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Why A Clash Between Titans is Ripping Mathematics Apart

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TIMESTAMPS:
00:00 - The Proof That is Only True in Japan
02:03 - The abc Conjecture Explained
05:22 - Mochizuki’s Inter-universal Teichmüller (IUT) Theory
07:52 - The Flaw at Corollary 3.12 (Scholze vs. Mochizuki)
12:42 - The Digital Arbiter

For over a decade, mathematicians have been locked in a cold war over the abc conjecture. Proposed in 1985, this deceptively simple equation (a + b = c) holds the key to the deepest relationship between the addition and multiplication of prime numbers. A verified proof of the abc conjecture would instantly unlock a cascade of mathematical breakthroughs, offering a more elegant proof for Fermat’s Last Theorem, settling the Mordell conjecture, and revolutionizing arithmetic geometry.

But in 2012, Kyoto University's Shinichi Mochizuki dropped a 500-page bombshell: Inter-universal Teichmüller theory (IUT). To some, it is a revolutionary new mathematical universe. To others, it is an impenetrable, unverified language. We break down the absolute chaos of this scientific schism.

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20 Comments

@TuringApp Creator 2 months ago Pinned

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@hiromichiw 1 month ago

Mochizuki should work a lot harder in helping other mathematicians understand his theory.

@justneoh8253 2 months ago (edited)

My impression is that this work of Mochizuki belongs to what Wolfgang Pauli remarked as "That is not only not right; it is not even wrong"

@Tact-v8g 1 month ago (edited)

It's not tearing math apart. Almost everyone is in agreement that the proof should be reworked, to make it digestible and not too confusing. As Gerd Faltings said, '... explain it better'

@jamieoglethorpe 2 months ago

This is something that has happened before in mathematics. I'm thinking of Zermelo's proof of the Well-Ordering Theorem using the Axiom of Choice, which was vehemently rejected by the mathematical establishment. He eventually spelt out the axioms he used in his proof. His response was that his was legitimate proof. Opponents were welcome to reject the specific axiom, but the proof stood.

It is the responsibility of the Japanese school to explain their formalism in a way that the mathematical community can understand, if only by illustrating how it can be used to prove familiar theorems. Presenting a dense paper using unfamiliar language without a path that those who are unfamiliar with it can follow. Mastering things like this can take years. Think of Riemann's geometry and tensor calculus before Einstein used them for General Relativity, which made them worth studying. Mastering GR clearly made it worthwhile to both mathematicians and physicists.

@inazuma3gou 1 month ago

Mathematicians: Mathematics is a universal language
Mochizuki: Hold my bear

@futureshockpod 1 month ago

All math, so they say, has one tongue,
The same for the old and the young.
But truth, it appears,
Needs consensus of peers—
And sometimes the jury is hung.

@sil1235 2 months ago (edited)

The video mentions formal verification, but it is already under way - sort of. Two separate Lean efforts are based in Japan: ZEN University’s LANA Project and a RIMS project led by Shinichi Mochizuki. The immediate task is making IUT’s definitions and disputed arguments precise enough to encode; neither has formalized the claimed abc proof. Full verification is the long-term goal.

@profskmehta 2 months ago

Can’t imagine what is Mochizuki’s language. I hope eventually he will rewrite his proof in the standard functions and symbols. I am curious whether he uses any known result in his proof!

@numeristas 3 weeks ago

Well said

@mikeoffthebox 2 months ago

Scholze and Stix make a very specific objection to Mochizuki's proof which is much shorter than the proof itself - surely this would be much more accessible to automated proof checking?

@ferdinandbardamou5508 2 months ago

Scholze and Stix seem to have made a honest effort to approach the work of the other two. Other than that, the entire situation is perfectly within expectations, when people spend their time on nonsense mathematics, or nonsense in general.

@bernardfinucane2061 2 months ago

Great synopsis of a sticky problem.

@srikanthan1000 2 months ago

This is still going on ????…….😮😮😮

@itellu3times 1 month ago

You said: (@14:10) "But there is a catch! A computer cannot formalize what a human does not first understand."
OK that's a catch, but the bigger catch is if the computer CAN formalize what a human does not first, or ever, understand! What if Lean says it's all great and yet humans still can't understand it?
And kudos to you for mentioning this.

@9uwa_toki 2 months ago

私は日本人ですが、日本でもほとんどの人はこの問題を理解していないし、できないし、IUT理論を証明として認めていないと思います。
多くの人は証明が正しいか間違っているか、判断する段階にたどり着けません。証明として認めるかどうか以前の問題です。

「日本でしか認められていない」ではなく、「日本の、さらに限られた一部のグループ内でしか認められていない」が正しいでしょう。

@kamusaua667 2 months ago

Perkenalkan, nama saya Ahmad khanif.
Saya berasal dari Indonesia.
Saya menemukan sebuah aksioma perkalian baru.
Berapapun panjang angkanya,digit berapapun,dari angka berapapun.
Selama berupa baris angka, kelipatan dari angka 1.
Baik itu angka pengali atau yang dikalikan.
Caranya tetap linear, dan sama .
Bahkan, tidak butuh hafal perkalian sama sekali.
Yaitu, menulis angka A sebanyak angka pengali B.
Dengan cara harfiah, bisa dikatakan mustahil.
Jika angka pengalinya semakin besar.
Dengan aksioma saya, memungkinkan untuk menulis angka A sebanyak angka pengali B, secara deskriptif dan devinitif.
Yang menarik, justru, semakin besar nilai angka pengalinya.
Usaha yang dilakukan , dalam menulis angka A,berbanding terbalik dengan nilai angka pengalinya itu sendiri.
Dan justru, semakin kecil usaha yang dilakukan.

@thatpodcastshowforU 1 month ago

Interesting to know that validation via AI also has a limitation that a computer cannot verify something that a human cannot understand first completely.

@tsentenari4353 1 month ago

Settling the question by formalizing the proof seems like way to go here.
When I asked Perplexity whether attempt are being made, and what their current state is, this was the answer:

"The key development is Project LANA, an effort to formalize the crucial step of Mochizuki's Inter-universal Teichmüller theory (IUT) in the Lean proof assistant — specifically the passage from Theorem 3.11 to Corollary 3.12 of IUT-III, the exact step that critics have flagged as defective.

Project LANA was initiated by Fumiharu Kato (ZEN University) in autumn 2023 after he encountered Lean formalization through the Liquid Tensor Experiment. He brought in Johan Commelin (Utrecht), Adam Topaz (Alberta), Kiran Kedlaya (UC San Diego), and — from December 2024 — Yuichiro Hoshi of RIMS Kyoto, an IUT insider. The project's existence was publicly announced on March 31, 2026.

Through a series of bootcamps (Kamakura-Zushi Feb 2025, Kelowna May 2025, Higashi-Ginza July 2025, Zaandam Nov 2025, San Diego Feb 2026), the group identified a "wall": whether, after accounting for the three "indeterminacies" (Ind1, Ind2, Ind3), a particular diagram commutes or a particular isomorphism is the identity. As of the July 2026 report, LANA had not reconstructed the required proof of compatibility — the wall had not been crossed, and no final verdict on correctness was issued. Notably, LANA's analysis locates a problem at roughly the same place Scholze–Stix did, though it phrases it differently and stops short of their negative conclusion.

Independently, Mochizuki himself became interested in Lean after the July 2025 ZMC conference in Tokyo and began a parallel formalization effort with his own group. His side produced "low-resolution" Lean code attempting to fill the problematic point, but it still contained black boxes and was not a complete formal proof."