[FOM] Certificates are fully practical

[Rempe-Gillen, Lasse]

Timothy Y. Chow wrote:

> I think it's overstating the case to say that no mathematician cares what happens with proofs that are too long to be actually verified.  Consider examples such as Catalan's conjecture or Kepler's conjecture.  In both cases, they were reduced to a finite but infeasible computation a rather long time before they were completely settled.  If it were the case that "no mathematician cared" then the reduction to a finite computation would presumably have been considered no better than no proof at all.  But that's not in fact how they were viewed.  The reduction to a finite computation was regarded as "almost" a proof of the conjecture itself.

Vinogradov's theorem and Helfgott's recent proof of the odd Goldbach conjecture should perhaps also be mentioned in this context. 

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Professor Lasse Rempe-Gillen
Pure Mathematics Cluster Coordinator and
 Deputy Head of Department for REF
Dept. of Math. Sciences, Univ. of Liverpool, Liverpool L69 7ZL
Office 520; tel. +44 (0)151 794 4025, fax +44 (0)151 794 4061
http://pcwww.liv.ac.uk/~lrempe
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