American Regions Mathematics League
The American Regions Mathematics League, is an annual, national high school mathematics team competition held simultaneously at four locations in the United States: the University of Iowa, Penn State, UNLV, and the newly added site at the University of Alabama in Huntsville. Past sites have included San Jose State University, Rutgers University, and Duke University.
ARML is a prestigious, national math tournament that is often called the "World Series of Mathematics Competitions". Teams consist of 15 members, which usually represent a large geographic region or a large population center. Some math and science magnet schools, such as Thomas Jefferson High School for Science and Technology, VA, and the Academy for the Advancement of Science and Technology, NJ, also field teams. The competition is held on the first Saturday after Memorial Day.
As of 2014, over 150 teams competed with around 2000 students.
ARML problems cover a wide variety of mathematical topics including algebra, geometry, number theory, combinatorics, probability, and inequalities. Calculus is not required to successfully complete any problem, but may facilitate solving the problem more quickly or efficiently. While part of the competition is short-answer based, there is a cooperative team round, and a proof-based power question. ARML problems are harder than most high school mathematics competitions.
The contest is largely made possible by the monetary contribution of D. E. Shaw & Co. among other smaller contributors.
Competition format
The competition consists of four formal events:- A team round, where the entire team has 20 minutes to solve 10 problems. Each problem is worth 5 points, for a possible total of 50 points
- A power question, where the entire team has one hour to solve a multiple-part question requiring explanations and proofs. This is usually an unusual, unique, or invented topic so students are forced to deal with complex new mathematical ideas. Each problem is weighted for a possible 50 points.
- An individual round, where each team member answers five groups of two questions each, with ten minutes per pair. Starting in 2009, the individual round expanded from eight questions to ten. Each problem is worth 1 point, for a grand total of 150 points possible for the team. Only 12 students nationwide received a perfect score in 2014. This round's format is similar to that of the Target Round in MATHCOUNTS.
- A relay, where the team is broken into five groups of three. Within each group, the first team member solves a problem and passes the solution to the next team member, who plugs that answer into their question, and so on. The allotted time is six minutes, but extra points are given for solving the problem in three minutes. Solving the relay in 3 minutes gives 5 points, solving it in 6 minutes gives 3 points. The whole process is done twice, making the maximum 50 points possible for the team.
- The teams are scored based on the number of points they attained with the maximum being 300 points. Team score ties are broken by first considering the sum of the Team and Power Rounds, then the Relay Round total.
In recent years, there has been a super relay, where two groups of seven team members both work to give a correct answer to the fifteenth team member. That last team member substitutes two answers into his problem. For logistical reasons, the Super Relay has never counted towards the team score. It was instituted as a "filler" while scores are tabulated. Candies and other goodies are sometimes rewards for the super relay round.
Also in recent years, a song contest has become an informal event at ARML. Each school is allowed to have any number of their students perform a song related to mathematics, usually a parody of a popular song, with its lyrics replaced.
The format of the ARML competition is based on the NYSML competition, but is generally considered more difficult than the NYSML competition. This format also inspired the Great Plains Math League.
History
The New York State Mathematics League held its first competition in 1973, a competition intended for New York state teams. A team from Massachusetts asked to participate in the 1974 NYSML competition, and it took first place. This led to the creation of the Atlantic Regions Mathematics League in 1976, which became the American Regions Mathematics League in 1984.When the Atlantic Regions Mathematics League was founded, the competition was held at a single eastern site that changed from year to year:
| Year | Location |
| 1976 | C. W. Post College |
| 1977 | Brown University |
| 1978 | Rutgers University |
| 1979 | Brown University |
| 1980 | Rutgers University |
| 1981 | University of Maryland College Park |
| 1982 | University of Maryland College Park |
| 1983 | Pennsylvania State University |
After 1983, the coordinators decided to keep the competition at Penn State University. ARML expanded to two sites in the late 1980s and to three sites in 1995. In 2008, ARML added a fourth site at the University of Georgia in Athens to better accommodate students in the Southeast, which moved to the University of Alabama in Huntsville in 2020.
