The First Sixty-Six Years of the Putnam Competition

tary Academy at West Point [1]. That competition was sponsored by Elizabeth Lowell Putnam in honor of her late husband William Lowell Putnam, who was a member of the Harvard class of 1882. That competition went so well that plans were made to have an annual competition in which all interested institutions could participate. This came about in 1938, when the first official Putnam competition was sponsored by the Mathematical Association of America. The examination was prepared and graded by members of the Harvard mathematics department and Harvard students were excluded the first year. There were both individual and team competitions. The questions were drawn from calculus, the theory of equations, differential equations, and geometry. (The problems are included at the end of this article.) Prizes in the first few years were $500, $300, and $200 for the top three teams and $50 each for the top five ranking individuals, who were designated as Putnam Fellows. By the year 2003 the prizes for the top five teams were $25,000, $20,000, $15,000, $10,000, and $5,000, while Putnam Fellows received $2,500 each. Moreover, each year one Putnam Fellow receives the William Lowell Putnam Fellowship for graduate study at Harvard. The first competition had 163 individuals and 42 teams. The number of participants exceeded 1,000 for the first time in 1961, when 1,094 individuals and 165 teams took part. In 2003 there were 3,615 students representing 479 institutions and 401 teams. The number of participants in the 2003 competition alone exceeds the total number of participants in the first seventeen competitions from 1938 through 1957. (The competitions were suspended from 1943-1945 because of World War II; in 1958 there were two competitions-one in the spring and one in the fall.) Coincidentally, in both 1980 and 1981 there were exactly 2,043 participants. Through 2003, there have been 96,534 participants. The 100,000 mark will likely be reached in 2004. The 1946 contest, coming right after the war, had the lowest participation ever with just 67 contestants and 14 teams. Table 1 provides the list of the number of participants in each of the sixty-four competitions through 2003. In the first twenty-two competitions the number of questions varied from eleven to fourteen, but beginning with the 23rd competition in 1962, the exams have consisted of a three-hour morning session and a three-hour afternoon session, each having six questions worth ten points apiece. Institutions entering teams must designate the three team members before the competition is held. The team score is the sum of the ranks of the three team members. Thus, a team whose members finish in twenty-first, fortyninth, and one hundred and second places has a score of 172. The lower a team's score, the higher its ranking. This method of team scoring places great weight on the lowest scoring member of the team since there is much bunching at lower scores. For example, in 1988 a team member with a score of ten ranked 1496, but a team member with a score of nine ranked 1686. In 2001 a score of one point generated 1469.5 team points, whereas a score of zero on that exam resulted in 2292 team points. Thus, a few