mathematical physics

14. Andrew Wiles

Accolades: Wolf Prize (1995/6); Abel Prize (2016)

Sir Andrew John Wiles, a prominent British mathematician, gained widespread recognition for resolving Fermat’s Last Theorem , once regarded as the “most challenging mathematical problem.”

In 1975, under the guidance of John H. Coates, Andrew Wiles started working on the Iwasawa theory, which he continued with American mathematician Barry Mazur.

His most groundbreaking contribution occurred in the early 1990s when he successfully proved a significant portion of the modularity theorem, formerly known as the Taniyama–Shimura conjecture. The modularity theorem, in essence, is related to Fermat’s Last Theorem and was enough to prove it.

Andrew Wiles on what it feels like to do mathematics pic.twitter.com/7egzT7Gp7F — Fermat’s Library (@fermatslibrary) April 28, 2023

13. Carl Gustav Jacob Jacobi

Known For : Jacobi’s elliptic functions; Jacobi transform

Carl Gustav Jacobi was one of the prominent mathematicians of the 19th century. His formulation of the theory of  elliptic functions is perhaps his greatest contribution to the field.  

Jacobi played a key role in advancing the study of differential equations and rational mechanics, notably contributing to the development of Hamilton-Jacobi theory.

Beyond this, his influence extended to the realms of mechanical dynamics and number theory, where he made fundamental contributions that enriched our understanding of these intricate mathematical domains.

12. Alan Turing

Known For : Cryptanalysis of the Enigma, Turing’s proof Accolades: Smith’s Prize (1936)

During the Second World War , the German intelligence network was considered almost impenetrable. Many allied nations feared that if they could not intercept important transmissions by the Nazi high command, they might eventually lose the war.

It was Alan Turing who, with his unprecedented mathematical and cryptanalytic abilities, made significant improvements over the Polish-made bombe and devised a machine that could decode the Enigma faster.

Post-war, Turing joined the National Physical Laboratory (U.K.), where he designed the Automatic Computing Engine, one of the earliest stored-program computers.

In the later stages of his career, Turing shifted his focus to theoretical biology. During this period, he mathematically predicted the Belousov–Zhabotinsky reaction , an occurrence later observed in the 1960s.

11. G.F. Bernhard Riemann

Known For : Riemann integral, Fourier series

Georg Bernhard Riemann was born in a small village near Dannenberg, Germany. Under the tutelage of Carl Friedrich Gauss, Riemann studied differential geometry and developed his theory of higher dimensions . His work is now known as Riemannian geometry.

Johann Gustav Dirichlet also played a significant role in shaping Riemann’s mathematical journey. Employing the Dirichlet principle, Riemann successfully formulated the renowned Riemann mapping theorem.

The legacy of Riemann’s mathematical contributions extends beyond his time, as some of his equations found application in Einstein’s General Relativity theory. His work continues to be foundational in diverse areas of mathematics and physics.

10. Henri Poincaré

Known For : Three-body problem, Chaos theory, Poincaré–Hopf theorem

According to Eric Bell, a notable Scottish Mathematician, Henri Poincare was probably one of the last Universalists, as he thrived in almost all known fields of mathematics at that time.

Poincare, during his lifetime, contributed numerous theories in the fields of mathematical physics, applied mathematics, and astronomy. He was instrumental in the formulation of the theory of Special Relativity .

His exceptional works on Lorentz transformation and the Three-body problem paved the way for mathematicians and astrophysicists to make discoveries about our planet and outer space.

His theoretical works even inspired famous artists, such as Picasso and Braque, to establish an art movement (Cubism) in the 20th century.

9. David Hilbert

Known For : Proof theory, Hilbert’s problems

David Hilbert was perhaps one of the greatest mathematicians of all time. He was instrumental in developing fundamental theories in the field of commutative algebra, calculus of variations, and mathematical physics.

Hilbert’s problems (a set of twenty-three mathematical problems, which he published in 1900) influenced groundbreaking studies in different fields of mathematics. Some of those problems remain unsolved to this date.

In his later years, David Hilbert devoted himself to physics. It was during this time he competed against Albert Einstein on general relativity.

8. Fibonacci

Known For : Fibonacci numbers

Fibonacci, also known as Leonardo of Pisa, was one of the most accomplished mathematicians of the High Middle Ages.

Perhaps his most significant contribution to the subject is Liber Abaci, a personal book through which he popularized the Indo-Arabic numeral system (0,1,2,3,4..) and the Fibonacci sequence in Europe.

Today, the sequence is used in computer algorithms and databases.

7. Bernoulli Family

In the world of mathematics, the Bernoulli family holds the highest place. Originating from Antwerp, Belgium, Jacob and his brother Johann Bernoulli were the pioneering mathematicians in the Bernoulli lineage.

Both Jacob and Johann worked together on infinitesimal calculus and are credited for theorems and justifications such as  Bernoulli numbers and the Brachistochrone curve .

Daniel Bernoulli, Jacob’s son, emerged as one of the most distinguished members of this illustrious family. His seminal work, Bernoulli’s Principle, provides a mathematical explanation for the functioning of a carburetor and an airplane wing . Additionally, Daniel made substantial contributions to the fields of probability and statistics.

6. Pythagoras

Known For : Pythagorean theorem, Theory of Proportions

Pythagoras of Samos was born around 570 BC, and like most ancient Greeks, not much is known about his early life. As a philosopher, his works influenced the likes of Plato and Aristotle, as well as Johannes Kepler and Isaac Newton.

Although its authenticity remains debatable, many mathematical findings are attributed to Pythagoras. Perhaps the most famous of them is the Pythagoras theorem (named after him). Many historians have, however, stated the theorem was known by the Babylonians well before the time of Pythagoras.

He may have also been responsible for discovering the Theory of Proportions.

5. Carl Friedrich Gauss

Accolades: Lalande Prize (1809), Copley Medal (1838)

Carl Friedrich Gauss was perhaps the most influential mathematician since the Ancient Greeks. His contributions in various fields of mathematics and physics are almost second to none. Gauss started showing signs of brilliance at the early age of seven when he could solve arithmetic progressions much faster than anyone in his class.

Some of his famous works include Gauss’ Law and Theorema Egregium, which concluded that the Earth could not be displayed on a map without some distortion. He was the first to speculate the possibility of non-Euclidean geometry, although his works were never published.

4. Issac Newton

Known For : Newton’s Laws of Motion, Calculus, Newtonian Mechanics

Sir Isaac Newton is one of the founding fathers of classical mechanics and infinitesimal calculus. His views on gravity remained universally accepted until Einstein’s theory of relativity.

Newton’s most remarkable contribution to mathematics is calculus (then called infinitesimals), which he developed independently of his contemporary Gottfried Wilhelm Leibniz .

It was Newton who first explained the reason behind tidal disturbances on Earth and helped validate Kepler’s laws of planetary motion. His works on optics gave us the first-ever refracting telescope.

3. Leonhard Euler

Known For : Euler’s conjectures, Euler’s equations, Euler’s numbers

In a tribute to Leonhard Euler’s immense contributions to mathematics, Pierre-Simon Laplace, a notable French astronomer and mathematician, wrote, “Read Euler, read him again and again; he is the master of us all.”

Mathematicians today hold Euler in the highest regard and consider him the most influential and greatest mathematician of the 18th century.

Euler made significant contributions to almost every major field in mathematics, including algebra, trigonometry, and geometry. In the realm of physics, his unparalleled works on fluid dynamics and Fourier series remain unmatched.

2. Archimedes

Known For : Archimedes’ principle; Hydrostatics

Born around 287 BC in Syracuse, Sicily, Archimedes was well-versed in mathematics, physics, and astronomy of that time. He was a polymath. However, most of his literary works have not survived.

