The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450 (contributed by members of that society). It is awarded every three years (formerly every five years) for a notable research work in analysis that has appeared during the past six years. The work must be published in a recognized, peer-reviewed venue. The current award is $5,000. There have been thirty-seven prize recipients. The first woman to win the award, Laure Saint-Raymond, did so in 2020. About eighty percent of the journal articles recognized since 2000 have been from Annals of Mathematics, the Journal of the American Mathematical Society, Inventiones Mathematicae, and Acta Mathematica. Past winners 1923 George David Birkhoff for Dynamical systems with two degrees of freedom. Trans. Amer. Math. Soc. 18 (1917), 119-300. 1924 Eric Temple Bell for Arithmetical paraphrases. I,II. Trans. Amer. Math. Soc. 22 (1921), 1-30, 198-219. 1924 Solomon Lefschetz for On certain numerical invariants with applications to Abelian varieties. Trans. Amer. Math. Soc. 22 (1921), 407-482. 1928 James W. Alexander II for Combinatorial analysis situs. Trans. Amer. Math. Soc. 28 (1926), 301-329. 1933 Marston Morse for The foundations of a theory of the calculus of variations in the large in m-space. Trans. Amer. Math. Soc. 31 (1929), 379-404. 1933 Norbert Wiener for Tauberian theorems. Ann. Math. 33 (1932), 1-100. 1938 John von Neumann for Almost periodic functions. I. Trans. Amer. Math. Soc. 36 (1934), 445-294 Almost periodic functions. II. Trans. Amer. Math. Soc. 37 (1935), 21-50 1943 Jesse Douglas for Green's function and the problem of Plateau. Amer. J. Math. 61 (1939), 545-589 The most general form of the problem of Plateau. Amer. J. Math. 61 (1939), 590-608 Solution of the inverse problem of the calculus of variations. Proc. Natl. Acad. Sci. U.S.A. 25 (1939), 631-637. 1948 Albert Schaeffer and Donald Spencer for Coefficients of schlicht functions. I. Duke Math. J. 10 (1943), 611-635 Coefficients of schlicht functions. II. Duke Math. J. 12 (1945), 107-125 Coefficients of schlicht functions. III. Proc. Natl. Acad. Sci. U.S.A. 32 (!946), 111-116 Coefficients of schlicht functions. IV. Proc. Natl. Acad. Sci. U.S.A. 35 (1949), 143-150. 1953 Norman Levinson for "his contributions to the theory of linear, nonlinear, ordinary, and partial differential equations contained in his papers of recent years" 1959 Louis Nirenberg for "his work in partial differential equations" 1964 Paul Cohen for On a conjecture