FOM: rigor and intuition
vladik at cs.utep.edu
Wed Feb 13 14:27:37 EST 2002
> Date: Wed, 13 Feb 2002 17:17:46 +0000
> From: Vladimir Sazonov <V.Sazonov at csc.liv.ac.uk>
> > Matt's good point is that mathematics is not only about theorems, Witten's
> > stateents are also very useful, and many such statements are eventually
> > and transformed into theorems.
> > Vladik
> What you said about Witten's "theorems" may be called hypothesis.
The reason why I brought Witten as an example is that his hypotheses are
strongly supported by intuitive arguments.
The general word "hypothesis" includes both such statements and a more usual
case when there is no strong and convincing supporting intuition.
> Quite respectable (pre)mathematical things. Anyway, I hope, they are
> written in a formal language (differential equations, integrals,
> or whatever else).
> If they can be checked experimentally, then
> the are physical laws. As you say, they are eventually proven!
> Then, no doubts, this is mathematics.
> (But what will you say if no proof, no experiments support this?
> Is it still mathematics/physics or something preliminary, probably
> even a wrong way?)
You are right, since there is no proof, a statement can turn out to be wrong.
(it happened with Poincare's hypotheses).
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