Harvard–MIT Mathematics Tournament


The Harvard–MIT Mathematics Tournament is an annual high school math competition that started in 1998. The location of the tournament, in Cambridge, Massachusetts, alternates between Harvard University and MIT. The contest is written and staffed almost entirely by Harvard and MIT students.

Tournament format

HMMT February is attended by teams of eight students each. Teams can represent a single school, or a regional math team as large as a state. In recent years, teams have represented over 20 states, as well as Africa, Asia, Europe, and South America.
HMMT February consists of three rounds: the Individual Round, the Team Round, and the Guts Round. No calculator or computational aids of any kind are allowed during the contest.

Individual Round

The Individual Round consists of exams in Algebra, Geometry, and Combinatorics. Each of the three exams is 50 minutes in length and contains 10 questions. The exams are short-answer, meaning that the answers can be any real number or even an algebraic expression. Before 2012, competitors had the option to choose between a General exam or two exams in Algebra, Geometry, Combinatorics, or Calculus.

Team Round

For the Team Round, the eight-person teams compete together on a 60-minute-long test. The Team Round is a collaborative event with proof-style problems, sometimes arranged into groups of several problems on the same theme. Thorough justifications are required for full credit. The Team Round is worth a total of 400 points, and problems are weighted according to difficulty. The event is similar to an ARML Power Round, but the problems are much harder and less numerous. This round is targeted at teams comfortable with rigorous mathematical proofs.

Guts Round

The Guts Round is an 80-minute team event with 36 short-answer questions on an assortment of subjects, of varying difficulty and point values. Each team is seated in a predetermined spot, and the questions are divided into groups of four. At the starting signal, each team sends a runner to an assigned problem station to pick up copies of the first set of four problems for each team member. As soon as a team has answers for one problem set, the runner may bring the answers to the problem station and pick up the next set. It is not expected that students will finish all the problems. Grading is immediate and scores are posted in real time, resulting in an exciting atmosphere for the competitors. The Guts round is worth a total of approximately 400 points.

Other events

HMMT February also features events on the Friday evening prior to the tournament. Some of these events include a dinner and social for students and coaches, and Mini-Events such as math talks about famous problems and math-related games.
The top 50 competitors at HMMT February are also invited to compete in the Harvard MIT Invitational Competition which is a five-question four-hour proof contest started in 2013. The problems are typically quite difficult: competitors can typically attain a high ranking by fully solving three problems.

Scoring and awards

HMMT February uses a unique scoring algorithm to rank the competitors on the Individual Rounds. While the problems on these tests are weighted according to difficulty, they are done so after the testing has completed. As explained here, this helps create a very fair method for weighting problems according to their actual difficulty as opposed to their perceived difficulty prior to the tournament. The weights assigned to each problem are calculated using a that takes into account which problems were solved by which students. The weights of the problems on the Team and Guts Rounds are given on the tests.
Prizes are given to the ten highest-scoring individuals overall, the top ten scorers on each of the subject rounds, the ten highest-scoring teams on the Team Round, and the ten highest-scoring teams on the Guts Round. The top ten teams overall will be named the Sweepstakes winners. The calculation of Sweepstakes scores is roughly half individual round performance and half collaborative round performance.

Difficulty

The difficulty of the competition is compared to that of ARML, the AIME, or the Mandelbrot Competition, though it is considered to be a bit harder than these contests. The contest organizers state that, "HMMT, arguably one of the most difficult math competitions in the United States, is geared toward students who can comfortably and confidently solve 6 to 8 problems correctly on the American Invitational Mathematics Examination." As with most high school competitions, knowledge of calculus is not required; however, calculus may be necessary to solve a select few of the more difficult problems on the Individual Rounds.

Results

The results of HMMT February can be seen below:
YearOverall ChampionIndividual ChampionTeam Round A ChampionGuts Round Champion
2018AlphaStar Academy A* AirLuke RobitailleMoCoSwaggaSquadTJHSST
2017Phillips Exeter AcademyYuan YaoStar League A-StarPhillips Exeter Academy
2016Phillips Exeter AcademyYuan YaoPhillips Exeter AcademyFlorida A
2015Phillips Exeter AcademyAndrew HeStar League A-StarPhillips Exeter Academy
2014Phillips Exeter AcademyScott WuPhillips Exeter AcademyStar League A-Star
2013Phillips Exeter AcademyJames TaoPhillips Exeter AcademyPhillips Exeter Academy
2012Phillips Exeter AcademyXiaoyu HePhillips Exeter AcademyPhillips Exeter Academy
2011Saratoga High School/SFBAXiaoyu HeNorth CarolinaSaratoga High School/SFBA
2010Phillips Exeter AcademyBen GunbyTJHSSTAAST
2009TJHSSTIce PasupatLehigh Valley ARMLLehigh Valley ARML
2008Phillips Exeter AcademyBrian HamrickNew York City Math TeamQuagga
2007The WOOTlingsArnav TripathyThe WOOTlingsTJHSST
2006Phillips Exeter AcademyNimish RamanlalTJHSSTAAST
2005Phillips Exeter AcademyThomas MildorfTJHSSTFlorida
2004TJHSSTTiankai LiuTJHSSTPhillips Exeter Academy
2003TJHSSTTony ZhangTJHSSTAAST
2002Newton South High SchoolRicky LiuNewton South High SchoolLexington High School
2001Lexington High SchoolRicky LiuLexington High SchoolNewton South High School
2000Newton South High SchoolRicky LiuNewton South High SchoolNewton South High School
1999Newton South High Schooln/aNewton South High Schooln/a
1998Lexington High Schooln/aLexington High Schooln/a

HMMT November

HMMT November has been held since 2008 for teams of six students. Students are required to come from the United States to participate, and no student may compete in both November and February in a given school year. The tournament is similar in style to HMMT February, and is organized by the same Harvard and MIT students. Instead of three topic tests, HMMT November has two Individual Rounds: a General Test and a Theme Test. Additionally, the Team Round is entirely short answer, instead of proof-based. HMMT November is considered to be an easier alternative to HMMT February. The results of HMMT November can be seen below:
YearOverall ChampionIndividual ChampionTeam Round ChampionGuts Round Champion
2015Shenzhen Foreign Languages SchoolYi Fan ZhuShenzhen Foreign Languages SchoolShenzhen Foreign Languages School
2014Phillips Exeter AcademyJianqiao XiaPhillips Exeter AcademyInternational Academy East
2013Beijing STFXGeyang QinPhillips Exeter AcademyBeijing STFX
2012Western Mass ARMLDhroova AiylamPhillips Exeter AcademyWestern Mass ARML
2011Phillips Exeter AcademyForest TongLexington High SchoolBrookline High School
2010Phillips Exeter AcademyRavi JagadeesanPhillips Exeter AcademyLexington High School
2009ABRHSXiaoyu HePhillips Exeter AcademyABRHS
2008Western Mass ARMLSam TrabuccoWestern Mass ARMLWestford Academy

Sponsors

HMMT is currently sponsored by the MIT Mathematics Department, Optiver, D.E. Shaw & Co, the Harvard Mathematics Department, Flow Traders, the Susquehanna International Group, and Jane Street Capital.

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