USA Mathematical Talent Search (USAMTS): A Complete Guide

If you’re a problem-solving junkie who loves sitting with a tough question until it clicks, the USA Mathematical Talent Search (USAMTS) will feel like home. Think thoughtful, take-home problems, careful proofs, and a chance to measure your skills against top students across the country without the pressure of a stopwatch.

This guide is your all-in-one playbook for USAMTS. We’ll cover what USAMTS is, how awards work, who’s eligible, how to register and submit solutions, and practical strategies for writing winning proofs. If you’re wondering when the current cycle runs, how scoring works, or what past top performers did well, you’ll find it here.

• What Is USAMTS?
• USAMTS Awards and Prizes
• How to Qualify for USAMTS
• How to Compete in USAMTS
• How to Win USAMTS
• USAMTS Previous Winners
• Frequently Asked Questions
• Takeaways

What Is USAMTS?

The USA Mathematical Talent Search (USAMTS) is a national, proof-based mathematics competition open to all U.S. middle and high school students who have not yet completed high school.

Unlike timed, in-person exams, USAMTS gives participants several weeks to work on each round’s problems. Each round consists of five problems—one puzzle and four proof-based questions—and allows the use of books, calculators, or online resources, as long as all reasoning and writing are entirely the student’s own.

Round 1 problems for the 2025–2026 cycle have already been released, with a submission deadline of October 7, 2025, at 10 p.m. Eastern (7 p.m. Pacific). Problems are available on the USAMTS website, and participants can submit their solutions either online (preferred) or by mail, as long as they are postmarked by the deadline.

After submission, volunteer graders review each solution and provide individualized feedback to help participants improve for later rounds.

In essence, USAMTS focuses not on speed but on depth of thought, clarity, and creativity. It’s a contest that rewards patience and precision, offering students the chance to engage deeply with mathematics over time and grow through detailed feedback after every round.

USAMTS Awards and Prizes

At USAMTS, recognition goes to a wide swath of high-performing students, not just for the top few. Roughly the top 45% of participants receive awards, up to a cap of 500 prize recipients. Prizes typically include mathematical books, software subscriptions, and a USAMTS-themed T-shirt. Higher-tier recipients also get priority in selecting their prize books.

The table below summarizes the four main prize categories and what recipients typically receive:

All prize winners also receive a free one-year subscription to Wolfram software and a USAMTS T-shirt featuring one of that year’s official problems.

In addition to tangible prizes, strong performance at USAMTS can open doors to other major math competitions. Students who score 68 points or higher (out of 75) automatically qualify for the AIME, while top scorers may also receive direct invitations to the USA(J)MO through coordination with the MAA.

How to Qualify for USAMTS

You do not need to win a regional contest or be selected by a team to take part in USAMTS. The competition is open to all students who meet the basic requirements and are ready to take on its proof-based challenges. Below is a detailed breakdown of who can join and what you’ll need to prepare before participating.

Eligibility

To join USAMTS, you must:

• Be a U.S. citizen or U.S. resident. Students living abroad may still compete as long as they provide a U.S. mailing address for prize delivery.
• Not have completed high school by the time of participation. The contest is open to only middle and high school students.
• Be able to write mathematical proofs independently. There is no minimum grade requirement, so younger participants with sufficient skills are welcome.

Registration and account setup

Once you meet the eligibility requirements, the next step is to register through the official USAMTS website. Here’s what the process involves:

• Create or log in to your USAMTS account. Returning competitors can reuse their old accounts, but it is important to check that all details are updated.
• Fill out the registration form with your full name, U.S. mailing address, current grade level, and email address.
• Registration is completely free, and there are no fees to enter or participate in any round of the competition.

Contest structure and participation

After registering, participants are automatically eligible for all future rounds of the current competition year. The contest is designed to measure mathematical creativity and reasoning across multiple problem sets.

• The USAMTS consists of three rounds each year, with five problems per round.
• You can join the contest even after Round 1. Participants who start later can still compete in Rounds 2 and 3, though they will not earn points for missed rounds.
• All problems are posted directly on the official website, and participants can choose to submit their work either online or by mail.

Permitted and restricted resources

USAMTS encourages independent exploration, but participants must adhere to its rules on resource use.

Here’s what you can and cannot do during a round:

• You may use books, journal articles, and reputable online materials to study or confirm mathematical principles.
• You may not ask for live help from anyone, including teachers, tutors, or online forums, while a round is active.
• You may reference standard theorems such as the Pigeonhole Principle, but less common results must either be proved in your solution or properly cited from a credible source.
• You may use software tools such as Mathematica or Python, provided you include all code, input, and output in your solution for verification.
• You may use AI tools for background learning, but not for generating or checking specific problem solutions.

