Airplanes crash. Proofs don't. Last year I asked if anyone could
give an example of a theorem which was published in a textbook
or reputable journal, accepted by the mathematicians who read
it and used by them in further work, and then found to be
false. No one ever came up with such an example.
I believe that an early "proof" of the four color theorem stood for
10-15 years before it was found to be incorrect.
Perhaps more to the point, mathematicians are shy of using results,
even their own, if the methods used to prove those results seem
suspicious. A formal proof would allay those suspicions.
D.N. Hoover
a.k.a.
hoove@oracorp.com