Subject: Re: [HM] Mistakes in mathematics
From: Antreas P. Hatzipolakis (xpolakis@otenet.gr)
Date: Mon Dec 20 1999 - 18:05:30 EST
> I wrote an article giving three examples of noted mathematicians
> erring in proofs of noted results. It appeared in Math. Intelligencer.
> It is also the case that Abel has an error in his proof on the quintic.
> It can however be readily remedied. Raymond Ayoub
From Zbl:
Ayoub, Raymond G.: Partial triumph or total failure?
Math. Intell. 7, No.2, 55-58 (1985).
Three examples of incorrect or incomplete proofs by outstanding
mathematicians are discussed. They are: Euler's proof (1749) of the
fundamental theorem of algebra, Stieltjes' proof (1885) of the Riemann
hypothesis and Appell's proof (1926) that Euler's constant is irrational.
The author gives short modern versions of the arguments; in the first
two cases he indicates where the proofs are wrong or incomplete, in the
last case he leaves it to the reader to find out. (Appell also found out
himself and retracted his proof within weeks.) He also speculates about
the influence these "proofs" might have had, for example because they
suggested ideas to other mathematicians. He draws no conclusions and ends
the article thus: "Perhaps in the final analysis, the significance of an
idea depends on the imagination and creativity of those dealing with it."
[ H.J.M.Bos ]
APH
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