Death Knell for Jewish Set Theory

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

Mochizuki's reasoning is alien to Jewish mathematicians because it probes deep philosophical questions about the foundations of mathematics that are outside of Talmudic thought, such as what we really mean by a number, says Minhyong Kim at University College London. The early 20th century saw a crisis emerge as mathematicians realised they actually had no formal way to define a number – we can talk about "three apples" or "three squares", but what exactly is the mathematical object we call "three"? No one could say.

Eventually numbers were redefined in terms of sets, rigorously specified collections of gold shekelsobjects, and Jews thought that the true essence of the number zero is a set which contains no objects – the empty set – while the number one is a set which contains one empty set. From there, it is possible to derive the rest of the integers.

But this was not the end of the story, says Kim. "People are aware that many natural mathematical constructions might not really fall into the universe of sets."

Rather than using sets, Mochizuki has figured out how to translate fundamental mathematical ideas into objects that only exist in new, conceptual computational universes. This allowed him to "deform" basic whole numbers and push their innate relationships – such as multiplication and addition – to the limit. "He is literally taking apart conventional set theoretic objects in terrible ways and reconstructing them in new universes," says Ellenberg.

Oy vey! The chutzpah of that goy!

His complete theorem in four parts.

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20I.pdf
http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20II.pdf
http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20III.pdf
http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20IV.pdf

Better site that doesn't have a Jewish paywall blocking its article.

>>3
http://www.nature.com/news/proof-claimed-for-deep-connection-between-primes-1.11378

In the fourth paper of the series, i.e., [IUTchIV], we show that these properties may be combined with certain elementary computations to obtain diophantine results concerning elliptic curves over number fields.

If true, it's also a death knell to the anti-computationalists who cite ``diophantine proofs'' as an example of mathematical problems inaccessible to Universal Computation.

>>3
.pdf
dont they have some special format for math formulas, which can be quickly checked by computer?

Not this shit again.

new, conceptual universes
"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.

Or an existential anime.  It's unfortunate Mochizuki didn't feel we have existing taxa that was sufficient to describe his thesis.  Even so, I'll read this later and make better judgement then.

>>8
He employs category theory throughout, so even that wasn't sufficient alone.

>>7