Archimedes was one of the pioneers of geometry, who derived formulas for the area of a circle, volume, and surface area of a sphere. His method of determining the value of pi remained unchallenged and the only known way to calculate the circumference of a circle for decades.

The Fields Medal, the preeminent honor in mathematics, features a right-facing portrait of Archimedes along with a quote attributed to him.

“Transire suum pectus mundoque potiri” — Rise above oneself and grasp the world.

1. Euclid

Known For : Euclidean geometry; Euclidean algorithm

Euclid of Alexandria was a Greek mathematician widely regarded as the founder of geometry. Euclid’s Elements, a compilation of 13 books, is considered one of the oldest and most influential books on mathematics.

While Euclid’s Elements is primarily celebrated for its foundational contributions to geometry, now recognized as Euclidean geometry, it also provides a thorough introduction to elementary number theory.

Euclid’s achievements extend beyond geometry, with his works on optics earning widespread acknowledgment for their significance in the field.

Euclid’s systematic approach in his work — starting from axioms and then logically obtaining complex results, has influenced some of the greatest minds of later generations. Newton’s Principia Mathematica is a perfect example of it.

Famous Mathematicians of the 21st Century 

17. alessio figalli.

Read the article in @QuantaMagazine about the latest work of Alessio Figalli ( @AFigalli ), Joaquim Serra and Xavier Ros ​Oton ( @ros_xavi ). @ETH_en @UniBarcelona https://t.co/Ph130FI0kE pic.twitter.com/mIwNoKxBOc — @ETH_MATH (@eth_math) October 8, 2021

Known For : The theory of optimal transport

Alessio Figalli has established himself as a leading figure in the study of partial differential equations, metric geometry, and their applications. 

In 2018, he was awarded the Fields Medal for his contributions to the theory of optimal transport , which addresses the optimal ways to transport one distribution of mass to another while keeping the associated transportation cost as low as possible.  

Figalli’s research goes beyond optimal transport, extending into areas like geometric measure theory, functional inequalities, and Monge-Ampère equations. Not only has his work significantly advanced the theoretical aspects of these subjects, but it has also yielded practical applications in diverse fields, including economics and physics.

18. Manjul Bhargava

Known For : Profound contributions to number theory

Manjul Bhargava has enhanced our understanding of representing integers through quadratic forms, a key aspect of number theory.

His work includes groundbreaking results related to the distribution of values of quadratic forms and higher-degree polynomial equations. He developed efficient techniques to study the distribution of integers represented by these equations, deepening our understanding of the arithmetic properties of these forms. 

Bhargava introduced the concept of higher composition laws, generalizing the well-known composition laws for quadratic forms. These laws have applications in algebraic number theory. He also explored the rational points on elliptic curves , which have applications in both pure and applied mathematics. 

Bhargava has received many awards and honors for his work, including the Fields Medal in 2014.

19. Maryam Mirzakhani

Known For : Providing insights into Riemann surfaces and their moduli spaces

Maryam Mirzakhani gained international recognition for her groundbreaking work in mathematics, especially in the field of geometry and dynamical systems. She made history in 2014 by becoming the first woman to be awarded the Fields Medal. 

Her early work focused on the moduli space of Riemann surfaces. She developed new methods to calculate the Weil-Petersson volumes of these moduli spaces , providing new insights into the geometry of hyperbolic surfaces. 

She also studied Teichmüller dynamics , which involves understanding the behavior of geometric structures on surfaces. Her research provided detailed insights into the dynamics of the mapping class group and the geometry of moduli spaces, connecting complex analysis, geometry, and dynamics. 

Unfortunately, she passed away in 2017 at the age of 40. However, her legacy continues to inspire young students, particularly women, to pursue careers in math and contribute to the advancement of the discipline. 

20. Maryna Viazovska

Known For : Solving the sphere-packing problem in dimension 8

Maryna Viazovska is famous for her involvement in a collaborative effort related to the “sphere-packing problem.” It’s a classical problem in math that involves determining the most efficient way to arrange identical spheres in a given space in such a way that they do not overlap or leave voids. 

In 2016, Maryna Viazovska was part of a group of mathematicians who provided a groundbreaking solution to this problem. The solution involves finding the optimal way to pack spheres in eight-dimensional space, which has applications in coding theory and other areas.

Her contributions were recognized with the prestigious Fields Medal, which she was awarded in 2022. She became the first person with a degree from a Ukrainian university to ever receive this distinguished award.

Beyond the academic realm, her achievements have been acknowledged on a broader scale. For example, in December 2022, she was honored as one of the BBC 100 Women.

21. Grigori Perelman

Known for : Solving Poincaré conjecture

Grigori Perelman has made notable contributions to the fields of geometric analysis, geometric topology, and Riemannian geometry. He gained international fame for his work on the Poincaré conjecture, a longstanding problem in topology. 

This problem remained unsolved for almost a century until Perelman claimed to have proved it in a series of papers posted online between 2002 and 2003. 

He won numerous awards and prizes for his contributions, including the Fields Medal and a one-million-dollar prize from the Clay Mathematics Institute. However, he declined most of them and withdrew from active participation in the mathematical community. 

His refusal of prestigious awards and his decision to step away from the academic world have made him a somewhat mysterious figure in the mathematical community. 

More to Know 

What is the fields medal, and why is it prestigious.

The Fields Medal is one of the highest honors a mathematician can receive. It is often described as the “Nobel Prize of Mathematics.” It is named after Canadian mathematician John Charles Fields, who came up with the idea of establishing this award. 

First awarded in 1936, the Fields Medal is given every four years during the International Congress of Mathematicians. It is awarded to mathematicians under the age of 40. 

Recipients receive a gold medal, global recognition, and a monetary prize, which, as of 2006, amounts to CA$15,000.

Are there any famous female mathematicians?

Of course, there have been many accomplished female mathematicians who have made major contributions in this field throughout history. The most popular names are 

1. Hypatia was a prominent ancient Greek mathematician and astronomer who lived in Egypt during the late 4th and early 5th centuries AD. She is known for her detailed commentaries on Euclid’s famous mathematical work “Elements.” She also worked on Diophantus’s “Arithmetica,” which ultimately contributed to the development of algebraic concepts.

2. Sofya Kovalevskaya  was the first woman to earn a doctorate in mathematics and become a full professor in Europe. She is best known for her Cauchy-Kovalevskaya theorem , which deals with the uniqueness of solutions to specific types of partial differential equations, specifically those related to the theory wave. 

3. Emmy Noether is best known for her work in abstract algebra, particularly in the development of Noether’s theorem . This theorem played a critical role in the development of modern theoretical physics, including the formulation of the theory of relativity and quantum mechanics.

4. Mary Cartwright worked in the fields of dynamical systems, chaos theory, and differential equations. Her contributions to Cartwright–Littlewood Theorem helped us understand the stability of solutions to differential equations. 

5. Karen Uhlenbeck is known for her groundbreaking work in geometric analysis and gauge theory. She is the first, and so far only, woman to win the Abel Prize , one of the most prestigious awards in mathematics. 

What are some unsolved problems in mathematics today?

While there are countless unsolved problems in mathematics, some have puzzled mathematicians for decades or even centuries. The most popular ones are: 

1)  P versus NP problem : It asks whether every problem for which a proposed solution can be quickly verified by a computer (NP, “nondeterministic polynomial time”) can also be solved quickly by a computer (P, “polynomial time”). It is also one of the seven Millennium Problems . 

2) The Riemann Hypothesis : It deals with the distribution of prime numbers. The hypothesis has remained unproven since its formulation in the 19th century.

3)  The Twin Prime Conjecture : It proposes that there are infinitely many pairs of twin primes (which are prime numbers having a difference of 2, for example, 41 and 43 or 71 and 73). Although there is strong numerical evidence, there is no rigorous proof. 

