| Ano | Nome | Motivo da premiação |
| 1923 | George David Birkhoff | por Dynamical systems with two degrees of freedom (Transactions of the American Mathematical Society, volume 18 (1917), pp. 199-300) |
| 1924 | Eric Temple Bell | por Arithmetical paraphrases (I, II, Transactions of the American Mathematical Society, volume 22 (1921), pp. 1-30, 198-219) |
| Solomon Lefschetz | por On certain numerical invariants with applications to Abelian varieties (Transactions of the American Mathematical Society, volume 22 (1921), pp. 407-482) |
| 1928 | James Waddell Alexander | por Combinatorial analysis situs (Transactions of the American Mathematical Society, volume 28 (1926), pp. 301-329) |
| 1933 | Marston Morse | por The foundations of a theory of the calculus of variations in the large in m-space (Transactions of the American Mathematical Society, volume 31 (1929), pp. 379-404) |
| Norbert Wiener | por Tauberian theorems (Annals of Mathematics, Series 2, volume 33 (1932),pp. 1-100) |
| 1938 | John von Neumann | por Almost periodic functions and groups (I, II, Transactions of the American Mathematical Society, volume 36 (1934), pp. 445-492, e volume 37 (1935), pp. 21-50) |
| 1943 | Jesse Douglas | por Green's function and the problem of Plateau (American Journal of Mathematics, volume 61 (1939), pp. 545-589); The most general form of the problem of Plateau (American Journal of Mathematics, volume 61 (1939), pp. 590-608) e Solution of the inverse problem of the calculus of variations (Proceedings of the National Academy of Sciences, volume 25 (1939), pp. 631-637) |
| 1948 | Albert Charles Schaeffer e Donald Spencer |
por Coefficients of schlicht functions (I, II, III, IV, Duke Mathematical Journal, volume 10 (1943), pp. 611-635, volume 12 (1945), pp. 107-125) e em (Proceedings of the National Academy of Sciences, volume 32 (1946), pp. 111-116, volume 35 (1949), pp. 143-150) |
| 1953 | Norman Levinson | |
| 1959 | Louis Nirenberg | |
| 1964 | Paul Joseph Cohen | por On a conjecture of Littlewood and idempotent measures (American Journal of Mathematics, volume 82 (1960), pp. 191-212) |
| 1969 | Isadore Singer | |
| 1974 | Donald Samuel Ornstein | por Bernoulli shifts with the same entropy are isomorphic (Advances in Mathematics, volume 4 (1970), pp. 337-352) |
| 1979 | Alberto Calderón | |
| 1984 | Luis Caffarelli | |
| Richard Burt Melrose | |
| 1989 | Richard Schoen | |
| 1994 | Leon Simon | |
| 1999 | Demetrios Christodoulou | |
| Sergiu Klainerman | |
| Thomas Wolff | por seu trabalho na área da análise de Fourier. |
| 2002 | Daniel Tătaru | por On global existence and scattering for the wave maps equations (Amer. Jour. of Math. 123 (2001) no. 1, 37–77) |
| Terence Tao | |
| Lin Fanghua | |
| 2005 | Frank Merle | |
| 2008 | Alberto Bressan | |
| Charles Fefferman | |
| Carlos Kenig | |
| 2011 | Gunther Uhlmann | |
| Assaf Naor | |
| 2014 | Simon Brendle | |
| 2017 | András Vasy | por Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces, Inventiones Mathematicae, 194 (2013), 381513. |
| 2020 |
Camillo De Lellis |
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| Larry Guth |
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| Laure Saint-Raymond |
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