Submission requirements

USAMTS math problems require detailed written solutions that demonstrate clear reasoning. To ensure your work is accepted, follow these submission guidelines:

• Submit solutions online through the official platform or by mail, postmarked by the deadline.
• Online submissions must be a single PDF file that includes your name, username, USAMTS ID, round number, and problem number on every page.
• Start each problem on a new page to keep your work organized.
• Participants can resubmit updated files before the deadline if they make revisions.
• Each problem is graded on a 0 to 5 scale, based on accuracy, completeness, and clarity.
• After grading, participants receive individualized feedback and comments from the judging team.
• If you believe there was a mistake in grading, you may file a protest request for re-evaluation.

Rule clarifications and extensions

Occasionally, special circumstances or questions about the problems may arise. In these cases, USAMTS allows for limited exceptions and official clarifications.

• You may request a 24-hour extension once per contest year in case of emergencies.
• If you believe a problem is unclear, you can contact the organizers. Any clarification deemed necessary will be announced publicly to all participants.
• The contest director reserves the right to issue new clarifications or procedural adjustments to maintain fairness.
• Any violation of the contest’s honor code, such as plagiarism or unauthorized assistance, may result in disqualification or a reduction in score.

How to Compete in USAMTS

Getting started with USAMTS is simple but requires attention to detail. Below is a clear, step-by-step guide to help you complete each stage, from registration to submission.

1. Register or sign in.

Begin by creating an account on the official USAMTS website. Returning participants can log in using their existing credentials and update their information for the new contest year. Make sure your contact details are accurate, as all contest updates and feedback are sent through your USAMTS account.

2. Access and solve the problems.

When a round opens, five proof-based problems will appear on your dashboard. You’ll have several weeks to solve them, giving you time to explore ideas and refine your reasoning. You can use resources for reference or exploration, but all written solutions must be entirely your own.

Using reference materials:

• You may consult textbooks or online materials, but you cannot request help from public forums such as AoPS or Stack Overflow.
• If you cite a result that is not considered “well known,” include a proof or clear citation.
• Every problem can be solved using standard mathematical knowledge without advanced or obscure results.

Using computers:

• You may use programs or calculators (such as Python, WolframAlpha, or GeoGebra) to support your work.
• If you include a computer-assisted result, you must also include your source code, inputs, outputs, and explanations for the grader.
• If a computer only helped you identify a pattern that you later proved on your own, no code submission is needed.

3. Format and submit your solutions.

Once you’ve completed your work, combine all your solutions into a single PDF and submit it through the USAMTS portal. Typed submissions are preferred, but handwritten work is acceptable if scanned clearly and neatly labeled.

Using LaTeX for USAMTS:

LaTeX is the recommended formatting system for writing mathematical proofs since it produces clean, professional layouts and is widely used in academia. Students can use free online tools like Overleaf or TeXer, and a beginner’s guide is available on the official USAMTS site.

If you’re not comfortable with LaTeX, you can still submit well-formatted work written in Microsoft Word or handwritten clearly.

Making diagrams:

If a problem involves geometry or visual reasoning, diagrams are often expected. Graders may deduct points if a diagram would have clarified your solution but was omitted. Keep the following in mind:

• Keep diagrams neat and accurate, using a straightedge and compass if drawing by hand.
• For digital solutions, tools like GeoGebra or Asymptote are excellent options.

4. Review feedback and results.

After grading concludes, you can view your scores and comments on the USAMTS website. Study the feedback carefully to improve your explanations and proofs. 

Students who perform well across all three rounds are listed on the official leaderboard and may receive certificates or other distinctions.

5. Build your skills.

To strengthen your problem-solving and proof-writing abilities, USAMTS recommends several helpful resources:

• AoPS Wiki offers a wide range of math tutorials, strategies, and practice problems.
• “How to Write a Math Solution” by Richard Rusczyk provides a clear guide to writing strong, logical proofs.
• The Art of Problem Solving by Richard Rusczyk and The Art and Craft of Problem Solving by Paul Zeitz are two essential books that teach the strategies and techniques needed to excel in competitive math.
• Participating in other math contests such as MATHCOUNTS or AMC can be great practice, though USAMTS focuses more on deep reasoning than on speed.

How to Win USAMTS

Here are some focused strategies to help you perform your best and aim for a top score in the USAMTS:

1. Understand the competition structure.

Before working toward a high score, familiarize yourself with how USAMTS operates. Each round contains five problems that require formal proofs rather than short numerical answers. Participants are given several weeks to work on these problems, allowing time to explore different approaches and refine their reasoning.

USAMTS problems are designed to test both mathematical skill and clarity of communication. The best competitors know how to balance creativity with precision and how to write solutions that are both elegant and easy to follow.

2. Build a strong foundation in proof writing.

Success in USAMTS depends on your ability to express mathematical reasoning clearly. Unlike timed contests, this competition rewards well-structured arguments and complete justifications. To strengthen your proof-writing skills, focus on the following:

• Study different proof techniques. Practice direct proofs, induction, contradiction, and construction. Learn when each method is most effective.
• Review official past solutions. Examine how top-scoring proofs are organized and how they explain each step logically.
• Be thorough. Avoid skipping intermediate steps or assuming results without explanation. Graders look for complete reasoning rather than brief answers.

