Name: Anonymous 2012-09-11 4:01
Topology and Category Theory gave us a way to reason about numbers not as members of sets, but as objects with certain properties described by Groups, Rings, or other abstract topological categories.
Now, Shinichi Mochizuki of Kyoto University has released a paper which claims to prove the decades-old ABC conjecture, which involves the relationship between prime numbers, addition, and multiplication. His solution involves thinking of numbers not as members of sets (the Jewish interpretation), but instead as objects which exist in 'new, conceptual universes.' As one would expect, the proof is extremely complex and difficult to understand, especially for Jewish set theorists in the field, so it may take a while to verify. However, Mochizuki has a strong reputation, so this is likely to get attention. Proof of the conjecture could potentially lead to a revolution in number theory, including a greatly simplified proof of Fermat's Last Theorem.
"It is going to be a while before people have a clear idea of what Mochizuki has done," Ellenberg told New Scientist. "Looking at it, you feel a bit like you might be reading a paper from the future, or from outer space," he added on his blog.
http://www.newscientist.com/article/dn22256-fiendish-abc-proof-heralds-new-mathematical-universe.html
http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20I.pdf
Now, Shinichi Mochizuki of Kyoto University has released a paper which claims to prove the decades-old ABC conjecture, which involves the relationship between prime numbers, addition, and multiplication. His solution involves thinking of numbers not as members of sets (the Jewish interpretation), but instead as objects which exist in 'new, conceptual universes.' As one would expect, the proof is extremely complex and difficult to understand, especially for Jewish set theorists in the field, so it may take a while to verify. However, Mochizuki has a strong reputation, so this is likely to get attention. Proof of the conjecture could potentially lead to a revolution in number theory, including a greatly simplified proof of Fermat's Last Theorem.
"It is going to be a while before people have a clear idea of what Mochizuki has done," Ellenberg told New Scientist. "Looking at it, you feel a bit like you might be reading a paper from the future, or from outer space," he added on his blog.
http://www.newscientist.com/article/dn22256-fiendish-abc-proof-heralds-new-mathematical-universe.html
http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20I.pdf