The 2006 competition saw significant expansion. Around 120 teams and a total of around 1800 students competed, which was around 25% larger than during any other year. The attendance at the western site, UNLV, nearly doubled.
Past Team Winners
| Year | Team | Score |
| 1976 | New York City A | 117 |
| 1977 | Massachusetts A | 148 |
| 1978 | Fairfax-Montgomery | 135 |
| 1979 | New York City A | 129 |
| 1980 | New York City A | 113 |
| 1981 | New York City A | 166 |
| 1982 | New York City A | 132 |
| 1983 | New York City A | 132 |
| 1984 | New York City A | 162 |
| 1985 | Montgomery County, Maryland A | 157 |
| 1986 | New York City A | 183 |
| 1987 | New York City A | 170 |
| 1988 | Chicago A | 197 |
| 1989 | Chicago A | 187 |
| 1990 | Ontario A | 197 |
| 1991 | Ontario A | 200 |
| 1992 | Georgia A | 172 |
| 1993 | Thomas Jefferson A | 190 |
| 1994 | New York City A | 183 |
| 1995 | New York City A | 126 |
| 1996 | San Francisco Bay Area A | 179 |
| 1997 | Minnesota Gold | 125 |
| 1998 | Massachusetts A | 171 |
| 1999 | San Francisco Bay Area A | 187 |
| 2000 | Chicago A/San Francisco Bay Area A | 172 |
| 2001 | San Francisco Bay Area A | 191 |
| 2002 | Thomas Jefferson A | 190 |
| 2003 | Thomas Jefferson A | 155 |
| 2004 | Thomas Jefferson A | 166 |
| 2005 | Lehigh Valley Fire | 172 |
| 2006 | North Carolina A | 186 |
| 2007 | Phillips Exeter Red | 171 |
| 2008 | New York City A | 170 |
| 2009 | Lehigh Valley Fire | 215 |
| 2010 | Lehigh Valley Fire | 204 |
| 2011 | Lehigh Valley Fire | 232 |
| 2012 | North Carolina A | 223 |
| 2013 | San Francisco Bay Area A | 234 |
| 2014 | PEARL A | 260 |
| 2015 | San Francisco Bay Area A | 211 |
| 2016 | San Francisco Bay Area A | 210 |
| 2017 | San Francisco Bay Area A | 245 |
| 2018 | Thomas Jefferson High School for the Science and Technology A1 | 234 |
| 2019 | Thomas Jefferson High School for the Science and Technology A1 | 245 |
Past Individual Winners
| Year | Team |
| 1977 | Randal Dougherty |
| 1978 | Fred Helenius |
| 1979 | Irwin Jungreis |
| 1980 | Paul Feldman |
| 1981 | Benji Fisher |
| 1982 | Noam Elkies |
| 1983 | David Zuckerman |
| 1984 | Mike Reid |
| 1985 | Ken Fan |
| 1986 | John Overdeck |
| 1987 | Danny Cory |
| 1988 | Michael Zieve |
| 1989 | Sam Vandervelde |
| 1990 | Akira Negi |
| 1991 | Andrew Schultz |
| 1992 | Robert Kleinberg |
| 1993 | Jeremy Bem |
| 1994 | Noam Shazeer |
| 1995 | Daniel Stronger |
| 1996 | Nathan Curtis |
| 1997 | Davesh Maulik |
| 1998 | Gabriel Carroll |
| 1999 | Gabriel Carroll |
| 2000 | Tiankai Liu |
| 2001 | Gabriel Carroll |
| 2002 | Ruozhou Jia |
| 2003 | Anders Kaseorg |
| 2004 | Aaron Pixton |
| 2005 | Ryan Ko |
| 2006 | Samuel Dittmer |
| 2007 | Tao Ran Chen |
| 2008 | Qin Xuan Pan |
| 2009 | Zhuo Qun Song |
| 2010 | Ben Gunby |
| 2011 | Zhuo Qun Song |
| 2012 | Allen Liu |
| 2013 | Allen Liu |
| 2014 | Darryl Wu |
| 2015 | Brice Huang |
| 2016 | Daniel Kim |
| 2017 | Brian Reinhart |
| 2018 | Luke Robitaille |
| 2019 | David Chen |