William Lowell Putnam Mathematical Competition

The William Lowell Putnam Mathematical Competition, often abbreviated to the Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regardless of the students' nationalities). It awards a scholarship and cash prizes ranging from $250 to $2,500 for the top students and $5,000 to $25,000 for the top schools, plus one of the top five individual scorers (designated as Putnam Fellows) gets graduate tuition waived at Harvard (Putnam Fellow Prize Fellowship), and the top 100 individual scorers have their names mentioned in the American Mathematical Monthly's October issue (alphabetically ordered within rank). It is widely considered to be the most prestigious university-level mathematics examination in the world, and its difficulty is such that the median score is often zero or one (out of 120) despite being attempted by students specializing in mathematics.

The competition was founded in 1927 by Elizabeth Lowell Putnam in memory of her husband William Lowell Putnam, who was an advocate of intercollegiate intellectual competition. The exam has been offered annually since 1938 and is administered by the Mathematical Association of America.

Competition layout

The Putnam competition now takes place on the first Saturday in December, and consists of two three-hour sittings separated by a lunch break. The test is supervised by faculty members at the participating schools. Each competitor attempts to solve twelve problems, 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. In earlier years, the twelve questions were worth one point each, with no partial credit given. The examination is considered to be very difficult: it is typically attempted by students specializing in mathematics, but the median score is usually zero or one point out of 120 possible, and there have been only four perfect scores as of 2010. In 2003, of the 3,615 students taking the exam, 1024 (28%) scored 10 or more points, and 42 points was sufficient to make the top percentile.

At a participating college, any student who wishes to take part in the exam may compete (limited by the number of exams a school receives); but the school's official team consists of three individuals whom it designates in advance. A team's score is the sum of the ranks of its three team members, with the lowest cumulative rank 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 an official team member. For example, in 2010, MIT had two of the top five scorers on the examination and seven of the top 24, while Caltech had just one student in the top five and only four in the top 24; yet Caltech took first place among teams while MIT took second.

The top five teams win $25,000, $20,000, $15,000, $10,000, and $5,000, in that order, with team members receiving $1,000, $800, $600, $400, and $200, respectively.

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 the American Mathematical Monthly. Many Putnam Fellows have gone on to become distinguished researchers in mathematics and other fields, including three Fields Medalists—Milnor, Mumford, and Quillen—and two Nobel laureates in physics—Feynman and Wilson.^[1]

Winners

Top-scoring teams

Teams ranked by historical performance

Below is a table of teams by the number of appearances in the top five and number of titles.

The following table lists Teams finishing in Top Five (as of 2014 competition):

For a recent analysis, the following table lists teams that finished in the top five since 2000 (as of 2014 competition):

The following table lists Teams with First place finishes (as of 2014 competition):

Putnam Fellows

Since the first competition, the top five (or six, in case of a tie) scorers on the examination have been named Putnam Fellows. Within the top five, Putnam Fellows are not ranked. Students are not allowed to participate in the Putnam Competition more than four times. For example, if a high school senior chooses to officially participate, he/she effectively chooses to forfeit one of his/her years of eligibility in college (see Gabriel D. Carroll). This makes it even more of a remarkable feat to become a Putnam Fellow four times. In the history of Competition, only eight students have been Putnam Fellows four times, with twenty others winning the award three times. The following table lists these students:

The following table lists all Putnam fellows from 1938 to present, with the years they placed in the top five.

Elizabeth Lowell Putnam Award winners

Since 1992, the Elizabeth Lowell Putnam Award has been available to be awarded to a female participant with a high score. The year(s) in which they were Fellows are in bold.

Notes

References

• Gallian, Joseph A. (October 2004), "The First sixty-six years of the Putnam competition", American Mathematical Monthly 111: 691–699, doi:10.2307/4145042, retrieved 21 November 2012 

External links

Wikimedia Commons has media related to Putnam Fellows.

• William Lowell Putnam Mathematical Competition official site
• William Lowell Putnam Mathematical Competition results
• William Lowell Putnam Competition problems, solutions, and results archive
• Archive of Putnam Problems and Student Solutions
• Archive of Problems 1938-2003
• The Harvard-United States Military Academy Mathematics Competition of 1933: Genesis of the William Lowell Putnam Mathematical Competition
• Searchable data base for information about careers of Putnam Fellows
• A comprehensive history of the Putnam competition. An electronic update of Gallian's 2004 paper.