Just heard a fantastic quote on iterative development from Goro Shimura, talking about his colleague Yutaka Taniyama in the BBC documentary about Fermat’s last theorem:
Taniyama was not a very careful person as a mathematician. He made a lot of mistakes, but he made mistakes in a good direction so eventually he got the right answers. I tried to imitate him but I found out that it is very difficult to make good mistakes.
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