4) 3n+1 problem : it is a simple mathematical sequence that starts with any positive integer and repeatedly applies certain operations . This conjecture asks whether all sequences eventually reach the number 1.

5)  The Goldbach Conjecture : It was proposed by the German mathematician Christian Goldbach in a letter to Euler in 1742. It  suggests that every even integer greater than 2 can be expressed as the sum of two prime numbers.  

Read More 

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15 Famous Physicists Alive Today And Their Contribution  

10 Fun Math Games That Will Make You Smarter

Varun Kumar

I am a professional technology and business research analyst with more than a decade of experience in the field. My main areas of expertise include software technologies, business strategies, competitive analysis, and staying up-to-date with market trends.

I hold a Master's degree in computer science from GGSIPU University. If you'd like to learn more about my latest projects and insights, please don't hesitate to reach out to me via email at [email protected] .

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Leave a reply cancel reply, 21 comments.

What about Einstein

Where have you been living…, ? under a rock perhaps? Einstein was “…outted…” decades ago as a plagiaristic Jew and used by the Jew World Order to make Jews look smarter than everyone else… Jews control the mass media and therefore use it to convince the masses that theya re the victims, when in fact they are the criminals.

Einstein was incapable to graduate his high school and he did not ‘sparked’ at all in all schools he started an didn’t graduate, but he knew to cheat. The preliminaries of his theory of relativity he co-authored in Germany was published as ‘original’ in U, and his friend’s name and contribution to this theory was forgotten. The theory itself is practically impracticable and founded an ‘relative’ truths that only Ein Stein and a lot of other rock-heads could verify; as for example: the parallel lines meet in infinite or the straight line light cubs when passing near a star, a planet or other celestial body. This is the Judaic conspiration in science. Newton’s gravitational line will never curb.

Bro you are literally a Nazi

Let’s keep the antisemitism down to a dull roar.

Having said that, Einstein was a physicist, not a mathematician.

Albert Einstein is NEVER a Pure Mathematician.

As for Applied Mathematician, or, Applied Mathematical Scientist/Applied Scientific Mathematician:

Yes, truth is: Einstein is “50%” – because of the other “50% of Einstein’s science career” as Scientist is provided by Einstein’s 1st Lawful Wife: she is GOD’S both Mathematician & Scientist: Ms Mileva Marity Maric who is GOD’S Gift to Albert Einstein as his [lifetime] wife & co-author [GOD is a living Witness to all these Einstein’s “secrets”…] in the closed collaboration & research works on mathematical natural sciences w/ her initiative INNOVATION IDEAS that help Einstein at least 81% in completing all their (both Einstein’s & Marity-Maric’s] 11 Papers from 1896 to 1912 [before Einstein did separate off from her 1913-1914 & ultimately did divorce her 1919, against GOD’S WiLL thus causing Einstein’s Scientific Career slowed & full of mistakes, HARDLY to progress, particularly Einstein’s General Relativity in 1915 [which 96% Mathematics & Science Formulation & Explanation originated from Marity Maric, including the “G” Cosmological Constant, which comes from Marity Maric ORIGINALLY way way back in 1908-1912, which originally Marity Maric mathematically showed to Einstein that the Universe is mathematically tenable if it is moving & expanding to the utmost annoyance & REJECTION by Einstein back then (1908-1912) to have even SHOUTED at Mileva Marity Maric for contesting his (Einstein’s) idea of the Static Universe based on Einstein’s computation mathematics as “corrected & reconstructed mathematically by Mileva Marity Maric (during 1908-1912)”. Thus, all 11 Papers from 1896 to 1912 – including the 1905 papers – are Co-AUTHORED both by Einstein & Marity Maric (Einstein’s 1st Lawful Wife who KNOWS Mathematics & Natural Physics more than Albert Einstein. This is the Truth and GOD is the WITNESS to all these “secrets” of Albert Einstein.

Bro. JOSUE, pls wait for the LinkedIn Publication of my Paper on these “historical secrets” of Albert Einstein & about the “true Albert Einstein” – that will reveal them & correct the History of Albert Einstein, including the “History of Mileva Marity Maric” to put JUSTICE to the Truth in the History of Relativity Theory & all other 10 Papers during 1896 to 1912 Milestone Timeline of Albert Einstein’s life. After Einstein’s decision in separation from his wife, Einstein had hard times & difficulty in progressing his scientific career; GOD (“The Old One”) stopped communicating to Einstein, even until his dying moments in April 17-18, 1955, could hardly formulate his final Paper Cosmic Relativity to figure out the GUT by which Einstein struggled 40 yrs from 1915 to 1955 in his death bed at Princeton Hospital, 1:15 AM, 18 April 1955, to figure out his Grand Unified Theory (of Forces) to complete FAILURE – all for which & by which REASON alone results from Einstein’s GREATEST Mistake of his scientific career: Einstein’s inhuman treatment upon & gross separation/divorce off his wife: Mileva Marity Maric against GOD’S WiLL.

Right now, Einstein has been suffering in the Spirit World and the ONLY way to ‘cure’ his suffering is for Einstein to reveal to Earth & all humanity who the “true Albert Einstein is” and about the truth on Mrs Mileva (Marity) Maric Einstein in the context of truth on “co-authorship” for & of all the 11 Papers which Einstein falsely declared to the World that he is the sole author – in the period from 1896 to 1912. This is so because in the Spirit World, no one can keep secrets or, lies before GOD. – Gpw Bernard Bautista Rementilla

World famous physicist & mathematican

what about Arayabhata?????? he discovered the 0 as well as the decimals

Should the writer of the comment be a Jew, for the content to pass the Jewish censorship?

Please search the basics, where does Algebra come from Geometry Trigonometry Who provided Zero to the western world

They were Muslims. I know you don’t like it. But sorry mate you can’t change the fact. If you are not bias and a writer to teach others instead of promoting your thoughts you would do research.

Kid, your article is written well but you need to research before writing.

Ahem … Where the hell is Cauchy? Where are Leibnitz and Pascal? Why is Pythagoras here instead of Diophantus? Where the hell is Kurt Goedel?

I’d have thought that Cauchy, Riemann, Euler, Gauss, and Newton would form the top 5, not necessarily in that order …

This is a complete nonsense. How could a unknown “Srinivasa Ramanujan” be in the ranking while neither Galois nor Abel is ?

Hi, Mr VARUN, w/ all due respect [since it is your opinion; nevertheless…] concerning your List (contents; or, personalities that are not in the List; or, are not to be included bit is/are in the List) & sequence about your 16 Greatest Mathematicians – I’m sorry but I disagree w/ you in the context of application coverage significance (say in: improving, advancing the mathematical technique principle, theorem, etc., ; historical value, depth, & breadth. Also, kindly we MUST specify: there are 2 Types of Mathematicians: Pure Mathematicians & Applied Mathematicians… [If I am student of mathematics who values the works of mathematicians in history, the, I would only be confused …. I appreciate you efforts, anyway; but pls consider those students of mathematics in weighing the facts & truth of their (mathematicians’) contributions in history of mathematics: pure mathematics…; or, applied mathematics.

Mulatu Lemma is also one of the top mathematician discovering the Mulatu Numbers. Google read about this mathematician.

He is known for discovering the Mulatu Numbers. Great mathematician.

He is one of the best mathematicians who published numerous papers on peer reviewed journals

Mulatu Lemma was selected as the top professor of 2023 by IAOTP.

