Omnis scientia questio est. Much has been said about this paper over the last century, and there is little profit in running over the 23 problems here. What the reviewer has always found interesting and profitable are the first six pages of introduction and the coda on the last page. The first six pages state, briefly, knowledge lies in the question, and the coda says that the answer will vary from age to age as mathematics develops. Inbetween, Hilbert stresses accessability; abstraction and generality; the rethinking of mathematics again and again to make it possible for those of today to cope with the amount, width and depth of its developments; and finally the unity of mathematics. Then there are the warnings: death lies in inactivity: no questions – and in stasis: refusal to adopt the “sharper tools and simpler methods” which mathematical developments bring.
Reprinted from Bull. Am. Math. Soc. 8, 437–479 (1902; JFM 33.0976.07) which is a translation from Gött. Nachr. 1900, 253–297 (1900; JFM 31.0068.03).