# 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

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/