Apery’s Constant, revisited

In a funny coincidence, Apery’s Constant came up in a discussion on mathoverflow.net about correct mathematical results which were dismissed by other mathematicians at first.  Quoting from Wikipedia:

However, in June 1978 Roger Apéry gave a talk entitled “Sur l’irrationalité de ζ(3).” During the course of the talk he outlined proofs that ζ(3) and ζ(2) were irrational, the latter using methods simplified from those used to tackle the former rather than relying on the expression in terms of π. Due to the wholly unexpected nature of the result and Apéry’s blasé and very sketchy approach to the subject many of the mathematicians in the audience dismissed the proof as flawed. Three of the audience members suspected Apéry was onto something, though, and set out to fill in the gaps in his proof.

— Wikipedia

It goes to show you that even in mathematics, things aren’t always black and white.  People outside of math think that when you answer a math question that either you’re right or you’re wrong.  But, in reality, sometimes even when you’re correct it takes a while before other people properly understand your results and why it’s correct.  Especially if you’re like Apery and don’t clearly explain your answer!

Moral:  Write your solutions clearly and completely!

P.S.  mathoverflow.net is a new website of questions and answers by and for researchers in mathematics.  Most of the questions and discussion are at the level of current math research (it’s definitely not the place for homework questions/answers), but there is also plenty of questions about suggestions for undergraduate books, math tricks for cocktail parties, and other relaxed topics.

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  1. Pingback: Apery for a Third Time « OU Math Club

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