HMMT (Harvard-MIT Math Tournament): A Complete Guide

Ever wondered what it’s like to test yourself against some of the world’s brightest high school math whizzes? HMMT (Harvard-MIT Math Tournament) offers a chance for talented students to tackle creative math challenges at Harvard and MIT. In this article, we’ll explore everything you need to know about HMMT, from its format and prizes to how you can win.

• What Is HMMT?
• HMMT Awards and Prizes
• How to Qualify for HMMT
• How to Get into HMMT
• How to Win HMMT
• HMMT Previous Winners
• Frequently Asked Questions
• Takeaways

What Is HMMT?

HMMT (or the Harvard-MIT Math Tournament) is a semiannual international math competition for high school students, run by student volunteers of Harvard University and the Massachusetts Institute of Technology. It was founded in 1998 and has now become one of the largest and most prestigious math contests at the pre-college level.

In fact, HMMT has grown so big that it can’t accommodate all the applications it receives. So, it decides which teams and individuals get to participate in tournaments using lotteries.

Individuals and teams alike can register. If you register as an individual, you’ll be grouped with other fellow individual contestants for the team rounds.

November vs. February tournament

HMMT is held twice a year, every November and February. However, despite sharing the same organizers, the two tournaments have different formats and difficulty levels.

Here’s a quick overview of their differences:

Overall, the November tournament is designed to be slightly more accessible while still challenging for strong math students since it requires good problem-solving skills—but not the same depth of specialized knowledge as February. This makes the November tournament ideal for those newer to national-level contests or looking for an introduction to HMMT-style problems.

Meanwhile, the February tournament requires significant mathematical prowess, including strong proof-writing and advanced problem-solving techniques. Because of that, it usually attracts national Olympiad qualifiers, AIME high scorers, and other elite-level students.

Types of tests

HMMT has several types of tests, each designed to assess different problem-solving skills. Computational aids (from books, notes, and calculators to abaci) and drawing aids (like graph paper and compasses) are not allowed.

There are three types of tests, and the November and February tournaments slightly differ in what you can expect from some of them:

Individual tests

Each test will consist of 10 problems, which you’ll answer within 50 minutes. For the November tournament, there are two individual tests:

• General round. Short-answer problems from across all high school math topics—like algebra, geometry, number theory, and combinatorics.
• Theme round. Short-answer problems tied together by a central topic (such as all related to circles, modular arithmetic, or sequences).

Meanwhile, the February tournament has three tests:

• Algebra
• Geometry
• Combinatorics

Team round

This collaborative round emphasizes communication, speed, and strategy, requiring you to answer 10 problems within 60 minutes.

The November team round only asks for short answers since the focus is on accuracy and efficiency rather than formal proof writing. Meanwhile, the February tournament is entirely proof-based. Your team will need to submit fully written, logically structured solutions, making it more difficult and time-intensive than the November format.

Guts round

The Guts round is a unique, fast-paced team event held at the end of the day. You’ll have 80 minutes to answer 636 short-answer questions on different subjects.

The way the round works is that teams receive sets of problems in batches. After finishing a batch, they submit answers for instant grading and receive the next batch. Scores are posted in real time, adding competitive pressure.

HMMT Awards and Prizes

Prizes will be awarded to the top scorers in each category, and ties won’t be broken. Here’s an overview of how many teams/individuals get recognition:

Winning HMMT is no small feat. It’s one of the most prestigious high school math contests out there. Taking home that kind of honor shows off your problem-solving skills and gives your college application an impressive boost.

How to Qualify for HMMT

To compete in HMMT, you should first check if you meet certain criteria and submit a few documents.

Eligibility

To be eligible for HMMT, you must:

• Be under 21 years old on the date of participation
• Participate in only one HMMT tournament per academic year
• Belong to only one organization in a given season
• Participate in your school team if your school submits an application for a season

Required documents

To participate in HMMT, you should submit the following:

• Online registration form. All competitors should apply through the official HMMT online registration system. This form will just ask for personal details, school/organization info, and team roster (if applicable).
• Team roster and coach info. Team applications should include a roster of all team members. You’ll also need to designate an adult coach or chaperone for the team. HMMT requires that an adult (age 21 or older) accompany the team on contest day to serve as a proctor.
• Consent and waiver forms. If you’re under 18, your parent/guardian may need to sign a consent or liability waiver form for you to participate (especially if traveling to Cambridge). HMMT typically provides any required waiver or permission forms after acceptance.

