Schnee (schnee) wrote,

abc conjecture

As reported by Nature, a purported proof of the abc conjecture has been announced:

Mathematician Shinichi Mochizuki of Kyoto University in Japan has released a 500-page proof of the abc conjecture, which proposes a relationship between whole numbers — a 'Diophantine' problem.


Like [French mathematician Lucien] Szpiro, and also like British mathematician Andrew Wiles, who proved Fermat’s Last Theorem in 1994, Mochizuki has attacked the problem using the theory of elliptic curves — the smooth curves generated by algebraic relationships of the sort y2=x3+ax+b.

There, however, the relationship of Mochizuki’s work to previous efforts stops. He has developed techniques that very few other mathematicians fully understand and that invoke new mathematical ‘objects’ — abstract entities analogous to more familiar examples such as geometric objects, sets, permutations, topologies and matrices. “At this point, he is probably the only one that knows it all,” says [Columbia University, NY mathematician Dorian] Goldfeld.

To call this exciting would be an understatement.

Tags: mathematics
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