For high school students with a passion for mathematics, the Harvard/MIT Mathematics Tournament (HMMT) is the perfect competition to test your skills. Featuring original math puzzles and problems created by students and professors at Harvard and MIT, HMMT is an opportunity for talented mathematics minds from around the world to solve challenging problems and connect with like-minded peers.

What is the Harvard/MIT Mathematics Tournament (HMMT)?

HMMT is an annual mathematics competition open to high school students internationally. Founded in 1989 by students at Harvard and MIT, HMMT aims to engage young mathematicians with creative problem-solving in a collaborative setting. The competition consists of math puzzles and questions tailored to various difficulty levels. The problems require logic, calculus skills, number theory knowledge, and the ability to think originally and see alternate approaches.

HMMT has gained prestige among high schools and universities due to the caliber of students it attracts and its ties to Harvard and MIT. Success in the competition is a meaningful award for any college application, demonstrating not just strong math foundations but also an enthusiasm for problem-solving required to excel at top schools. Past participants have gone on to study at MIT, Stanford, Cambridge, and more.

Is HMMT Prestigious?

HMMT is a prestigious mathematics competition, given its status as the oldest and largest math tournament of its kind, and association with two of the top higher education institutions worldwide. Solving the original and complex problems in HMMT requires conceptual understanding, logical reasoning, and mathematics intuition that exemplifies the skill level required to attend top schools and be successful within any field that requires mathematical ability.

The competition is known for its highly engaging and collaborative environment, where students work together in teams to solve problems, gain insights from diverse perspectives, and form friendships with others passionate about mathematics. Success in HMMT, either individually or as part of a team, demonstrates a meaningful achievement that provides a competitive edge for university admissions. The competition offers high-performing students the opportunity to connect with world-class mathematicians and gain mentorship to support their future studies. Overall, HMMT is a great experience that challenges and rewards mathematically talented students.

Who is Eligible to Participate?

HMMT is open to all high school students with a strong foundation and interest in mathematics. Students in grades 9 through 12 from any location or background may participate. While most attendees come from high schools that provide enrichment courses in calculus, statistics, and number theory, prerequisites are not officially required. Students only need to have patience for solving complex problems, curiosity about mathematics, and an interest in thinking originally.

Teams consist of up to 4 students, and individuals are also welcome to compete on their own. Students compete based on their grade level. There are nominal team registration fees, however, generous scholarships are available for those with financial need. Travel grants are also offered on a case by case basis. The goal of HMMT is to make the competition as accessible as possible to any motivated mathematics students looking to challenge themselves and connect with a community of like-minded peers.

Timeline and Structure of HMMT

HMMT takes place over two weekends throughout the year. One is in November and another is in February. The November HMMT is held at Harvard, while February is held at MIT. While the two may seem similar, there are crucial differences between the two rounds. From the HMMT website,

“While both tournaments are intended to challenge strong math students from all around the world, the February contest demands a considerable amount of mathematical maturity and problem-solving experience. … Indeed, our February contest has, in previous years, attracted dozens of IMO medalists and top scorers on national Olympiads.” Check out this link for more information.

Regardless of the weekend, the competition kicks off on Friday evening with an opening ceremony, followed by a full day of puzzles on Saturday in various locations at the respective school. An awards ceremony takes place on Sunday morning before students return home.

The competition features a collection of mathematics puzzles and word problems that require logic, estimation, probability, and geometry skills to solve. Problems are designed by Harvard and MIT students and professors to stimulate mathematical thinking in creative ways. Questions range from 10-15 multiple choice options to 3-4 extended written response problems. The February one is proof-heavy and attendants are expected to be strong in writing long and complex proofs, while the November one features short-answer questions that are more computationally aligned.

Students work both individually and in teams to complete problems, with some designed specifically for collaboration. Problems are worth varying point values, with more complex questions earning higher points. Finally, awards are given based on both individual and team performance.