Contest fees

You don’t need to pay anything when applying. However, if you win the lottery, the cost to participate is $80 per team and $10 per individual competitor. The contest fees are collected on-site, and you can pay with cash or check.

If cost is a concern, HMMT offers financial aid, which you can apply for at the same time as your registration. But before it can be considered, you should first be accepted in the registration lottery.

Registration deadline

Here’s an overview of the important dates for the HMMT registration process:

Stay on top of these dates so you don’t miss a thing.

How to Get into HMMT

HMMT accepts both teams and individuals to participate. Here’s how you can get into the tournament:

Applying as part of a team

This is probably the easier way to participate in HMMT since your coach will be handling much of the process. As a member of a team, here’s what you’ll have to do:

1. Talk to your math team coach or club advisor. Ask them if they’re planning or are interested in organizing an HMMT team. If yes, tell them you’d like to join.
2. Create your HMMT account. Register an HMMT account or log in if you already have an existing account.
3. Join your team’s online roster. Your coach or team leader will send you an invitation through the HMMT registration system. Accept it so your name appears on the official team list. Your coach will submit the application, and you’ll just need to wait if your team has been accepted in the lottery.
4. Sign waivers. If your team is accepted, log back into your HMMT account and fill out the waivers.
5. Bring your share of the fee. Check with your coach how your team will divide the $80 contest fee, or if the club funds or a sponsor will cover the cost for the team.

Applying as an individual

If you’re applying as an individual, you’ll be doing all the registration work. Fortunately, the process is quite straightforward. Here’s what to do:

1. Ensure your school doesn’t plan on applying. This step is very important since if your school suddenly announces that it’s planning on creating an HMMT team, you can’t apply as an individual anymore. You’ll have to be part of your school’s team during the team rounds rather than be teamed up with other individual competitors.
2. Complete the online application. If you’re sure that you can apply as an individual, log in to the HMMT registration portal. Select “Individual Application,” choose the tournament you want to join, and fill out your personal details.
3. Wait for the lottery results. Wait for an email letting you know if you were accepted, waitlisted, or not selected.
4. Confirm your spot. If you’re accepted, log back in to your HMMT account to confirm your participation. Complete any consent forms. If you’ve been waitlisted, you’ll also need to confirm whether you want to be added to the waitlist or not.

How to Win HMMT

You’re never sure if you’ll be part of the next HMMT since participation is decided by lottery. However, if you’re going to register for the tournament, you should be ready to go if you do get accepted. So, here is how to prepare for and win the HMMT:

1. Master the fundamentals of high school math.

HMMT problems can cover any and all topics from the high school math curriculum. So, to excel, you need a strong foundation in core areas like:

• Algebra
• Geometry
• Trigonometry
• Probability
• Combinatorics
• Number theory.

HMMT already gives you an idea of the difficulty of the problems you’ll need to solve. For example, February tournaments explicitly focus on algebra, geometry, and combinatorics.

Build a short “must-know” list to make it easier to review concepts, from Vieta’s formulas to angle-chasing with cyclic quadrilaterals. Calculators are off-limits, so it’s also good to practice mental arithmetic, factor spotting, and clean algebra.

If you’re aiming for the February tournament, you should also practice writing succinct arguments since the contest requires proofs.

2. Practice with past contests and similar problems.

There’s no better preparation for HMMT than solving HMMT problems. The organizers provide an archive of past HMMT problems and solutions on their website, and working through them can give you a feel for the question styles, difficulty, and common themes.

In fact, the HMMT team specifically recommends reviewing certain past years as representative contests. They suggest November 2009 and 2011, and February 2010 and 2013, as good samples of difficulty. Time yourself and simulate exam conditions for the individual rounds or team rounds to build familiarity and speed.

Beyond HMMT itself, try other high-level math contests too. Problems from the American Invitational Mathematics Exam (AIME) and the USA Mathematical Olympiad (USAMO) are great practice, since HMMT difficulty spans those levels.

