FOM: rigor and intuition

Vladik Kreinovich vladik at
Mon Feb 11 15:16:41 EST 2002

> There is also a question about rigor and intuition in proofs, somewhat
> different from the question previously being discussed.  Proofs may be
> more or less rigorous and more or less intuitive.  Some prominent
> mathematicians (notably the geometers Gromov and Thurston) have 
> preferred to find intuitive proofs and present their proofs intuitively,
> and think there are more important things to do than worry about how to
> present the proofs rigorously.  This is perhaps a more interesting example
> of rigor giving way.

I agree 100% that most mathematicians prefer proofs presented in a clear and 
understandable way, and having taking classes from Gromov I think he is good at 

I would be, however, very careful as classifying this phenomenon as "rigor 
giving way". This phrase seems to imply, to me, a meaning that Gromov does not 
actually prove his results (in the normal mathematical sense of this word), 
just presents some intuitive arguments for them. This is absolutely not true. 
He HAS proofs - as judged by the math community and by the referees of his 
numerous papers, but he does not present them in all gory detail in his 
lectures and his papers. 

I am not sure if Matt had this meaning in mind or not, I just wanted to 
emphasize that this phrase may be interpreted this way.  

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