FOM: rigor and intuition

[Vladik Kreinovich]

> 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 
proven
> > and transformed into theorems.
> > 
> > Vladik
> 
> What you said about Witten's "theorems" may be called hypothesis. 

I agree. 

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).

Yes.

> 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). 

Vladik