Even the International Mathematical Olympiad (IMO) and its shortlist problems can be useful practice for the toughest HMMT questions. As you practice, analyze your solutions and mistakes, and look for patterns in what techniques or tricks come up.

3. Work on team skills and collaboration.

A big part of HMMT is actually team-based. So, to win as a team, you’ll need excellent collaboration under pressure. Practice working with your teammates before the tournament to develop strategies for dividing work and communicating effectively.

For example, in the Guts Round, speed and coordination are important, so decide who will write answers, who will run solutions up to the grading station, and how you’ll split up problems. You could perhaps assign teammates to their strength areas, but also be ready to cross-check each other’s work. During practice sessions, simulate a Guts Round by doing sets of problems in timed intervals to see how your team can improve its rhythm.

For the Team Round, if you’re in the February contest, all problems require written proofs, so make sure at least a couple of team members have solid proof-writing skills and can clearly explain their reasoning to the group.

Develop a communication protocol as well. For instance, if someone has a partial answer, how do you all decide whether to move on or keep pushing on that problem?

4. Read each problem carefully.

HMMT problems tend to have tricky wording. Because of that, even though you may be tempted to rush because of the time pressure, read each problem carefully. Pay attention to details and make sure you understand exactly what is being asked in each problem.

Build a “pre-solve checklist” of terms you should watch out for. For example, if you see the word “divisible by,” you might have to use modular arithmetic or lifting the exponent. Or, if you read “paths/graphs,” then you might be dealing with invariants or parity.

5. Be creative and open-minded.

What sets HMMT apart is the creativity of its problems. Standard methods won’t always work, so be ready to think outside the box.

For example, you could turn a geometry ratio into vectors or complex numbers to answer a certain problem. Or, you could try turning a counting recursion into a generating function.

Basically, don’t restrict yourself to one approach. If your current strategy doesn’t seem to be working, be willing to try something else.

HMMT problems often require seeing connections between different areas of math. The more willing you are to “play with numbers” (like coordinate bashing in geometry vs. classical synthetic approaches, or combinatorial arguments vs. generating functions), the better your chance of finding a solution.

HMMT Previous Winners

Over the years, HMMT has seen many impressive champions. Here are a few examples of past winners and top performers at the tournament:

• Luke Robitaille. An impressive individual competitor who claimed first place in 2018, 2020, 2021, and 2022.
• Lehigh Valley Fire. A math team from Pennsylvania, they won the February 2024 Sweepstakes Championship, taking first place in the overall team standings.
• PRISMS Falcons. The team from the Princeton International School of Math and Science (PRISMS) were the November 2023 Sweepstakes Champions (and also won that year’s Guts Round).
• Sicheng Zhou. A PRISMS member who was also the Individual Champion in the HMMT November 2023 tournament.
• Westchester Area Math Circle. A community-based team that was the Sweepstakes Champions of HMMT in November 2022. One of their members, Qiao Zhang, was the 2022 November individual champion

Frequently Asked Questions

1. How challenging is the Harvard MIT Math Tournament?

HMMT is extremely challenging, especially the February tournament, which has a difficulty mid-AIME to Olympiad. The November tournament is slightly easier, but its difficulty is for mid-AMC to upper-AIME, so it’s still rigorous.

2. What math topics are on HMMT?

HMMT covers all high school math topics. In the February tournament, the individual rounds are split into algebra, geometry, and combinatorics tests. Meanwhile, the November HMMT contain a mix of problems from all areas of math.

3. What is the most prestigious math competition?

The most prestigious math competition for high school students globally is the International Mathematical Olympiad (IMO), which is basically a world championship of math for pre-college students.

Takeaways

• HMMT (Harvard-MIT Math Tournament), jointly run by Harvard and MIT students, attracts international and domestic students each year with its two major contests (November and February), with different formats and difficulty levels.
• Registering for the HMMT is technically as easy as just submitting an application form. However, because the tournament receives so many applications, whether you get accepted will depend on whether you get chosen in the lottery.
• Want to keep challenging and improving your math skills? We can help you plan your extracurriculars so they can lead you to your academic and professional goals.