3. Plan your time carefully during each round.

You typically have several weeks to complete and submit your work, so pacing matters. Begin early to leave room for revisions and error-checking. Here’s an effective approach:

• Spend the first few days reading all five problems carefully and identifying which ones you can tackle first.
• Work on easier or more familiar problems to build momentum before moving to harder ones.
• Leave at least three days at the end for editing and formatting your final solutions.

Avoid waiting until the final week, since rushed work often leads to small but costly mistakes.

4. Write with clarity and structure.

Your proofs should read like clear explanations, not rough notes. Graders are mathematicians who value precise communication. To make your solutions stronger:

• Begin each problem on a new page and clearly label your name, ID, and problem number.
• Define variables, terms, or notation before using them.
• Use complete sentences and logical transitions between steps.
• Keep your work neat and consistent if handwritten, or properly formatted if typed.

Well-organized presentation often helps earn full credit even when minor details are imperfect.

5. Check your reasoning and verify results.

Before submitting, take time to verify that every argument in your solution is valid. Even small logical errors can reduce your score. You can do this by:

• Substituting specific values to test edge cases or examples.
• Re-reading your proofs from start to finish to make sure they make sense without extra explanation.
• Having a friend or teacher (outside of contest periods) review old, completed rounds to point out unclear steps for practice.

If you use a computer or software to confirm results, include the relevant code, input, and output in your solution so graders can understand what you did.

6. Learn from feedback.

After each round, USAMTS graders provide personalized comments. Use these carefully to improve future performance. If feedback mentions missing justifications or unclear explanations, make those your priority next time.

Comparing your own work to the official solutions after results are posted is also valuable. This helps you recognize alternative methods and refine your problem-solving style for future rounds.

7. Develop long-term consistency.

Winning in USAMTS often comes from sustained effort across all three rounds. Build a regular problem-solving routine even between rounds to stay sharp:

• Solve one or two problems from past contests each week.
• Keep a personal “proof journal” where you summarize what you learned from each problem.
• Review your old work before the next round begins to remind yourself of common mistakes and strengths.

Consistent, thoughtful practice is the most reliable way to move from participant to top scorer.

USAMTS Previous Winners

Each year, the United States of America Mathematical Talent Search recognizes top-performing students for their exceptional problem-solving and proof-writing skills.

Top performers

The following table lists just a few of the many standout participants from the 2024–2025 contest (Year 36), based on the official USAMTS leaderboard:

For the full leaderboard and additional score groups, visit the official USAMTS leaderboard.

Score distribution

Below is a breakdown of how many participants achieved each high score—from perfect scores down to the AIME-qualifying threshold—in the 2024–2025 USAMTS cycle:

These numbers reflect the official leaderboard’s top range. For full distribution (all scores), visit the USAMTS leaderboard for Year 36.

The 2025–2026 contest (Year 37) is currently ongoing and has not yet been graded. Results are typically released in early December following the final submission period.

Frequently Asked Questions

1. How many students compete in USAMTS?

The official USAMTS site does not publish the total number of participants each year. However, if you add together the numbers given in the “Problem Statistics” section for the most recent contest (2024-2025), they total 941 competitors.

2. What is the difference between USAMTS and other math competitions like AMC or AIME?

Unlike AMC or AIME, which are timed multiple-choice or short-answer contests, USAMTS focuses on proof writing. Participants are given several weeks to solve five problems per round and must submit complete, well-written justifications. It emphasizes depth of reasoning, clarity, and communication over speed or memorization.

3. How do I participate in USAMTS?

Students can register directly through the official USAMTS website. The competition is entirely online and open to all U.S. students in middle or high school. After creating an account, participants can download each round’s problems, write their solutions, and upload their submissions before the deadline. No teacher sponsorship or team membership is required.

4. When will USAMTS 2025–2026 results be released?

The 2025–2026 USAMTS (Year 37) is currently ongoing. Once all three rounds have been completed and graded, official results are expected to be released in early December 2025.

5. What topics or math areas does USAMTS cover?

USAMTS problems draw from a wide range of high school and early college mathematics, including algebra, geometry, number theory, and combinatorics. Some problems may also touch on topics from probability or mathematical reasoning. The focus is always on logical proof writing and creative problem-solving rather than rote computation.

Takeaways

The USAMTS is one of the most rigorous proof-based math contests in the country. Here are the key points to remember about the USAMTS:

• Competing in USAMTS develops advanced problem-solving, critical reasoning, and mathematical writing skills that are valuable for success in higher-level math and STEM fields.
• The contest encourages independent work and creative approaches since students complete their proofs at home and submit written solutions for evaluation.
• Top-performing students are recognized on the official leaderboard and often advance to other prestigious programs such as the AIME and the USAMO.
• Success in USAMTS requires consistency, clarity, and strong proof-writing ability, making it ideal preparation for university-level mathematics and research.
• Working with a college admissions consultant can help you effectively present your USAMTS achievements on college applications. AdmissionSight’s expert team helps translate the problem-solving, analytical, and written communication skills developed through USAMTS into strong personal statements and academic narratives.