Hi, Bro. Varun KUMAR, peace be you & safe good health wish for you from me & w/ prayers ‘from’ our One Absolute Original 1st & Last Parental GOD. Now,

Re: Of your Article here – w/ & by all respect, I’m sorry but, I re-constructively do not agree: both in names & sequencing. Pls remember your “central theme is: ‘The Famous & Greatest Mathematicians’ … [More so if – as always it is: after ‘Mathematicians’, usually suffixed – ‘of All Time’]. Why I don’t agree – “re-constructively” – Well, 1stly: How I wish you’re gifted by/allowed by GOD to “enter” the Spirit World & be able to see, talk to each of the mathematicians you enlisted & the sequencing [numerically] you assigned to each & ASK in silent using your heart & mind [don’t speak using voicing physically, etc., it won’t work]; USE Heart & purity of your purpose, while looking at each straight to the eyes: Speak using your Heart * Mind; of course pray 1st to GOD & ask humbly His Permission; Ask “all possible questions” about the ‘history of mathematics and mathematicians strictly & strictly living are existing & living (respectively) in their own time – you will be BOTH amazed & disappointed about your expectations: How come..?

1. Suggestion only & Clue – OBJECTIVELY: Pls in final writing off after your review, back to your 16 Greatest & Famous Mathematicians; pls from their respective time to present: kindly CONSIDER the following A. Breadth, B. Depth, and C. Historical Significance: (in the context their respective Mathematical Contribution as to its “application importance” both in theory and practice, from their time to the present contextual applicative coverage to scope of the current level of mathematical development & advancement history stage ‘where we are NOW’.

2. Bear in mind: there are two (2) Major Categories of Mathematicians: A. Pure Mathematicians and B. Applied mathematicians. Again, based on [breadth, depth, and historical significance], if your mathematician chosen is “not only “Pure Mathematician” but is also “Applied Mathematician” w/ equally & more so & yes, more so highly regarded as his ‘application mathematical contribution’ is practically universal, of great impact to natural sciences/applied sciences & engineering! Then, that’s another ADDED Credit Points.

For Example(s). David Hilbert and Carl F Gauss and Albert Einstein are “admiring fans” of GF Bernhard Riemann; yet Riemann’s mathematical contribution(s) are so vast covering wide range of ‘applied/natural sciences & even to engineering & medical technology sciences – Today! and even James Clerk Maxwell (1 greatest applied mathematician and 1 greatest mathematical scientist of all time had his famous Electro-Magnetic Theory (EMT) Equations did/do PROVE in yet only 1 most amazing natural mathematical proof available thus far – as when it is used upon/ in Modern Applied Medical Science to Human Health Parameter(s) Determination involving: Energy, Frequency & Resonance! as to have provided Application Specimen of Proof to & that this Riemann’s Hypothesis is TRUE – yes, it’s TRUE and Accurate Mathematical (not Theory & not just Hypothesis but) a Riemannian Principle of Most Advanced Mathematical Theorem yet w/ the greatest impact & application [in terms of breadth, depth, and historical importance] to both “Pure Number Principle, Prime Number System Theorem, and others, in addition to its (“Riemann Hypothesis’s”) application Medical Sciences of Today’s 21st Century!

Also, GF Bernhard Riemann’s Mathematical Works are [esp. Riemann’s Non Euclidean Geometry (NEG) encompasses/embraces & even extends beyond via Vector Duality Matrix Field (Group) Principle of Mathematics! the NEG of Gauss [C,F. Gauss, one greatest mathematician of all time w/ equally famous greatest mathematician of all time Leonard Euler!) upon knowing Riemann’s NEG in 1854, left his own NEG System & so excited before a distinguished mathematical physicist, W.E. Weber in attendance right after Riemann’s New & Higher Dimensional NEG Lecture 1854, & Gauss, clasping his hands! finding in Riemann his student: “my hero!” & did spend the rest of his remaining lifetime on Earth studying Riemann’s NEG till he died on 23 February, 1855. NEXT –

3. Consider the greatest specifics of mathematical significance of their mathematical works in Number System, in Proofs of Number Theorems, and so on,, so vast & equally of practical application values of their works: the Triumvirate Pillars of Modern Mathematics w/ Riemann: Isaac Newton, C. F. Gauss & Leonard Euler, far greater than Euclid’s Work ‘despite’ that whose mathematics did some impact “bases in mathematical proof theorems” [of geometry approach] some 23 centuries later in his life (he died ‘mid-3rd century’ approx.)] because, after Isaac Newton [wow! 1 of the most Important (few) Applied Mathematicians of all time & equally 1 greatest mathematical physicist of all time (he died 31 March, 1727 ], it is discovered in Science Community Authority that “Euclid Elements” or, Euclidean Geometry can Hardly HOLD True & can HARDLY Fit In the complex mathematical laws of “Natural Phenomena” – any more; but not Riemann NEG! Wow – a very complex COOL Truth of Nature’s Laws! Yes, Wow! It is Albert Einstein who 1st sensed & did apply & [he is correct!] Riemann’s Geometry [NEG] to his [Einstein’s most famous (one of the most famous mathematical field natural science applications!)] General Relativity, 1915 AD.! And other proof examples … we have these open to all in our History of Mathematicians; History of Applied Natural Mathematical Sciences and History of (Individual) Mathematician’s Life, provided by Authorities on the Subject – your Title-Subject. Thank you. Gpw_BBR

Dr. Lemma is one of the best mathematicians. The world is blessed to have him, and it is an honor to know him.

Mulatu Lemma is one of the finest mathematicians who discovered the Mulatu Numbers in 2011. He enjoys playing with mathematics and introducing new theorems. He has published over 170 papers. I believe he will continue to publish more.

Well known on his breakthrough discoveries such as Mulatu number, Mulatu Lemma is one of the contemporary exceptional mathematicians. His publication portfolio in pure mathematics has reached 200.

Carl Friedrich Gauss: The Greatest Mathematician Essay (Biography)

Carl Friedrich Gauss was also known as Johann Friedrich Carl Gauss, the greatest mathematician in history with contributions in the field of geometry, statistics, number theory, astronomy, potential theory, geophysics, astronomy, and many others.

Carl Friedrich Gauss was born in Burnwick, Germany on April 30, 1777. Being the only child of poor parents, he did not go to school from a young age. However, Gauss could do complex calculations in his head. He held this capability even before he learned how to talk. He taught himself to read. Gauss’ father did not support his education as he did not think that it could be used to help feed the family. One of Gauss’ teachers convinced his father to let him stay back after class to study. From the time that he could calculate he started with arithmetical experimentation and solved his first complex problem at the age of eight.

According to Jeremy John, Gauss’ teachers and parents recommended him to the Duke of Burnswick in 1791, who financially helped him to continue his education locally and further at the University of Göttingen from 1795 to 1798 (Gray par.3). Before this, he attended the Collegium Carolinum (now Braunschweig University of Technology ) from 1792 to 1795. In 1798, Gauss came back to Burnswick but worked and lived alone. During the first year of his return to Burnswick, he worked on and developed the four proofs that are now used in the fundamental theorem of algebra. In 1799, Gauss defended his doctorate, under the supervision and mentorship of J.F. Pfaff, from the University of Helmstedt (“Carl Friedrich Gauss Biography – German Mathematician”).

During his school and college years, Gauss was way ahead of his colleagues and classmates when it came to studying elementary geometry, algebra, and analysis. He was also very comfortable with number theories and arithmetic. Gauss wanted to conduct empirical investigation and experimentation with arithmetic. According to the Encyclopaedia of World Biography, in 1792 Gauss discovered that a regular polygon with 17 sides can be constructed without any complex tools, only with the help of a ruler and compass alone (“Karl Friedrich Gauss Biography”.). The result was not as significant as the way that led to the result. For example, an analysis of the factorization of polynomial equations was conducted. Riami in his presentation shared that Gauss’ Ph.D. was based on the fundamental theorem of algebra which Gauss proved in 1797 (Raimi par. 4).

