art of problem solving math competitions

The USA Mathematical Talent Search (USAMTS) is a free proof‑based math contest for US middle and high school students. Students receive written feedback on their work, and can earn prizes based on their performance.

Solve the Problems

Each round consists of 1 puzzle and 4 proof-based problems. The problems vary in difficulty, so there is something challenging yet approachable for everyone.

Write Your Solutions

Unlike most other contests, you’ll have over a month to solve the problems and write up your solutions. You’re also allowed to consult certain reference material.

Get Feedback

Our graders not only give you a score, but also personalized written feedback to help you develop your mathematical and writing skills.

At the end of the year, the top 45% of students will receive prizes, including math books and T-shirts. Prizes may include Wolfram software subscriptions as well. The USAMTS is also one way to qualify for the American Invitational Mathematics Examination (AIME).

Interested? Join our mailing list to receive updates about the USAMTS, such as announcements that problems are available or that scores have been released. To compete, register today! Students can register any time during the year, even if the first round has already completed.

About the Art of Problem Solving Initiative

Founded in 2004, the Art of Problem Solving Initiative, Inc. was created by people who love math and love teaching to help students access the study of advanced mathematics.

The Initiative began by running the USA Mathematical Talent Search , a nationwide math contest sponsored by the National Security Agency which continues to run to this day. In each round, this contest gives students a full month to work on five challenging proof-based problems. Students then get individual feedback on their work, including comments on their mathematical reasoning and on their proof-writing skills. By taking away the usual time pressures seen in many math contests, students have the opportunity to go more deeply and to explore.

For many years, the Initiative also ran the Local Programs Initiative which provided fiscal sponsorship to math circles and clubs across the country.

Now, the main project of the Initiative is Bridge to Enter Advanced Mathematics (BEAM) , a project to help underserved students find a realistic pathway towards becoming scientists, mathematicians, engineers, and programmers. During the summer after 7th grade, students are invited to participate in a free three-week residential program on a college campus where they gain the academic and social/emotional preparation to succeed in future programs for advanced study. They then receive academic advising throughout 8th grade and high school to help them and their families find the best opportunities for their educations.

The Art of Problem Solving Initiative receives support from Art of Problem Solving (AoPS) , which develops resources for high-performing middle and high school students including the largest online community of avid math students in the English-speaking world. The AoPS online school has trained many winners of major national mathematics competitions, including several gold medalists at the International Math Olympiad, Davidson Fellows, and winners of the Intel and Siemens Talent Search competitions.

The Art of Problem Solving Initiative is a 501(c)(3) charitable organization. It continues to be led by expert mathematicians and educators to this day. Please consider joining our contributors by donating to support advanced math education.

Financial Information

The Art of Problem Solving Initiative, Inc. makes its financial statements available for public inspection in the interest of greater transparency. Please see below to learn more about the organization.

• Tax return (Form 990)
• Audited financial statements
• Tax return (Form 990) (Note that due to a change in fiscal year these cover a shortened period.)

Contest Math 6A and Contest Math 6B together offer a full year of contest preparation to help students succeed at top middle school math contests. It is the first level of our middle school contest series.

Live instructors build the prealgebra fundamentals for students and prepare them to face challenges at national math contests, like MATHCOUNTS and the MAA AMC 8.

View the course syllabus for full class information and a list of topics.

Students who complete Contest Math 6A are ready for Contest Math 6B. Similar to Honors Math 6: Prealgebra, this course takes conceptual understanding to the next level — while also integrating a special focus on highly challenging problems and practice contests for students who want to participate in math competitions.

To determine if your student is ready for this course or others at the Virtual Campus, learn more here .

Our expert instructors use the Art of Problem Solving curriculum to teach Contest Math 6: Prealgebra. AoPS curriculum is a much broader and deeper exploration of challenging mathematics than a typical math curriculum.

This course will require both the Prealgebra and Competition Math for Middle School textbooks.

