Partial triumph or total failure?
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.''
scientific article; zbMATH DE number 3889468