The Mathematical Problems of David Hilbert

About Hilbert's address and his 23 mathematical problems

Hilbert's address of 1900 to the International Congress of Mathematicians in Paris is perhaps the most influential speech ever given to mathematicians, given by a mathematician, or given about mathematics. In it, Hilbert outlined 23 major mathematical problems to be studied in the coming century. Some are broad, such as the axiomatization of physics (problem 6) and might never be considered completed. Others, such as problem 3, were much more specific and solved quickly. Some were resolved contrary to Hilbert's expectations, as the continuum hypothesis (problem 1).

Hilbert's address was more than a collection of problems. It outlined his philosophy of mathematics and proposed problems important to his philosophy.

Although almost a century old, Hilbert's address is still important and should be read (at least in part) by anyone interested in pursuing research in mathematics.

In 1974 a symposium was held at Northern Illinois University on the Mathematical developments arising from Hilbert problems. A major mathematician discussed progress on each problem and how work on the problem has influenced mathematics. Also, 23 new problems of importance were described. The two-volume proceedings of the symposium was edited by Felix Browder and published by the American mathematical Society in 1976. See also Irving Kaplansky's Hilbert's problems, University of Chicago, Chicago, 1977.

There is also a collection on Hilbert's Problems, edited by P. S. Alexandrov, Nauka, Moscow, 1969, in Russion, which has been translated into German.

This site on the web

The address itself is available here in html format. It is 107k with 45 small gif files (since html doesn't do all the mathematical symbols yet). So it may take a little while to load. Also, there is a brief table of contents which links into the address itself.

Other sites on the web

Hilbert's original German text Mathematische Probleme is located at http://www.mathematik.uni-bielefeld.de/~kersten/hilbert/rede.html.
Ivor Grattan-Guinness' article "A sideways look at Hilbert's twenty-three problems of 1900" appeared in the Notices of the AMS, 2000. It's on the web in PDF form at http://www.ams.org/notices/200007/fea-grattan.pdf.
Jeremy Gray's article: "The Hilbert problems 1900-2000" appeared in the Newsletter 36 of the European Mathematical Society 2000, 10-13. It's on the web at http://www.mathematik.uni-bielefeld.de/~kersten/hilbert/gray.html.
Maxim Vsemirnov's Hilbert's Tenth Problem page at the Steklov Institute of Mathematics at St.Petersburg, and Yuri Matiyasevich's book Hilbert's Tenth Problem.

March, 1997.
David E. Joyce
Department of Mathematics and Computer Science
Clark University
Worcester, MA 01610

These files are located at http://aleph0.clarku.edu/~djoyce/hilbert/