Contest Math 6A Prealgebra starts by formalizing the rules of arithmetic that students learned in elementary school. Students are then introduced to the topics of number theory and algebra, including common divisors and multiples, primes and prime factorizations, basic equations and inequalities, and ratios. Students are further challenged by contest problems that incorporate multiple concepts and skills, and sometimes require out-of-the-box thinking.

Contest Math 6B ‍‍Students study percents and square roots, dive into geometric tools and strategies, and are introduced to discrete mathematics and statistics — all while continuing to develop their general problem-solving strategies and capacity to untangle complicated problems often seen in math contests.

Our instructors hold classes virtually, in a small-sized (10-16 students) videoconferencing classroom.

There are about 1 to 3 hours of homework each week. There is one timed final exam at the end of the course.

Visit our tuition page to learn more about our drop and refund policies.

Each course runs for 18 weeks and offers two timing formats. Both cover the same course material.

• One 105-minute lesson per week, or
• Two 55-minute lessons per week

THIS SUMMER - Accelerated Contest Math 6B, offering a 9 week session covering the same material as the other class formats. Look for class ID 25017 to enroll.

• Two 105-minute lessons per week

How two high school students solved a 2,000-year-old math puzzle

A high school math teacher at St. Mary's Academy in New Orleans, Michelle Blouin Williams, was looking for ingenuity when she and her colleagues set a school-wide math contest with a challenging bonus question. That bonus question asked students to create a new proof for the Pythagorean Theorem, a fundamental principle of geometry, using trigonometry. The teachers weren't necessarily expecting anyone to solve it, as proofs of the Pythagorean Theorem using trigonometry were believed to be impossible for nearly 2,000 years.

But then, in December 2022, Calcea Johnson and Ne'Kiya Jackson, seniors at St. Mary's Academy, stepped up to the challenge. The $500 prize money was a motivating factor.

After months of work, they submitted their innovative proofs to their teachers. With the contest behind them, their teachers encouraged the students to present at a mathematics conference, and then to seek to publish their work. And even today, they're not done. Now in college, they've been working on further proofs of the Pythagorean Theorem and believe they have found five more proofs. Amazingly, despite their impressive achievements, they insist they're not math geniuses.

"I think that's a stretch," Calcea said.

The St. Mary's math contest

When the pair started working on the math contest they were familiar with the Pythagorean Theorem's equation: A² + B² = C², which explains that by knowing the length of two sides of a right triangle, it's possible to figure out the length of the third side.

When Calcea and Ne'Kiya set out to create a new Pythagorean Theorem proof, they didn't know that for thousands of years, one using trigonometry was thought to be impossible.  In 2009, mathematician Jason Zimba submitted one, and now Calcea and Ne'Kiya are adding to the canon.

Calcea and Ne'Kiya had studied geometry and some trigonometry when they started working on their proofs, but said they didn't feel math was easy. As the contest went on, they spent almost all their free time developing their ideas.

"The garbage can was full of papers, which she would, you know, work out the problems and if that didn't work, she would ball it up, throw it in the trash," Cal Johnson, Calcea's dad, said.

Neliska Jackson, Ne'Kiya's mother, says lightheartedly, that most of the time, her daughter's work was beyond her. 

To document Calcea and Ne'Kiya's work, math teachers at St. Mary's submitted their proofs to an American Mathematical Society conference in Atlanta in March 2023.

"Well, our teacher approached us and was like, 'Hey, you might be able to actually present this,'" Ne'Kiya said. "I was like, 'Are you joking?' But she wasn't. So we went. I got up there. We presented and it went well, and it blew up."

Why Calcea' and Ne'kiya's work "blew up"

The reaction was insane and unexpected, Calcea said. News of their accomplishment spread around the world. The pair got a write-up in South Korea and a shoutout from former first lady Michelle Obama. They got a commendation from the governor and keys to the city of New Orleans. 

Calcea and Ne'Kiya said they think there's several reasons why people found their work so impressive. 

"Probably because we're African American, one," Ne'Kiya said. "And we're also women. So I think-- oh, and our age. Of course our ages probably played a big part."

Ne'Kiya said she'd like their accomplishment to be celebrated for what it is: "a great mathematical achievement."

