# The William Lowell Putnam Mathematical Competition

The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students, awarding scholarships and cash prizes ranging from \$250 to \$2,500 for the top students and \$5,000 to \$25,000 for the top schools. The competition was funded in 1927 by Elizabeth Lowell Putnam in memory of her husband William Lowell Putnam (Harvard 1882), who while alive was an advocate of intercollegiate intellectual competition. The exam has been offered annually since 1938 and is administered by the Mathematical Association of America.

The Putnam competition now takes place on the first Saturday in December, and consists of two three-hour sittings separated by a lunch break. Each competitor attempts to solve twelve problems, nearly all mathematical proofs, which can typically be solved with only basic knowledge of college mathematics but which require extensive creative thinking.

Each of the twelve questions is worth 10 points, and the most frequent scores above zero are 10 points, for a complete solution; 9 points, for a nearly complete solution; and 1 point, for the beginnings of a solution. The examination is considered to be very difficult: it is typically attempted by students specializing in mathematics, but the median score is usually one or two points out of 120 possible, and perfect scores are exceptionally rare. In 2003, of the 3615 students taking the exam, 1024 (28%) scored 10 or more points, and 42 points was sufficient to make the top 102.

At a participating college, as many students as wish to take part in the exam may enter; but the school’s official team consists of three individuals whom it designates in advance. Team scoring is analogous to that used in cross-country running; a team’s score is the sum of the ranks of its three team members, with the lowest team score winning. It is entirely possible, even commonplace at some institutions, for the eventual results to show that the "wrong" team was picked — i.e., that some students not on the official team outscored the official team members. The top five teams win \$25,000, \$20,000, \$15,000, \$10,000, and \$5,000 respectively, with \$1,000, \$800, \$600, \$400, and \$200 for team members.

The top five individual scorers are named Putnam Fellows and awarded \$2,500. One of them is also awarded the William Lowell Putnam Prize Scholarship of \$12,000 plus tuition for graduate study at Harvard University. Sixth through 15th place individuals receive \$1,000 and the next ten receive \$250. The names of the top 100 students are published in American Mathematical Monthly.

In December 2003, the examination was taken by 3615 students from 479 colleges. The 2004 examination was held on December 4. The 2005 examination was held on December 3.

Many contestants have gone on to become distinguished researchers in mathematics and other fields. A number of them have received the Fields Medal or the Nobel Prize in Physics