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 forty-one 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 == ℝ3 .'' Essays on Fourier analysis in honor of Elias M. Stein (Princeton, NJ, 1991), 321–384, Princeton Math. Ser., 42, Princeton Univ. Press, Princeton, NJ, 1995 L2 -critical generalized KdV equation.'' J. Amer. Math. Soc. 15 (2002), no. 3, 617–664 [written with Yvan Martel] L2 critical nonlinear Schrödinger equation.'' Invent. Math. 156 (2004), no. 3, 565–672 [with Pierre Raphael] Cm .'' Ann. of Math. (2) 164 (2006), no. 1, 313–359. L1 .'' Acta Math. 207 (2011), no. 2, 291–373 [written with Jeff Cheeger and Bruce Kleiner] S3 and the Lawson conjecture.'' Acta Math. 211 (2013), no. 2, 177–190. ℝ2 .'' Ann. of Math. (2) 186 (2017), no. 2, 607–640 [written with Xiumin Du and Xiaochun Li]