apak@oddjob.UUCP (Adrian Kent) (01/22/86)
I'm trying to think of great, surprising uniqueness theorems in mathematics;
results of the form "The only quasi-sober, Reaganomic hemi-demi-semi-group is
the group of 3 by 3 matrices with entries algebraic functions of pi."
The motivation for this is that, if a currently popular theory of nature
(superstring theory) is to work, it will require such a theorem. (Actually,
the theory already contains a couple of surprising uniqueness results, but
what it still needs - the selection of an ugly-looking 6-manifold on grounds
of uniqueness - seems much harder.) My current feeling is that the required
result would be much more surprising than almost any previous uniqueness
result anywhere in mathematics. So I'd be very interested in people's best
candidates. I'll post a summary to the net, if there's interest.
regards,
ak
"Salome, dear, NOT in the fridge."ark@alice.UucP (Andrew Koenig) (01/22/86)
Well, there's the classification of the finite simple groups. This theorem was recently discussed in an article in Scientific American. It is actually the result obtained by looking at a collection of some 500 journal articles with a total of 15,000 pages or so. Its result is something like "All finite simple groups fall into one of the following classes, except for the following specific groups: ..."