The American Mathematical Society awards two prizes named in honor of Prof. Frank Nelson Cole, a senior member of the AMS who made a bequest to the society in 1928 upon his retirement. This bequest was subsequently augmented by Frank's son Charles. Two separate Cole Prizes are awarded at regular intervals for outstanding contributions in algebra and number theory.
Among prominent mathematicians to have received the award were Walter Feit and John G. Thompson (1965, in recognition for the Feit-Thompson theorem in group theory), Michel Raynaud and David Harbater (1995, for their solution of Abhyankar's conjecture), and Andrew J. Wiles (1997, for his proof of Fermat's last theorem).
The following table lists winners of the Frank Nelson Cole Prize in algebra.
| year | winner(s) |
| 1928 | L. E. Dickson |
| 1939 | A. Adrian Albert |
| 1944 | O. Zariski |
| 1949 | R. Brauer |
| 1954 | Harish-Chandra |
| 1960 | S. Lang, M. A. Rosenlicht |
| 1965 | W. Feit, J. G. Thompson |
| 1970 | J. R. Stallings, R. G. Swan |
| 1975 | H. Bass, D. G. Quillen |
| 1980 | M. Aschbacher, M. Hochster |
| 1985 | G. Lusztig |
| 1990 | S. Mori |
| 1995 | M. Raynaud, D. Harbater |
| 2000 | A. Suslin, A. J. de Jong |
| 2003 | H. Nakajima |
| 2006 | J. Kollár |
| 2009 | C. Hacon and J. McKernan |
The following table lists winners of the Frank Nelson Cole Prize in number theory.
| year | winner(s) |
| 1931 | H. S. Vandiver |
| 1941 | C. Chevalley |
| 1946 | H. B. Mann |
| 1951 | P. Erdős |
| 1956 | J. T. Tate |
| 1962 | K. Iwasawa, B. M. Dwork |
| 1967 | J. B. Ax, S. B. Kochen |
| 1972 | W. M. Schmidt |
| 1977 | G. Shimura |
| 1982 | R. P. Langlands, B. Mazur |
| 1987 | D. M. Goldfeld, B. H. Gross, D. B. Zagier |
| 1992 | K. Rubin, P. Vojta |
| 1997 | A. J. Wiles |
| 2002 | H. Iwaniec, R. Taylor |
| 2005 | P. Sarnak, |
| 2008 | M. Bhargava |