In spite of the community's celebration of the students' work, St. Mary's Academy president and interim principal Pamela Rogers said that with recognition came racist calls and comments. 

"[People said] 'they could not have done it. African Americans don't have the brains to do it.' Of course, we sheltered our girls from that," Rogers said. "But we absolutely did not expect it to come in the volume that it came."

Rogers said too often society has a vision of who can be successful.

"To some people, it is not always an African American female," Rogers said. "And to us, it's always an African American female."

Success at St. Marys 

St. Mary's, a private Catholic elementary and high school, was started for young Black women just after the Civil War. Ne'Kiya and Calcea follow a long line of barrier-breaking graduates. Leah Chase , the late queen of Creole cuisine, was an alum. So was Michelle Woodfork, the first African American female New Orleans police chief, and Dana Douglas, a judge for the Fifth Circuit Court of Appeals. 

Math teacher Michelle Blouin Williams, who initiated the math contest, said Calcea and Ne'Kiya are typical St. Mary's students. She said if they're "unicorns," then every student who's matriculated through the school is a "beautiful, Black unicorn."

Students hear that message from the moment they walk in the door, Rogers said. 

"We believe all students can succeed, all students can learn," the principal said. "It does not matter the environment that you live in."

About half the students at St. Mary's get scholarships, subsidized by fundraising to defray the $8,000 a year tuition. There's no test to get in, but expectations are high and rules are strict: cellphones are not allowed and modest skirts and hair in its natural color are required. 

Students said they appreciate the rules and rigor.

"Especially the standards that they set for us," junior Rayah Siddiq said. "They're very high. And I don't think that's ever going to change." 

What's next for Ne'Kiya and Calcea

Last year when Ne'Kiya and Calcea graduated, all their classmates were accepted into college and received scholarship offers. The school has had a 100% graduation rate and a 100% college acceptance rate for 17 years, according to Rogers.

Ne'Kiya got a full ride in the pharmacy department at Xavier University in New Orleans. Calcea, the class valedictorian, is studying environmental engineering at Louisiana State University. Neither one is pursuing a career in math, though Calcea said she may minor in math.

"People might expect too much out of me if I become a mathematician," Ne'Kiya said wryly. 

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Art of Problem Solving: Competition Math for Middle School Paperback – January 1, 2011

• Language English
• Publisher Aops Inc.
• Publication date January 1, 2011
• ISBN-10 1934124206
• ISBN-13 978-1934124208
• See all details

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Product details

• Publisher ‏ : ‎ Aops Inc. (January 1, 2011)
• Language ‏ : ‎ English
• ISBN-10 ‏ : ‎ 1934124206
• ISBN-13 ‏ : ‎ 978-1934124208
• Item Weight ‏ : ‎ 1.2 pounds
• Best Sellers Rank: #387,792 in Books ( See Top 100 in Books )

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• Mathematics competitions

Mathematics competitions are contests that typically challenge top mathematics students to solve problems more difficult than those typically tested by standardized tests or in the classroom.

Math competitions differ widely in difficulty and content. Most test a broader range of mathematics curriculum and some focus on methods of mathematical problem solving .

See the list of mathematics competitions for details about local, national, and international mathematics contests.

• New competitions in P2P
• Resources for mathematics competitions
• Academic competitions
• AoPS Competitions

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10 Best Math AI Solvers to Solve Math Problems Online

Tackling challenging math problems can be a time-consuming endeavor. Math AI solvers make learning math simple. These AI-powered tools use machine learning and advanced algorithms to rapidly analyze math problems at all grade levels. Whether you’re a high school student or at the college level, an AI math problem solver can help save you time, ensure accuracy, and boost your school success.

With 24/7 convenience, they can be used anytime to get instant help with confusing math problems. When curating our list of top 10 best math AI solvers, we looked at several important factors, such as pricing, features, strengths, and weaknesses. Let’s explore these tools and learn in which areas they excel:

Mathful – Best Overall Math AI Solver to Solve Math Problems

Mathful is a valuable AI math solver often used by students to get help with complicated math problems. It delivers step-by-step guidance that breaks down the problem to make it easier to digest. The tool also provides the final answer to allow students to verify their solutions and gain confidence in their math skills.