According to Riami in his presentation, when deciding on what to become, Gauss had wanted to become a philologist, but he instead became a mathematician (Raimi par. 7). The discovery which led him to become a mathematician was the construction of 17 sides of a regular polygon mentioned above. The first paper that was ever published by Gauss was written on algebraic number theory, the Disquisitiones Arithmeticae, in 1801. His second major publication was written when he rediscovered the Ceres asteroid. Many astronomers were working on rediscovering the asteroid, but it was Gauss, who was able to succeed. Gauss applied the method of least squares to help him calculate the orbit and find out when the Ceres asteroid would reappear (“Gauss, Carl Friedrich”).

Gauss was working as an assistant of the Duke, who increased his stipend and treated him quite well. However, Gauss wanted something more, he wanted an established post for himself and the one that was on his mind was a Professor of Mathematics. Gauss was not interested in becoming a professor and teaching elementary arithmetic to students who were not interested in studying Mathematics. Astronomy intrigued him and offered him the alternative that he was looking for. This led to him being accepted to the “Challenge of Hanover”, the project that lasted from 1818 till 1832, and resulted in some major achievements. Gauss invented the heliotrope during this time. Also, he discovered that there is an intrinsic measure of curvature leading to the clarity of why a map of Earth could never be drawn exactly as it was.

The 1830s were a time when Gauss gained interest in terrestrial magnetism. Weber and Gauss worked together Math Rochestor among other sources, in developing the first electric telegraph. This led to the discovery of the potential theory, something that is important in the physics that we study today. Gauss did not share some of his discoveries mainly because he began to doubt the truth of Elucidean geometry and worked on proving a logical alternative.

According to Encyclopedia.com, Gauss’s personal life was generally isolated (“Carl Friedrich Gauss”). He developed a romantic relationship with Wolfgang Bolyai, with whom he would discuss geometry foundations, but this relationship ended when Bolyai returned to Hungary to pursue his work. Gauss could only share his thoughts with Pfaff at the time but since Pfaff was someone who was guiding him with his doctorate, it was never on an equal level. Sophie Germain was someone Gauss shared letters with and discussed mathematics, but it never resulted in anything. Sophie was in Paris and Gauss never visited France. Gauss was someone who worked and lived alone. He did not have many friends and led an isolated life. Gauss did marry in 1805, to a woman named Johanna Osthoff, as mentioned in various sources for example by Riami in his presentation (Raimi par. 9). She bore him a son and a daughter but died during the birth of the third child. After the death of his first wife, according to the website, Encyclopedia.com, he married his wife’s best friend Minna Waldeck, who also gave him three children: two sons and a daughter (“Gauss, Carl Friedrich”). But Gauss was not happy till a later stage in his life when his youngest daughter took over the household. His sons moved to the US.

Gauss was a nationalist and royalist, as mentioned in the article on Encyclopedia.com (“Gauss, Carl Friedrich.”). He did not agree with Napoleon and thought that he would bring about a dangerous revolution with which Gauss did not agree. However, his religious views were the same as those of the political opponents. Gauss was not a religious man in front of people, and he preferred to keep his religious ideas and views to himself, as mentioned in Encyclopedia.com (Kenneth par. 5).

Gauss passed away in 1855 at the age of 77. He left much of his work unpublished, which was discovered after his death. When it was shared, it made a name for him for the end of the 1800s. From, most of the published works were in Latin, which was one of the many languages that Gauss knew, as well as French and Russian. He officially published 150 works. Gauss was awarded on many notations – he was appointed a Geheimrat – a privy councillor and was also featured on the 10 Deutsche Mark currency note, according to Jeremy John Gray (Gray par. 4). Gauss was also appointed as a foreign member of the Royal Society of London in 1801, and in 1838 he won the Copley medal, as mentioned in a few sources, such as the Famous Scientists page as well as by Riami in his presentation. Within the University of Göttingen, a statue has been erected of Gauss and Weber and is on the view (“Gauss Page”).

Gauss’ contributions to the field of mathematics, physics, and astronomy are fundamental and have paved the way for many other mathematicians, astronomers, and physicists to develop their theorems. It was Gauss who discovered the bell curve and Gaussian error curve (which has been named after him). He is usually named the most influential mathematician of a century.

Works Cited

“Carl Friedrich Gauss.” Bio. A&E Television Networks , 2015. Web.

“Carl Friedrich Gauss.” Famous Scientists , n.d. Web. 2015.

“Gauss, Carl Friedrich.” Complete Dictionary of Scientific Biography. Encyclopedia.com, 2008. Web.

Kenneth, O. May . “Gauss, Carl Friedrich.” . Encyclopedia.com., 2008. Web.

“Gauss Page.” Gauss Page , n.d. Web. 2015.

Gray, Jeremy John. “ Carl Friedrich Gauss Biography – German Mathematician .” Encyclopedia Britannica Online, 2014. Web.

“Karl Friedrich Gauss Biography.” Encyclopaedia of World Biography Online . Encyclopaedia of World Biography, n.d. Web. 2015.

Raimi, S. “Johann Carl Friedrich Gauss.” Prezi.com , 2012. Web.

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1. IvyPanda . "Carl Friedrich Gauss: The Greatest Mathematician." June 1, 2022. https://ivypanda.com/essays/carl-friedrich-gauss-biography/.

Bibliography

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Essays and thoughts on mathematics

Many distinguished mathematicians, at some point of their career, collected their thoughts on mathematics (its aesthetic, purposes, methods, etc .) and on the work of a mathematician in written form.

For instance:

• W. Thurston wrote the lovely essay On proof and progress in mathematics in response to an article by Jaffe and Quinn ; some points made there are also presented in an answer given on MathOverflow ( What's a mathematician to do? ).
• More recently, T. Tao shared some personal thoughts and opinions on what makes "good quality mathematics" in What is good mathematics? .
• G. Hardy wrote the famous little book A Mathematician's Apology , which influenced, at least to some extent, several generations of mathematicians.

Personally, I've been greatly inspired by the two writings listed under (1.) -- they are one of the main reasons why I started studying mathematics -- and, considering that one of them appeared on MathOverflow , I'd like to propose here -- if it is appropriate -- to create a " big-list " of the kind of works described in the above blockquote.

I'd suggest (again, if it is appropriate) to give one title (or link) per answer with a short summary.

• A related question, which I've found very interesting, is Good papers/books/essays about the thought process behind mathematical research .
• Only slightly related (but surely interesting): Which mathematicians have influenced you the most?
• A single paper everyone should read? is not quite related, but still somewhat relevant (especially the most up-voted answer).
• reference-request
• soft-question
• 1 $\begingroup$ Hardy's apology is available here: math.ualberta.ca/~mss/misc/A%20Mathematician%27s%20Apology.pdf $\endgroup$ –  Goldstern Oct 5, 2015 at 15:33
• $\begingroup$ This seems a little broad--can you be a bit more specific? I gave one answer, but do you want things like Dyson's "Birds and Frogs" or Gower's "Two cultures"? $\endgroup$ –  Kimball Oct 5, 2015 at 22:29
• $\begingroup$ @Kimball, first of all, thanks for your answer, the book you suggested seems very interesting. Then, yes, I've read both those articles and, although they didn't come to my mind when I asked the question, they are surely two very insightful additions to this list. Thanks again. :) $\endgroup$ –  user81051 Oct 6, 2015 at 18:12

22 Answers 22

There are many snippets that can be found. I like the following bit of the foreword by Thurston to J. H. Hubbard's Teichmüller Theory . I share the remarks because I think you simply can't have enough of Bill Thurston's insights:

