1. The Putnam Exam During Year Zero
USMA-Harvard Math Competition of 1933
Presented By:
CPT Michelle Isenhour
Western Michigan University

2. Putnam Mathematical Competition
Conducted by the MAA
Began in 1938 and has prospered since
Named after the late William Lowell Putnam
12 questions in two three-hour sessions
Individual and team awards

3. The Legacy of Putnam
1921 – Putnam suggested the development of academic competition
1928 – English competition between Harvard and Yale (Harvard won)
Yale and Princeton declined further competitions in English
Cambridge declined competition in Economics

4. The Trouncing… November 1932 – Army trounced Harvard in football 46-0
President Lowell proclaimed that Harvard “could just as easily win any contest of a more academic nature”

5. The Challenge…
“…I would very much like to test our method of teaching mathematics against that of your institution. I, frankly, think our method is superior to yours, and would like to try it out.”
-Major General Connor, Superintendent of
the United States Military Academy in a letter to President Lowell

6. Preparations for the Competition
Rules delegated to department heads
Lieutenant Colonel Harris Jones, USMA
Professor William C. Graustein, Harvard
Exchanged information about curricula, pedagogy, and students

7. West Point Curricula Four semester core curriculum Subjects
Freshmen: 8 hours per week
Sophomores:4 hours per week
Subjects
Algebra and Trigonometry
Solid and Analytic Geometry
Differential and Integral Calculus
Least Squares (upper 1/3 of class)

8. Harvard Curricula Freshmen Sophomores Met for 3 hours per week
Textbooks
Osgood and Graustein, Plane and Analytic Geometry
Osgood’s Introduction to Calculus
Sophomores
Under guidance of tutors
Subjects
Analytic Geometry
Algebra

9. Oscillation Begins… Resolved Issues Unresolved Issues
Topics examined: analytic geometry and calculus
Sophomores examined in May 1933
Unresolved Issues
West Point wanted contestants, Harvard 10
Home Team and Host
Length of Test

10. Continues… LTC Jones, USMA
Offered to lower the number of contestants to 15 and have his team travel to Harvard for the test on 20 May
Suggested one three-hour test claiming six-hours would “convert and interesting contest into dull drudgery and kill the enthusiasm of the competition”

11. Continues… Professor Graustein, Harvard
Established the number per side as 10
No expectation that the Military Academy would bear any part of the expense
Two three-hour sessions with the second more challenging
Twice as much calculus as analytic geometry and include theoretical questions on test
Allow formula cards, logarithm tables, and Pierce’s Integral Tables as references
Harvard would be happy to travel to West Point

12. …and Ends LTC Jones, USMA
Agreed to two-part test and use of Pierce’s Integral Tables
Scoring would be that used in cross-country meets

13. Completing the Committee
President of the MAA – the body which stands for collegiate mathematics in this country
Professor Arnold Dresden seemed almost ‘ordained’ for the job and accepted the invitation

14. Scope of the Examination (1 of 2)
Plane Analytic Geometry
Distance from a point to a line
Conics – Derivation of equations in rectangular and polar coordinates
General equation of the second degree; simplification by translations and rotation of coordinate axes
Locus problems involving applications of the above
Solid Analytic Geometry
Equations of straight lines and planes
Distance from point to a plane or line
Equations of spheres, cylinders, cones, surfaces of revolution
Elementary properties of quadric surfaces

15. Scope of the Examination (2 of 2)
Calculus
Curve tracing
Velocity, acceleration, rates
Radius and center of curvature
Evolutes
Taylor’s Theorem, functions of one variable
Series – tests for convergence, expansion of functions, integration
Applications to mechanics, center of gravity, moment of inertia, radius of gyration, attraction, fluid pressure, work
Elementary differential equations, first order, linear equations with constant coefficients, orthogonal trajectories, simple equations of higher order

16. Preparations for Battle – West Point
West Point Team Statement
“We are really series about this contest. We really mean it. We’re just dyne to meet those dumb Harvard guys, and we’re determinant to win. We all hope to make our integral signs.”

17. Preparations for Battle – West Point
From March 15 – May 20
Excused from parade 3 days a week
Excused from intramural athletics
Drilled in extra mathematics two afternoons a week

18. Preparations for Battle - Harvard
Confident of Victory
Took a lighter approach
Met with coach about four times
Assumed Harvard intellects would easily carry the day

19. “The Coordinate Clash, or Block that Abscissa”
Pre-game Publicity
Sports section of New York Times
“Sports of the Times” column by John Kieran on May 18, 1933
“The Coordinate Clash, or Block that Abscissa”

21. Other Headlines “Army meets Harvard in Mathematical ‘Go’”
“Squads at West Point Begin Contest in Calculus and Analytic Geometry”
“Harvard and West Point Line up on the Geometry Field”

22. The Test Part I – Friday, May 19: 3 hours
11 problems: 6 analytic geometry, 2 differential calculus, 3 integral calculus
Part II – Saturday, May 20: 3 hours
11 problems: 1 logarithms, 3 analytic geometry, 6 differential calculus, 1 integral calculus
Not as difficult, nor as challenging, as the first National Putnam Examination given on April 16, 1938

23. And the Winner is… “Crimson Bow to West Point Mathematicians”
“Harvard Mathematics Team Outfigured by West Pointers”

24. The After Math
All members of the Army team finished in the top 20 of their graduating class; seven of the ten spent over 20 years in the Army; most later became professors and obtained their Ph.D. None were mathematicians; all were engineers

25. Putnam’s Legacy Harvard-USMA competition was not repeated
Putnam’s sons, George and August, consulted with George Birkhoff of Harvard to keep the dream alive
Birkhoff and colleagues from the department wrote the first national examination in 1938
Set up continuing principles for the competition
Teams consist of three people
Tests are administered by the MAA
Prizes are distributed to several top teams
and individuals

26. Conclusion
“Through the efforts of Birkhoff and many others, and the experience garnered from the Harvard-USMA Competition of 1933, the annual William Lowell Putnam Mathematics Competition came into existence in 1938 and has prospered in the 50 years since.”
-David C. Arney and George Rosenstein
“USMA-Harvard Math Competition”, 2000

27. References:
Arney, David C. and George Rosenstein. “USMA-Harvard Math Competition.” Available from
Arney, David C. “Army Beats Harvard.” Math Horizons. Sept. 1994: 14 – 17.
Kieran, John. “The Coordinate Clash, or Block That Abscissa!” New York Times 18 Mar. 1933: 17.
“Army ‘Mathletes’ Defeat Harvard, ; Cadet Smith is First in Calculus Affray.” New York Times 5 June 1933: 4.
Copy of Briefing Available from: