JF Ptak Science Books *Quick Post*

This is just a short bibliographic note on David Hilbert's great paper of 1900--this a result of trying to figure out where a particular French translation occurred in the history of the printing of the paper.

The paper in question is David Hilbert ** **"Problemes Mathematiques*"* , printed in Paris by Librairie armand Colin (28 Fevrier 1901, 12^{e} annee, No. 4) in the publication *Revue generale des Sciences pures et applique*s. This is a revised printing of the 2nd printing of Hilbert's "great problems" speech (taken from *The Archives of Mathematics)*, in which the he famously posed his 23 problems. "The Problems of Mathematics" was delivered to the Second International Congress of Mathematicians in Paris and outlined major issues of math

"...which would challenge mathematicians to solve fundamental problems in the maths for years to come. It was a speech full of optimism for mathematics in the coming century and he felt that open problems were the sign of vitality in the subject: The great importance of definite problems for the progress of mathematical science in general ... is undeniable. ... [for] as long as a branch of knowledge supplies a surplus of such problems, it maintains its vitality. ... every mathematician certainly shares ..the conviction that every mathematical problem is necessarily capable of strict resolution ... we hear within ourselves the constant cry: There is the problem, seek the solution. You can find it through pure thought... Hilbert's problems included the continuum hypothesis, the well ordering of the reals, Goldbach's conjecture, the transcendence of powers of algebraic numbers, the Riemann hypothesis, the extension of Dirichlet's principle and many more. Many of the problems were solved during this century, and each time one of the problems was solved it was a major event for mathematics".--*A Century of Advancing Mathematics* by Paul Zorn, pg 321.

It seems as though this is the second of the early printings of this classic (though third if you include an earlier and truncated French translation):

- Hilbert, "Mathematische Probleme", lecture held at the Paris ICM 1900,
*Nachrichten von der Koniglichen Gesellschaft der Wissenschaften zu Gottingen*(1900), HEFT 3, making this the third quarter of 1900), pp 253-297; revised version in*Archiv der Mathematik und Physik*1 (1901) 44-63, 213-237, and [58:3, pp. 290-329] - The first English translation (by Mary W. Newson) in
*Bulletin of the American Mathematical Society*, 8 (1901) 437-479 - French translations by L. Laugel (with corrections and additions) in
*Compte rendu du deuxieme congres international des mathematiciens tenu `a Paris du 6 au 12 aout 1900*, E. Duporcq, ed., Gauthier-Villars, Paris, 1902, pp. 58-114; (fragments).*L'Enseignement Mathematique*2 (1900) 349-354.