## Saturday, April 04, 2020 ... //

### Mochizuki's proof gets officially published

The $$abc$$ conjecture is a hypothesis in number theory (i.e. a Fermat-last-theorem-style claim in mathematics) that sort of imposes a bound on $$abc$$ assuming $$a+b=c$$, i.e. it finds a fuzzy relationship between the sum and product of three integers. See TRF texts.

If someone is Japanese, it doesn't mean that he is not world class in seemingly "Western" activities such as in directing Antonín Dvořák's New World Symphony. In the video, the most fashionable part of the composition, Covidio Pandemio, erupts at 22:16. ;-)

Since 2012, Šiniči Močizuki has claimed a proof of this old problem in mathematics using his whole new technological toolkit called the Inter-Universal Teichüller theory (a smoother synonym: arithmetic deformation theory). The alleged proof is long and difficult. In 2018, criticisms by those who still hadn't understood the proof escalated.

I am not sure whether this multi-faceted proof is correct although I have understood some parts of the arguably clever approach. My feeling is that the theory is a refined version of "how can you permute primes in such a way that the additive relationships between their products change just a little, in some measure of the change". But I am sure that the widely hyped criticism of Mochizuki's proof – criticism revolving around the hatred towards "Corollary 3.12" – is incorrect. In effect, that criticism says, using physics jargon,

You cannot ever use gauge-variant (non-gauge-invariant) quantities at intermediate steps of your derivations.
Well, that's rubbish, Ladies and Gentlemen. Both in physics and mathematics, gauge invariance is useful exactly because it can be used and should be used and it makes lots of derivations prettier and more effective. In physics, gauge invariance is needed for a manifestly Lorentz-invariant description of spin-1 particles. At the end, we can only measure gauge-invariant observables but it's important that this condition is imposed at the very end, "inside the apparatus". All the intermediate calculations may use gauge-variant quantities and it's a very powerful thing to do.

As I repeatedly argued, the main controversy about Močizuki's proof is analogous. He uses some mathematical structures that are "isomorphic to each other", i.e. analogous to being "related by a gauge transformation", but they are treated as different. And there is absolutely nothing wrong about it, whether or not his critics unjustifiably scream that "isomorphic objects must be equal". The criticism of Močizuki's proofs insist on the demonstrably wrong assumption that "there is something wrong about it".

At the sociological level, the criticism of Močizuki's proof has been extremely irrational and driven by cliques almost entirely located in the Western countries. These people just parrot nonsense after each other – this disappointing discourse shows how much our Western civilization has degenerated, even in circles that should be more intelligent such as those who are employed as mathematicians. It looks like they believe that their uninformed group think is powerful enough to change the mathematical facts.

Do you want the number of sexes to be 78? Just find fellow snowflakes and write petitions, sit in the streets. Do you want to kill Močizuki's proof? Do the same. The proof will become invalid as soon as you, the dudes, shout some gibberish.

At any rate, the proof was just retyped and published in Publications of the Research Institute for Mathematical Sciences (RIMS). It's a journal controlled by the community in Kyoto and Močizuki has quite some power there which means that the publication cannot be considered too independent a verification of the proof. But here you have an independent, standard enough presentation of the proof by another Japanese mathematician, Go Yamašita, who claims to have understood it:
A proof of $$abc$$ conjecture after Močizuki (294 pages PDF)
A new 8-page-long philosophical summary of the proof was written down by Ivan Fesenko. Davide Castelvecchi discusses the publication of the proof in Nature
Mathematical proof that rocked number theory will be published
but he can't resist to insert a subtitle saying that "experts" claim the proof to be "flawed". While the article features insulting gossip from anonymous trolls considering themselves stellar mathematicians, that's of course one of the relatively impartial texts about the published proof in the West. The typical "Western media" start with picking a more combative title, of course. Futurism.com chose the title
Mathematicians are shocked that this paper got published
Right. It is the same kind of "science journalism" as articles about the ingenious climate scientist Greta Thunberg and her evil opponents, the deniers. Our societies have been overfilled with aggressive stinky filth calling themselves "journalists" although they have nothing to do with the occupation of "journalism" as it was understood before our civilization began to decay away. They are really activists and trolls shoving increasingly dumb slogans down the throats of an increasing number of readers who are increasingly unwilling to use their brains.

Photo owned by Kyoto University

As someone told me on Twitter, understanding Mochizuki's technology in a truly "physical way" could be extremely important. It could be essential both for mathematics and physics.

Note that this war of the Western PC group think against the Japanese scientists etc. is likely to get even nastier now, in the devastating era of coronafascism, because Japan seems to be one of the countries that have abandoned "lockdowns" as a weapon against the flu-like virus. And make no mistake about it: Japan covers the news very differently. For example, the title in the Japan Times reads:
Genius triumphs: Japanese mathematician's solution to number theory riddle validated
Can you spot the difference from "Mathematicians shocked that a paper got published"? :-)

P.S.: Jona told us about a cool physics-like paper by Mochizuki where his theory is presented as an analogy to the evaluation of the one-dimensional Gaussian integral, by squaring it, something that theoretical physicists surely love.