Pure Mathematics in Crisis

With Professor Kevin Buzzard

Pure Mathematics in Crisis

Any number theorist would tell you that Fermat’s Last Theorem is proved. But I know of no human who understands the details of all of the mathematics involved. What does a group theorist mean when they say the classification of finite simple groups is finished? If you assume unpublished work which is “known to the experts”, whose job is it to publish that work? Does the work even need publishing, or should we just keep generating new experts instead? When was the last time your favourite journal published an erratum? Is is OK to make mistakes? Is everything OK or is human mathematics heading towards a cliff edge?

Computer scientists are doing pure mathematics in a new way, which has many problems of its own, but these problems are almost entirely disjoint from the issues that “human mathematics” currently faces. I will argue that mathematicians and computer scientists need to work more closely together because both sides can offer things which the other side needs.

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