Mathful is available 24/7, making it a convenient tool for students to get instant help with their math homework. Mathful acts as the ultimate solution for boosting academic success at all math levels. 

• Helps students gain a deeper understanding of math concepts with step-by-step guidance.
• Serves as a verification tool where students can check their work without costing a dime. 
• Enables students to complete their math homework with just one click. 
• Cannot be used to supplement a real classroom education. 

Solve Math Problems Instantly with Mathful’s AI Math Solver >>>

AI Math – Best AI Math Solver for All Grade Levels

AI Math is an innovative math AI solver designed to solve a wide range of mathematical problems, ranging from basic math concepts to more challenging equations. 

The way this unique tool works is by analyzing the math problem, finding potential solutions, validating those solutions, and returning the best possible results for the given problem.

While some math AI tools are only capable of solving basic math problems, AI Math is more diverse. Use it to solve math problems at all grade levels, from elementary to university and beyond. AI Math is trained on an extensive database of mathematical information and can guarantee 98% accuracy.

• Generates solutions to math problems with a high rate of accuracy.
• Designed to provide almost instant results for efficiency. 
• Covers all types of math and homework at all grade levels. 
• Requires a subscription after the initial trial period.

HIX Tutor – Best AI Math Solver for High Accuracy

HIX Tutor provides students with the solutions they need to understand and solve their math problems. 

With this powerful math solver AI tool, users can type in a math question or upload a document or image of the question. Using this input, Math AI Solver uses machine learning technology to perform dynamic calculations and give users the correct answer. 

HIX Tutor can provide solutions for math homework problems at all levels with a 98% accuracy rate. However, the tool goes beyond mere problem-solving by offering comprehensive calculations on how to solve the problem from start to finish. 

• Provides step-by-step solutions to math problems.
• Is less expensive than hiring a math tutor.
• Can type in math questions or upload documents or images of the problem.
• May have difficulty recognizing documents with messy handwriting.

HomeworkAI – Best All-in-One Solution for Homework Help

HomeworkAI is the ultimate homework assistant that can be used to get answers to any homework question, from math and science to history and geography. Its math AI solver acts as your personal AI tutor by providing comprehensive solutions to math problems that help students better understand the material.

This unique AI tool is available 24/7, making it a convenient and accessible resource for students who need immediate help with their homework. As the tool is free to try, students can get started right away by asking a math question that they’re struggling with. HomeworkAI can also help students prepare for important tests or exams by providing step-by-step instructions on how to work through certain math questions.

• Covers all school subjects, including math.
• Provides step-by-step explanations for each math problem.
• Supports multiple math problem input methods. 
• Some math solutions may be difficult to understand. 

Question AI – Best Homework AI Tool for Greater Academic Success

Question AI is a leading homework helper that uses powerful AI technology to instantly help with any school subject. Question AI is often used for any math problems, covering algebra, geometry, calculus, arithmetic, and trigonometry. Students often waste hours struggling with challenging homework questions they simply don’t understand. Question AI simplifies the homework process by breaking down the question to make it easier to learn. The math AI solver also promises a 99% accurate answer to the math question, allowing students to verify their own work.

Question AI serves as an innovative all-in-one product for AI homework help. It is a highly effective tool for helping students reach greater academic achievement.

• Covers all homework subjects, including all branches of mathematics. 
• Boosts student grades.
• Supports many different languages.
• Accuracy may be limited beyond core math subjects.
• The mobile app is not yet available. 
• Costs money after the free trial. 

QuickMath – Best Math AI Solver for High School and College Students

QuickMath is designed to automatically answer common math problems in algebra, calculus, and equations. The tool offers several options for solving math problems, including solving an equation, inequality, or a system. It can also simplify an expression, factor an expression, or expand a product or power. The diverse AI math solver can also graph, find the greatest common factor, and the least common measure. Advanced math solvers are also available for more complex math problems.

