The Sixty-Ninth William Lowell Putnam Mathematical Competition
Bibliographic record
Abstract
The results of the Sixty-Ninth William Lowell Putnam Mathematical Competition, held December 6, 2008, follow. They have been determined in accordance with the regulations governing the Competition. The contest is supported by the William Lowell Putnam Prize Fund for the Promotion of Scholarship, an endowment established by Mrs. Putnam in memory of her husband. The annual Competition is held under the auspices of the Mathematical Association of America. The first prize, $25,000, was awarded to the Department of Mathematics of Harvard University. The members of the winning team were Zachary R. Abel, Iurie Boreico, and Arnav Tripathy; each was awarded a prize of $1,000. The second prize, $20,000, was awarded to the Department of Mathematics of Princeton University. The members of the winning team were Peter Z. Diao, John V. Pardon, and Adrian I. Zahariuc; each was awarded a prize of $800. The third prize, $15,000, was awarded to the Department of Mathematics of the Massachusetts Institute of Technology. The members of the winning team were Qingchun Ren, Xuancheng Shao, and Yufei Zhao; each was awarded a prize of $600. The fourth prize, $10,000, was awarded to the Department of Mathematics of Stanford University. The members of the winning team were Young Hun Jung, Nathan K. Pflueger, and Jeffrey Wang; each was awarded a prize of $400. The fifth prize, $5,000, was awarded to the Department of Mathematics of the California Institute of Technology. The members of the winning team were Jason C. Bland, Zarathustra E. Brady, and Brian R. Lawrence; each was awarded a prize of $200. The five highest ranking individual contestants, the Putnam Fellows, in alphabetical order, were Brian R. Lawrence, California Institute of Technology; Seok Hyeong Lee, Stanford University; Arnav Tripathy, Harvard University; Bohua Zhan, Massachusetts Institute of Technology; and Yufei Zhao, Massachusetts Institute of Technology. Each received an award of $2,500. The next eleven highest ranking individual contestants, in alphabetical order, were Iurie Boreico, Harvard University; Adam C. Hesterberg, Princeton University; William A. Johnson, University of Washington; Cedric Lin, University of British Columbia; Anton S. Malyshev, Princeton University; John V. Pardon, Princeton University; Qingchun Ren, Massachusetts Institute of Technology; Oleg O. Rudenko, Florida Atlantic University; Colin P. Sandon, Massachusetts Institute of Technology; Jacob N. Steinhardt, Massachusetts Institute of Technology; and Alex Zhai, Harvard University. Each received an award of $1,000. The next nine highest ranking individual contestants, in alphabetical order, were Zachary R. Abel, Harvard University; Thomas D. Belulovich, Massachusetts Institute of Technology; Jason C. Bland, California Institute of Technology; Gabriel T. Bujokas, Massachusetts Institute of Technology; Konstantin Matveev, University of Toronto; Nathan K. Pflueger, Stanford University; Aaron H. Potechin, Princeton University; Dong Uk Rhee, University of Waterloo; and Adrian I. Zahariuc, Princeton University. Each received an award of $250.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.010 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.006 | 0.003 |
| Scholarly communication | 0.011 | 0.005 |
| Open science | 0.002 | 0.008 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.141 | 0.077 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".