FOM: rigor and intuition

[Vladimir Sazonov]

Vladik Kreinovich wrote:
> 

> 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. 
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?) 

Probably such peoples 
as Witten have also subconscious (semi)proofs in their heads. 
They cannot explain, but others can do this later. 


Vladimir