FOM: rigor and intuition
V.Sazonov at csc.liv.ac.uk
Wed Feb 13 12:17:46 EST 2002
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.
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.
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