From: rusin@vesuvius.math.niu.edu (Dave Rusin) Subject: Re: Problem for the 21'st century Date: 3 Oct 1999 20:52:07 GMT Newsgroups: sci.math Keywords: [missing] In article <37f7b499.757217109@news.erols.com>, wrote: >>In 1900 Hilbert gave 23 problems before the 1990 International Congress of >>Mathematics at Paris. A slightly expanded discussion is in the sci.math FAQ; see also 95/hilb.list Proceedings of a conference reviewing progress on the problems are in "Mathematical Developments Arising from the Hilbert Problems", Proc Symp Pure Math AMS, vol 28 (1976) Some are solved, some proved unsolveable, some open. But I would like to comment that Hilbert's list was directed to mathematicians, not to young students; in particular, they are not interpreted as narrow, "prove-this" questions. Rather, they are open-ended directives drawing attention to questions of the form, "What can one say about..." >5. Is this list truely the Holy Grail of mathematics? Well, some of the questions are particularly central to mathematics of the 20th century. For example, there are many results which state, "If the Riemann Hypothesis is true, then...". But some of the questions are now seen as comparatively minor. >6. Similarily, Is this list relevant to you or has late 20th cent. math > gone in other directions? Where? (Okay, that was 2 questions). To a large extent Hilbert's questions _caused_ 20th-century mathematics to be as it became. The developments of mathematical logic and algebraic geometry in particular strike me as having been engendered by Hilbert. Hilbert couldn't have foreseen the impact of computers and technology on mathematics and science, which have indirectly nutured many now-large areas of mathematics, which were mere backwaters in 1900: combinatorics, numerical analysis, operations research, ... dave