Errors in the Literature

Richard Schroeppel (
Fri, 18 Nov 1994 12:26:39 MST

Lyle Burkhead <> ...
> 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 the published mathematics literature contains a significant
number of errors. Most are at the typo level, but there are some
number of missing terms, missing hypotheses, and important wrong words.
Long calculations, and tables, frequently have errors. Many journals
have a section for Errata & Corrections. If QED could fix these prior
to publication, we would be better off.

> It is an illusion to think that QED is needed to "verify" a proof,
such as the Wiles proof, that has received the intense scrutiny of
many competent mathematicians.

How many mathematicians are competent to check the Wiles-Taylor-Ribet-...
Theorem in every important detail? Twenty? How many *will* do it?

Rich Schroeppel