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Shinichi Mochizuki has released a proof of the abc conjecture, which proposes a relationship between whole numbers

September 12th, 2012 . by Errol

“The abc conjecture, if proved true, at one stroke solves many famous Diophantine problems, including Fermat’s Last Theorem,” says Dorian Goldfeld, a mathematician at Columbia University in New York. “If Mochizuki’s proof is correct, it will be one of the most astounding achievements of mathematics of the twenty-first century.”

Mochizuki 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 Goldfeld.

Brian Conrad of Stanford University in California, says the abc conjecture “encodes a deep connection between the prime factors of a, b and a+b”.

Conrad says that the work “uses a huge number of insights that are going to take a long time to be digested by the community”.

Philip Ball, Nature, 10 September 2012


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