Re: Rigor in contemporary mathematics

Zdzislaw Meglicki (
Thu, 12 Aug 1993 09:43:32 +1000 (EST)

In <9308111300.AA02955@dilbert.CLI.COM> boyer@CLI.COM writes:

> The article by Jaffe and Quinn
> concerns the growing influence of superstring theory on mathematics,
> raises questions about rigor in proof in some recent mathematics, and
> recommends that conjectural work should be clearly distinguished from
> rigorous proof. Not a distinction that I, in my naivete, would have
> thought any contemporary mathematicians would have doubted.

The areas of mathematics which are most likely to be based on some
sloppy and unfinished ideas would also be the most difficult to verify
using automatic tools. Precisely because of their sloppiness and
intuitiveness. Much of modern Quantum Field Theory (including
superstrings) is based on such sloppy mathematics. The reason for that,
however, is that mathematics lags behind what is needed in physics in
this respect and the physicists, quite rightly I think, aren't prepared
to wait for the mathematicians to put their act together. This in many
ways has always been the case. Physicists were using analysis since
Newton, but the truly precise formulation of the theory came only 200
years later. Would QED be helpful in speeding up this process?

Zdzislaw Meglicki,,
Automated Reasoning Program - CISR, and Plasma Theory Group - RSPhysSE,
The Australian National University, G.P.O. Box 4, Canberra, A.C.T., 2601,
Australia, fax: (Australia)-6-249-0747, tel: (Australia)-6-249-0158