"Mathematics is a paradoxical, elusive subject, with the habit of appearing clear and straightforward, then zooming away and leaving us stranded in a blank haze. Why? It is easy to forget that mathematics is primarily a tool for human thought. Mathematical thought is far better defined and far more logical than everyday thought, and people can be fooled into thinking of mathematics as logical, formal, symbolic reasoning. But this is far from reality. Logic, formalization, and symbols can be very powerful tools for humans to use, but we are actually very poor at purely formal reasoning; computers are far better at formal computation and formal reasoning, but humans are far better mathematicians. The most important thing about mathematics is how it resides in the human brain. Mathematics is not something we sense directly: it lives in our imagination and we sense it only indirectly. The choices of how it flows in our brains are not standard and automatic, and can be very sensitive to cues and context. Our minds depend on many interconnected special-purpose but powerful modules. We allocate everyday tasks to these various modules instinctively and subconsciously. The term `geometry', for instance, refers to a pattern of processing within our brains related to our spatial and visual senses, more than it refers to a separate content area of mathematics. One illustration of this is the concept of correlation between two measurements on a set, which is formally nearly identical with the concept of cosine of the angle between two vectors. The content is almost the same (for correlation, you first project to a hyperplane before measuring the cosine of the angle), but the human psychology is very different. Each mode of thinking has its own power, and ideally, people harness both modes of thought to work together. However, in formalized expositions, this psychological > difference vanishes. In the same way, any idea in mathematics can be thought about in many different ways, with competing advantages. When mathematics is explained, formalized and written down, there is a strong tendency to favor symbolic modes of thought at the expense of everything else, because symbols are easier to write and more standardized than other modes of reasoning. But when mathematics loses its connection to our minds, it dissolves into a haze. I've loved to read all my life. I went to New College of Sarasota, Florida, a small college that was just starting up with a strong emphasis on independent study, so I ended up learning a good deal of mathematics by reading mathematics books. At that time, I prided myself in reading quickly. I was really amazed by my first encounters with serious mathematics textbooks. I was very interested and impressed by the quality of the reasoning, but it was quite hard to stay alert and focused. After a few experiences of reading a few pages only to discover that I really had no idea what I'd just read, I learned to drink lots of coffee, slow way down, and accept that I needed to read these books at 1/10th or 1/50th standard reading speed, pay attention to every single word and backtrack to look up all the obscure numbers of equations and theorems in order to follow the arguments. Even so, when something was ``left to the reader'', I generally left it as well. At the time, I could appreciate that the mathematics was an impressive intellectual edifice, and I could follow the steps of proofs. I assumed that such an elaborate buildup must be leading to a fantastic denouement, which I eagerly awaited -- and waited, and waited. It was only much later, after much of the mathematics I had studied had come alive for me that I came to appreciate how ineffective and denatured the standard ((definition theorem proof)^n remark)^m style is for communicating mathematics. When I reread some of these early texts, I was stunned by how well their formalism and indirection hid the motivation, the intuition and the multiple ways to think about their subjects: they were unwelcoming to the full human mind. John Hubbard approaches mathematics with his whole mind. If you page through the current book, you will see many intriguing figures. That is a first sign: figures are one of the most important ways to keep our thought processes going in our whole brains, rather than settling down into the linguistic, symbol-handling areas. Of course, the figures in your imagination are even more important. Geometric ideas can be conveyed with words and with symbols, sometimes more effectively than with pictures, but a lack of figures is a good indication of a lack of geometry. Another important part of human thinking is the emotional aspect. In mathematics, what is intriguing, puzzling, interesting, surprising, boring, tedious, exciting is crucial; they are not incidental, they shape how we think. Personally, my thinking was shaped by boredom: I develop intense urges to come up with `easy' methods in order to avoid tedious computations that are opaque to me. Hubbard, a principal participant in the mathematics he is discussing, has done an excellent job in conveying the drama."

There are also many very good interviews that can be found, such as this one with Connes , as well as the advice to young mathematicians in the Princeton Companion to Mathematics .

A Mathematician's lament by Paul Lockhart: Reflections on how badly mathematics are taught these days. Imagining how it would be if music was taught the same way.

Indiscrete Thoughts by Gian-Carlo Rota and Discrete Thoughts by Kac, Rota, and Schwartz.

Proofs and Refutations: The Logic of Mathematical Discovery by Imre Lakatos: The sequence of steps through which mathematical ideas can be made to grow in an informal setting is explained through Socratic dialogues between a teacher and students. A beautiful read.

Since you mentioned A Mathematician's Apology : Michael Harris' Mathematics Without Apology .

Here's an excerpt explaining the title:

These attempts at justifications are the 'apologies' of the title. They usually take one of three forms. Pure research in mathematics as in other fields is good because it often leads to useful consequences (Steven Shapin calls this the Golden Goose argument); it is true because it offers a privileged access to certain truths; it is beautiful , an art form. To claim that these virtues are present in mathematics is not wrong, but it sheds little light on what is distinctively mathematical and even less about pure mathematicians' intentions . Intentions lie at the core of this book. I want to give the reader a sense of the mathematical life -- what it feels like to be a mathematician in a society of mathematicians where the first and second lives overlap.

Love and Math: The Heart of Hidden Reality by Edward Frenkel is, in my opinion, a lot better than Lockhart's lament.

The Mathematical Experience by Philip J. Davis and Reuben Hersh is a wonderful collection of essays on mathematics and on the experiences and culture of mathematicians. Written back in the 1980's, it has extremely insightful discussions of many of the same topics that nowadays are discussed on MO. For example, the essay "The Ideal Mathematician," which describes a hypothetical "ideal" mathematician working on the made-up area of "non-Riemannian hypersquares" is absolutely hilarious. Highly recommended!

• 1 $\begingroup$ The "Ideal Mathematician" is, to my mind, a poor mathematician. (It was a caricature, yes, but one which was a little too extreme for me.) $\endgroup$ –  Todd Trimble ♦ Oct 5, 2015 at 16:29
• 1 $\begingroup$ @ToddTrimble, I disliked it too. For myself, the more bearing what I'm working on has on undergraduate or even high-school mathematics, the more excited I am about it. $\endgroup$ –  goblin GONE Aug 23, 2016 at 14:55

Mathematics as Metaphor by Yuri Manin (both the title of the linked book which is a collection of essays, as well as the title of one particular essay in there). At least some of the essays you can find online.

I Want to be a Mathematician , by Paul Halmos.

• $\begingroup$ Indeed I love that book. Thanks for adding it. $\endgroup$ –  user81051 Oct 6, 2015 at 18:13

Eugene Wigner: The Unreasonable Effectiveness of Mathematics in the Natural Sciences

The statement that the laws of nature are written in the language of mathematics was probably made three hundred years ago [It is attributed to Galileo]. It is now more true than ever before … Surely complex numbers are far from natural or simple and they cannot be suggested by physical observations. Furthermore, the use of complex numbers is close to being a necessity in the formulation of the laws of quantum mechanics. It is difficult to avoid the impression that a miracle confronts us here , quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind’s capacity to divine them. The closest explanation [for this mathematical universe] is Einstein’s statement that “the only physical theories which we are willing to accept are the beautiful ones” … the concepts of mathematics have this quality of beauty.

• 2 $\begingroup$ I have to disagree. Wigner's assertion that "mathematics is the science of skillful operations with concepts and rules invented just for this purpose" is the whole basis of his piece, and it doesn't have much to do with mathematics. The article is quasi-religious speculation based on this false premise. (The example that Wigner opens the article with is a case in point - he marvels at the appearance of $\sqrt{\pi}$ in the pdf for the normal distribution, as if this were magic. But probability theory was developed with very practical applications in mind.) $\endgroup$ –  Paul Levy May 23, 2017 at 9:31

A Drifter of Dadaist Persuasion by Matilde Marcolli, published in Art in the Life of Mathematicians (Edited by Anna Kepes Szemerédi) American Mathematical Society, 2015, pp.210-231

The Psychology of Invention in the Mathematical Field (Jacques Hadamard's 1945 essay)

• $\begingroup$ This book was very influential to me, and made a huge difference in helping me understand m own process of doing mathematics. $\endgroup$ –  Zach H Jul 17, 2017 at 17:13
• $\begingroup$ I love "the Poincare-Hadamard metaphor" described there! It says that our thoughts conscious and unconscious ones and their interactions could be explained via a mechanical model of states of a system of particles(the details inside). Very inspiring and still I haven't found an enough obstruction to the presented point of view there to the modern neuroscience, but I do not know much about it. An expertise needed! :) $\endgroup$ –  P. Grabowski Apr 14, 2020 at 18:42

The Mathematician by John Von Neumannn.