7 Tips for Success at HMMT

1. Review core mathematical concepts like statistics, probability, geometry, algebra, and calculus

The foundation for success must be your ability to understand the fundamentals of the wide aspects of math. Be sure to spend a great deal of time having a strong understanding of all of these topics, as this allows you to focus on more complicated and advanced concepts during the competition, instead of worrying about the basics. Develop mathematical intuition across these topics, and you will set yourself up for great success.

2. Practice creative problem-solving with sample word problems and puzzles to prepare for the abstract nature of HMMT questions

HMMT themselves provide large amounts of practice material and even problems of the week. Familiarizing yourself with the question-style of HMMT and the types of material they cover will lead you to do better in the contest, just because you can spend less time focusing on vocabulary, structure, and syntax, and more on the actual math. Additionally, looking at problems from competitions like the International Mathematical Olympiad will strengthen skills that translate to HMMT. Practice problems are absolutely essential. You will begin to detect patterns and trends in the questions they like to ask, and develop an intuition to approach these problems.

3. Work with your teammates beforehand to establish strategies for effectively collaborating under pressure

The HMMT is a heavy group competition, thus while you’re studying, you must work together and learn how to maximize the short time the competition runs over. Are there strengths that you have and weaknesses that your teammates can cover. Is one person better at communication and leadership? Talk with each other, and figure out the best ways you all can collaborate to maximize success.

4. Get plenty of rest and stay energized during the two-day competition

The weekend can be long and grueling, with a lot of stimulation from so many people in a new environment alongside the draining mental effort of the competition itself. To operate on peak efficiency, you have to make sure you sleep well, eat consistently and healthily, and do not burn yourself out before the last competition round is over. Without patience, concentration, logic, and the ability for your brain to work on fully power, your studying could all go to waste, thus take care of yourself physically and mentally.

5. Pay close attention to problem details and any clues provided

Remember that each of these problems are vetted and possible to solve within the time span, with a mathematical concept that you are familiar with. Do not get overwhelmed on first sight, so read carefully and be aware of the clues and hints that questions may give you. From your studying, there might be similar problems, similar patterns of questions, and be sure to connect your current problem to ones you have recognized. If there is something truly confusing, you may ask the competition facilitators for clarification!

6. Do not give up easily

These problems are definitely challenging and will require deep thought and team communication, thus if at first glance, if you are confused, do not give up then. Take a few minutes to think about the problem, piece by piece, and if you are still confused, skip the problem and come back later. With a bit more time, you may come at the problem from alternate perspectives or try working with a different partner, which allows different ways of thinking and an extra eyes on the problem can reveal an "aha" moment. Have trust in yourself that you are prepared for this competition.

7. Develop a growth-oriented mindset, staying curious and open to other possibilities

Unconventional and unique thinking is the hallmark of HMMT. Mathematicians constantly have to use concepts that they are familiar with in unconventional ways. Coming in prepared and knowledgeable about mathematics is of course necessary, but do not be afraid of letting go of your preconceived assumptions and connections that may prevent you from seeing the solution to the problem. Train yourself to be flexible in your solution! While you’re studying, if you get the question correct, see if there is another solution or another approach that is equally as valid. Be open to the weird world that is mathematics and you will be a successful competitor at HMMT.

One other option—the Lumiere Research Scholar Program

If you’re interested in pursuing independent research, consider applying to one of the Lumiere Research Scholar Programs, selective online high school programs for students founded with researchers at Harvard and Oxford. Last year, we had over 4,000 students apply for 500 spots in the program! You can find the application form here.

Also check out the Lumiere Research Inclusion Foundation, a non-profit research program for talented, low-income students. Last year, we had 150 students on full need-based financial aid!

Aaron Zheng is a sophomore at Harvard University, studying Bioengineering. He is passionate about biotechnology, business development, and aiding students to get to college, regardless of background. In his spare time, he looks to read, journal, and explore the world.

Image Source: HMMT logo