4 ms·

This is also the example used in Imre Lakatos fascinating essay 'Proofs and Refutations', about the nature of proof. https://math.berkeley.edu/~kpmann/Lakatos.

• memexy 6y ago
  Yup, it's a really good exposition of the process most math goes through before it is fully "rigorous". In one of Alan Kay's talks he mentions how Euler basically got all his proofs wrong but his intuitions were almost all correct and some people got PhDs by making his arguments more rigorous [0]. Gian-Carlo Rota has a similar story about most of his proofs being wrong but generally having the right intuitions and being on the right track. The paper is titled "Ten Lessons I Wish I Had Been Taught" and it's really good. He gives advice applicable to any domain where sharing knowledge is the key marker of progress: http://www.ams.org/notices/199701/comm-rota.pdf http://www.ams.org/notices/199701/comm-rota.pdf. -- 0: https://www.youtube.com/watch?v=oKg1hTOQXoY&feature=emb_title https://www.youtube.com/watch?v=oKg1hTOQXoY&feature=emb_titl... [~ 8min 15sec] There was a mathematician by the name of Euler. Whose speculations about what might be true formed 20 large books. That most of them were true. Most of them were right. Almost all of his proofs were wrong. And many PhDs in mathematics in the last, and this, century have been formed by mathematicians going to Euler's books, finding one of his proves [and] showing it was a bad proof. And then guessing that he, his insight was probably correct and finding a much more convincing proof.