Enigmas of Chance , by Mark Kac.

I would add "Letters to a Young Mathematician" by Ian Stewart

I recommend:

Vladimir Arnold: Yesterday and Long Ago . This is a very enjoyable and highly interesting collection of anecdotes and historical remarks. The latest Russian edition of this book contains some more chapters. Richard Hamming: You and Your Research , transcribed and edited by J F Kaiser, reprinted in Tveito et al: Simula Research Laboratory . This is the text of a lecture of Hamming.

Birth of a Theorem , by French candidate for Parliament Cédric Villani

• 4 $\begingroup$ Now French member of Parliament Cédric Villani. $\endgroup$ –  Michael Lugo Jul 17, 2017 at 15:16

Here are additional mathematicians' thoughts.

S. Ulam, Adventures of a mathematician .A recollection of his life, from Lwow to Los Alamos. I am linking to excerpts. The book is still available for purchase.

Advices to a Young mathematician , a collection of advice and anecdotes by M. Atiyah, B. Bollobas, A. Connes, D. McDuff and P. Sarnak.

A. Borel, Art and science (Math. Intelligencer vol.5 1983, translation from German). A text for a general audience about the relationship between art and mathematics.

R. P. Langlands Is there beauty in mathematical theories? , this text is actually about number theory, old and new.

T. Gowers The two cultures of mathematics , another take on the dichotomy between problem solving and theory building.

A. Connes A view of mathematics , a thorough exposition of A. Connes'philosophical stance about space and physics. Targeted at a scientific audience.

D. Mumford, the dawning of the age of stochasticity , from algebraic geometry to statistics.

Y. Manin, Interrelations between Mathematics and Physics , on the divergence between mathematics and physics in the XXe century.

M. Gromov, ergobrain , one of the most surprising inquiry about life and mathematics.

I end that list with a text from a french mathematician about the future of mathematics: Poincare, l'avenir des mathematiques .

Perhaps a little broader in range/scope than the original question intended — but then again, perhaps not — the essays collected in

Mathématiques, mathematiciens et société. Publications Mathématiques d'Orsay no. 86 74-16 (1974)

I was led to this when someone somewhere posted a link to Vergne's Témoignage d'une mathématicienne , which is one of the essays in this volume, and — I must confess — is the only one I've read, although the other ones do look interesting

In the Princeton Companion to Mathematics , there is a section entitled Advice to a Young Mathematician (pdf), containing essays by Atiyah, Bollobás, Connes, McDuff and Sarnak.

A Mathematician's Miscellany (reprinted, with additional material, as Littlewood's Miscellany by CUP in 1986) is worthwhile reading.

Clifford Truesdell published a series of essays as An Idiot's Fugitive Essays on Science Methods, Criticism, Training, Circumstances (Springer, 1984), which sets out in a forthright manner the author's views on mathematics and science.

A really nice article by Andrei Toom about mathematical education, especially in the US, got recently mentioned in a comment to this question.

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Archimedes: The Greatest Mathematician, Essay Example

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Introduction Archimedes worn born in Sicily, Italy (277BC-212BC ) and was arguably one of the greatest mathematicians that has ever lived. It is considered that during his youth he visited Alexandria in Egypt, a great centre of learning at that time,  here he studied with the successors of Euclid and during this period he invented the Archimedes Screw ( a type of pump); the pump still used in varying parts of the world today.

His main genius and contributions, however, were in the field of Mathematics.  The principal architect of what we know today as Pure Mathematics. His fascination with Geometry and his perfection with methods of integration enabled him to calculate volumes, surface areas and the masses of different bodies. Early works listed by Archimedes illustrated fragments that covered such mathematical areas as: polyhedra, measurements of a circle, plynths and cylinders, surfaces and irregular bodies, mechanics, catoptrics, sphere making and lengths in a year. [1]

The Works of Archimedes

There are a few surviving works (books) of Archimedes, these being: (1)  plane equilibriums (2 books); quadrature of the parabola, the sphere and cylinder (2 books); on spirals; on conoids, on floating bodies and measurements of a circle. A Professor J.L. Heiberg discovered in 1906 a further manuscript of Archimedes called the method.  This offered a valuable perspective on how Archimedes discovered many of his results.  (S. A. Paipetis 2010)[2]

Within the confines of the method it is possible to see the intricate working of how Archimedes developed integral calculus, based upon the theory of proportions by the insertion of polygons into an area that converge to a specific shape.

The Sand reckoner – One of the most remarkable pieces of mathematical genius from Archimedes.  He designed a system that would express numbers  8 X 10 63 and claimed that such a number would be large enough to count all the grains of sand that could be placed in the Universe.  A somewhat difficult concept to grasp considering we consider the Universe as infinite. [3]

Spirals –   The concept of a sphere being 4X that of a great circle, he calculates any segments of spheres and further that the surface of a sphere is 2/3rds of a circumscribed cylinder including the base. The work considers the measurement of three dimensional figures.

Floating Bodies – The concept in defining the principles of hydrostatics and the weight of a body immersed in liquid.  He examined the stability of different floating bodies according to different specific gravities. This including the determination of the exact value of ?.

Oddly enough the real genius of Archimedes work was not fully appreciated until after his death. It was Eutocius that brought many of his works into the light and it was not until the 6 th Century AD that full credit was made to the outstanding contribution to mathematics from Archimedes.  Many of his works found their way to the Great Library in Alexandria where they formed the basis of tuition for noted mathematical scholars like Heron, Pappus and Theon.

[1] Netz, Reviel. “The Works of Archimedes: The two books On the sphere and the Cylinder.” In The Works of Archimedes: The two books On the sphere and the Cylinder, by Reviel Netz, Eutocius (of Ascalon.) Archimedes, 12-13. Cambridge: University of Cambridge Press, 2005.

[2] S. A. Paipetis, Marco Ceccarelli. “The Genius of Archimedes – 23 Centuries of Influence on Mathematics .” In The Genius of Archimedes — 23 Centuries of Influence on Mathematics , by Marco Ceccarelli S. A. Paipetis, 380-381. New York: Springer, 2010.

[3] Tubbs, Robert. “What Is a Number?: Mathematical Concepts and Their Origins.” In What Is a Number?: Mathematical Concepts and Their Origins, by Robert Tubbs, 81. Baltimore: John Hopkins University Press, 2010.

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Famous Mathematicians

List and Biographies of Great Mathematicians

15 Famous Indian Mathematicians and Their Contributions

January 23, 2017 By admin

13. Bhāskara I Born in the district of Mysore, this small town lad grew up to be the shining star. His contributions are mainly his proof of the fact that zero stood for ‘nothing’(the idea initially introduced by Bhramagupta). He made many calculations to prove so; division, permutation and combination theories. He also proved how the earth appears to be flat even though it’s a sphere.

14. Bhaskara II Bhaskara II so called to avoid any confusion with the first. His work represented significant mathematical and astronomical knowledge. He is most known for his work in calculus and how it is applied to astronomical problems and computations. Not only did he deal with calculus but had vast knowledge over arithmetic, algebra, mathematics of planets and spheres.