QuickMath is geared toward high school and college-level students. The tool’s features and capabilities are always being improved to ensure that users have access to the most comprehensive AI math tools available. 

• Offers a wide range of standard and advanced math solvers.
• Available to download on the App Store and Google Play.
• Quick-solve tutorials are available to help users learn math concepts. 
• Math problems must be typed in and cannot be uploaded. 
• Not suitable for grade levels lower than high school.
• Some users may receive Timeout messages due to 15-second CPU time rules.

Smodin – Best AI Math Solver for Acing Math Exams

Smodin Math AI Homework Solver offers a fast and effective way to prepare for difficult math exams. The versatile homework helper uses machine learning and advanced algorithms to help students learn core math concepts and boost their grades in school. Simply input a question or assignment and Smodin instantly generates step-by-step solutions.  The math solver AI tool consists of a simple interface that allows students to enter a question to solve. At the click of a button, the tool starts working to analyze the problem and present the best answer based on the equation. 

While Smodin Math AI Homework Solver does lack advanced features and capabilities, it can be a useful tool for students who want to study before a big math test.

• Provides in-depth answers to math questions to help students ace math exams.
• Users are given 3 free credits a day to ask math questions. 
• The clean interface makes it easy to enter math questions to solve. 
• Offers no advanced math features or capabilities.
• Users must pay for a subscription after reaching the daily credit limit. 

StudyMonkey – Best AI Math Problem Solver for Personalized Learning

StudyMonkey is a diverse homework helper for students that uses complex machine learning capabilities to provide step-by-step guidance on many school subjects, including math.  The innovative math AI solver can be used by learners of all backgrounds and ages to improve their understanding of math concepts and enhance their academic success. With round-the-clock availability, this unique tool can save students significant time when completing homework assignments.

• Students can personalize their output based on the subject and grade level. 
• There is a free plan for users that only requires occasional homework help.
• Users can see a history of past questions and answers. 
• Users must purchase a paid plan to ask more than 3 questions daily.
• Answers to more complex math questions may not be as accurate. 
• Must upgrade to the $8 plan to use the Advanced AI Model. 

Interactive Mathematics – Best Math AI Tool for Solving Word Problems

Interactive Mathematics claims to be more accurate than ChatGPT, faster than a math tutor, and more powerful than a math calculator. The advanced AI math problem solver has been trained in a wide array of math subjects, such as basic algebra, advanced algebra, trigonometry, geometry, calculus, advanced calculus, physics, and more. It is also highly effective at solving math word problems with step-by-step solutions. 

With Interactive Mathematics, users can type in their math problems or copy and paste a photo. The tool then analyzes the problem and delivers near-instant results. 

• Efficient at solving math word problems.
• Optimized for mobile phones and tablet use.
• A subscription comes with additional discounts and bonuses. 
• Users can only ask 3 questions before having to upgrade to the paid version. 
• No app is yet available. 
• Pushes tutoring services when the tool is unable to give an accurate answer. 

SnapXam – Best AI Math Solver for On-the-Go

SnapXam is an AI-powered math tutor that can help students better understand different types of math, from calculus to trigonometry.  After entering the math problem, the tool quickly presents the final answer, as well as a step-by-step solution that shows how to work out the problem.

The unique AI math problem solver also provides access to informative YouTube videos that students can watch to learn more about different concepts in math. 

Upgrading to a Premium account can give students access to even more features and perks, including no ads, support for more than 100 math topics, and premium access to the iOS and Android apps.

• Students can get AI math help with only access to a smartphone. 
• Offers multiple solving methods.
• Covers more than 100 different math topics. 
• An ad-free environment is only available with the premium version.
• Geared toward older students. 
• Accuracy issues may occur with advanced math problems.

Completing math assignments can be a long and tedious process. Having access to the best math AI tools can help eliminate the stress and frustration that come with not understanding math problems. For convenience, efficiency, and unmatched accuracy, try some of the top math AI tools like Mathful for free today!

This is a guest post, created for informational purposes only, and should not be considered as professional advice. Readers are encouraged to conduct their own research and consult with relevant experts before making any financial or investment decisions.

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