15. Hemachandra His most significant contribution in mathematics was his initial version of the Fibonacci sequence. He was not only a mathematician but also a scholar, polymath, poet who wrote on grammar, philosophy and contemporary history. Therefore his contributions are not only restricted to math but over all the various different fields that he had mastered over.

The Best Writing on Mathematics 12

Mircea pitici,  series editor.

This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics makes mathematical writing available to a wide audience.

The year’s finest mathematical writing from around the world

The year's finest mathematical writing from around the world

The year's finest mathematics writing from around the world

The year's finest writing on mathematics from around the world

The year's finest writing on mathematics from around the world, with a foreword by Nobel Prize – winning physicist Roger Penrose

The year’s most memorable writing on mathematics

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T he period between 500 and 1200 AD was the golden age of Indian Astronomy. During this golden period an Indian wizard was born who contributed greatly to the conception of Astronomy and Mathematics. He was none other than Bhaskaracharya.

Bhaskaracharya was the leading mathematician and Astronomer of the 12th century, who wrote the first work with full and systematic use of the decimal number system. He was born near Vijjadavida (Bijapur in modern Karnataka). Bhaskaracharya’s name was actually ‘Bhaskara’ only but the title ‘Acharya’ was added and conferred to mean “Bhaskara the Teacher”. He is also known as Bhaskaracharya II.

Bhāskara and his works represent a significant contribution to mathematical and astronomical knowledge in the 12th century. He became head of the astronomical observatory at Ujjain, the leading mathematical centre in India at that time. Outstanding mathematicians such as  Varahamihira and Brahmagupta had worked there and built up a strong school of mathematical astronomy.

There are six well known works of Bhaskaracharya. They are :- Lilavathi – Mathematics, Bijaganita – Algebra, Ganitadhyaya – mathematical astronomy, Goladhyaya – sphere, Karanakutuhala – Calculation of Astronomical Wonders, Vasanabhasya – Bhaskara’s own commentary on the Siddhanta Shiromani, and Vivarana which is a commentary on the Shishyadhividdhidatantra of Mathematician and Astronomer Lalla .

Bhaskara was known not only for his mathematical scholarship, but also for his poetic inclinations. He wrote Lilawati in an excellent lucid and poetic language. It has been translated in various languages throughout the world. It was written for his daughter, Lilavati. The Lilavati deals with arithmetic and geometry; it is said that the name is after his daughter Lilavati, who was according to her horoscope to remain unmarried.

In his mathematical works, particularly Lilavati and Bijaganita, he not only used the decimal system but also compiled problems from Brahmagupta and others. He filled many of the gaps in Brahmagupta’s work, especially in obtaining a general solution to the Pell equation (x2 = 1 + py2) and in giving many particular solutions.

Bhaskara anticipated the modern convention of signs (minus by minus makes plus, minus by plus makes minus) and evidently was the first to gain some understanding of the meaning of division by zero. Bhaskara used letters to represent unknown quantities, much as in modern algebra, and solved indeterminate equations of 1st and 2nd degrees.

Brahmagupta was Bhaskara’s role model. To Brahmagupta he pays homage at the beginning of his Siddhanta Siromani. Using an astronomical model developed by Brahmagupta in the 7th century, Bhaskara accurately calculated the time that earth took to revolve around the Sun as 365.2588 days that is a difference of 3 minutes of modern acceptance of 365.2563 days.

Bhaskaracharya was the first to discover gravity , 500 years before Sir Isaac Newton. He is also known in the discovery of the principles of differential calculus and its application to astronomical problems and computations. Bhaskara’s work on calculus predates Newton and Leibniz by over half a millennium.

Bhaskara has given a very simple method to determine the circumference of the Earth. According to this method, first find out the distance between two places, which are on the same longitude. Then find the correct latitudes of those two places and difference between the latitudes. Knowing the distance between two latitudes, the distance that corresponds to 360 degrees can be easily found, which the circumference of the Earth.

He also showed that when a planet is farthest from, or closest to, the Sun, the difference between a planet’s actual position and its position according to the equation of the centre(which predicts planets’ positions on the assumption that planets move uniformly around the Sun) vanishes. He therefore concluded that for some intermediate position the differential of the equation of the centre is equal to zero.

Some other achievements of Bhaskaracharya were:

• The Earth is not flat, has no support and has a power of attraction.
• The north and south poles of the Earth experience six months of day and six months of night.
• One day of Moon is equivalent to 15 earth-days and one night is also equivalent to 15 earth-days.
• Bhaskaracharya had accurately calculated apparent orbital periods of the Sun and orbital periods of Mercury, Venus, and Mars. There is slight difference between the orbital periods he calculated for Jupiter and Saturn and the corresponding modern values.
• Earth’s atmosphere extends to 96 kilometers and has seven parts.
• There is a vacuum beyond the Earth’s atmosphere.

Bhaskaracharya, or Bhaskara II (1114 – 1185) is regarded almost without question as the greatest mathematician of all time and his contribution to not just Indian, but world mathematics is undeniable. He was perhaps the last and the greatest astronomer that India ever produced.

 Source:   Free Press Journal & Veda Wikidot

• Bhaskaracharya
• Brahmagupta
• mathematicians
• Mathematics
• Surya Siddhant

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Essay on Aryabhatta for Students and Children

500+ words essay on aryabhatta.

Essay on Arayabhatta – Aryabhatta was the first Indian mathematician and astronomer. He had immense knowledge in the field of mathematics. Moreover, he did he may discoveries during his era. For instance, some of them were the discovery of algebraic identities, trigonometrical functions, the value of pi, Place value system, etc.

Furthermore, he wrote many books which still help us in performing various calculations. Aryabhatta was a great influence to many youngsters. For he excelled in academics from a very early age. Moreover, he contributed much to the society his works and theories are still remembered and honored till date.

The Early Life of Aryabhatta

Aryabhatta was born in 475 A.D. Furthermore his birthplace eas not sure, but in his book the ‘Aryabhatiya’, he mentions that he was a native of Kusumapura the modern-day Patna. Moreover, from his historical records, the archaeologists believed that he continued his further studies in Kusumapura. Because in Kusumapura his major astronomical observatory was located.

Therefore, we can ascertain that Aryabhatta spent most of the time there. Further, some historians believe that he was also the head of Nalanda University in Kusumpura. Though these theories are all on a probable basis because no proper evidence was there except the books Arybhatta wrote in his lifetime. Yet some of his records were lost and are not found till date.

Work of Aryabhatta

Aryabhatta contributed greatly to the field of mathematics. For instance, he was responsible for discovering various trigonometrical functions which are useful for us in the modern era too.

Apart from his discoveries in the field of mathematics, Aryabhatta contributed immensely towards astronomy. He proposed the heliocentric theory which states the planets revolve around the Sun. with the help of this theory, he calculated the speed of the different planets with respect to the Sun.

Furthermore, he also calculated the sidereal rotation which is the rotation of the earth in reference to the stars. Moreover, he founded the sidereal year to be 365 days, 6 hours, 12 minutes and 30 seconds which varies with only 3 minutes and 20 seconds over the modern-day value.

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Contributions of Aryabhatta

Most noteworthy is that Aryabhatta correctly founded that the earth rotates on its axis. Furthermore, he also proposed the geocentric model of the solar system which described the earth to be the center of the universe. And the sun, the moon, and the planets revolve around it.

Aryabhata also explained the solar and lunar eclipses in his book. Consequently, he also proposed that the moon due to the reflection of the sunlight. He explained in his book that the lunar eclipse and the solar eclipse takes by the shadow-casting of the earth and the moon.

In conclusion Aryabhatta approximations in the field of astronomy were quite accurate. It provided the core to the computational paradigm which provides a base to the modern theories.

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