Quanyu Tang

Mathematics

[Quanyu Tang @Vieta__jumping]

We have proved the Bollobás–Nikiforov conjecture (2007) on the two largest adjacency eigenvalues.

Proof + Lean 4 formalization:
https://t.co/oE8cGr2PKZ

With Gabriel Coutinho, Yinchen Liu, Thomás Jung Spier, Quanyu Tang & Shengtong Zhang.

Paper in preparation.

[Quanyu Tang @Vieta__jumping]

@miaodeisu 😯

[Quanyu Tang @Vieta__jumping]

@integers_blog 👍

[孙宇晨（去过太空版）🧑‍🚀 @sunyuchentron]

孙宇晨奖
首期66个获奖数学问题正式公布
面向全球数学研究者
奖励重要数学问题上的突破性成果
66 Problems. One Frontier.
向未知发起挑战

[Quanyu Tang @Vieta__jumping]

爽翻天了，直接拿了两个里程碑级的奖！

[H.E. Justin Sun 👨‍🚀 🌞 @justinsuntron]

https://t.co/wTMb1gbXpN

[Quanyu Tang @Vieta__jumping]

我拿了其中三个奖😁

[H.E. Justin Sun 👨‍🚀 🌞 @justinsuntron]

https://t.co/z5PCEdqltE

[Quanyu Tang @Vieta__jumping]

@jiamimaodashu 只要你真用AI做数学超过一年的，基本就不可能想继续做数学了

[Quanyu Tang @Vieta__jumping]

Update: The Lean formalization is now registered in Palomar:

https://t.co/CINJCgGviy

[Quanyu Tang @Vieta__jumping]

We have proved the Bollobás–Nikiforov conjecture (2007) on the two largest adjacency eigenvalues.

Proof + Lean 4 formalization:
https://t.co/oE8cGr2PKZ

With Gabriel Coutinho, Yinchen Liu, Thomás Jung Spier, Quanyu Tang & Shengtong Zhang.

Paper in preparation.

[Tom Adamczewski @tmkadamcz]

Astra produced Lean disproofs of Smale's mean value conjecture (1981) and the Köthe conjecture (1930), at least as stated in the Formal Conjectures repo.

AIs I've asked think the results are legit and not misformalized, but I'm not competent to judge.

Links in replies

[Quanyu Tang @Vieta__jumping]

@BTCNewsGlobal Okay

[Quanyu Tang @Vieta__jumping]

@slimer48484 @octonion

[Steven Strogatz @stevenstrogatz]

Latest crazy story from the frontiers of math and AI -- a neurosurgery resident, with no training in advanced math, uses ChatGPT 5.6 to solve a major open problem in numerical linear algebra. https://t.co/xckiv4TCFc

[Lech Mazur @LechMazur]

Very cool! Terence Tao posted "A Digestion of the Proof of Sendov's Conjecture" at https://t.co/hoP7QIWIDp and shared his ChatGPT chat logs here: https://t.co/9tk5y5mDIN. I posted the completed Lean formalization on my site at https://t.co/J00PnykB1d and linked it in a comment on his blog but I forgot to mention that it was completed on X.

[Quanyu Tang @Vieta__jumping]

@LechMazur Congratulations! I’ve spent three years researching this conjecture and only recently made some unpublished partial progress—never expected it would be fully solved so soon
!

[Przemek Chojecki | PC @prz_chojecki]

AI disrupts the job of a mathematician.

From a paper-and-pencil slow thinking to fast LLM-based iterations and verifications.

It's like a professional Go player becoming a pro CS:GO player. There’s still Go in its name, but a totally different game valuing different skills.

That's why you see mixed reactions. We might need more mathematicians now than before, but at the same time this won't be the same kind of the job as before.

And many mathematicians that became mathematicians to think deeply and long about hard problems, won't be interested in continuing if the job turns into verification of AI outputs or simple prompting.

That's why it's depressing from a simply human perspective of a particular job. Something is ending.

From a perspective of science or mathematics (not mathematicians), this is the best time ever. AI will lead us to the new age of mathematical discoveries and boost science progress 100x. Just don't forget about the human aspect along the way and why we want to have scientific progress in the first place.

[Przemek Chojecki | PC @prz_chojecki]

The current wave of OpenAI Astra conjecture settling will be the last straw for academic mathematics.

And it will be very depressing in the short term.

To understand it, you have to know that modern mathematics is divided into many many silos of various domains. If you're working in one or doing a PhD/postdoc in one, you know of everyone else. You know what problems they work on, so that no one interferes with others' work.

Solving problems - especially known long standing conjectures - is hard and takes months, sometimes years to do. When you approach these problems you rarely work on 2-3 at a time due to limited time and mental capabilities.

Now because you know all the people that potentially could solve a given problem as well - you talk regularly at conferences, through emails, your departments - it’s fine. It's fine also because it is a slow process.

LLMs destroy all that. Something that you though about for months can be one-shotted out of the blue by an amateur.

It is demotivating and scary. And that's why the incentives in mathematics have to change as well as the role of human mathematicians. Exciting times we live in. Embrace the future.

[Quanyu Tang @Vieta__jumping]

@NarkajR [email protected]

[Quanyu Tang @Vieta__jumping]

@NarkajR Oh, first of all, I can’t open your link. Secondly, I don’t think this is something you should discuss with me publicly on X. I suggest contacting me by email instead.

[Quanyu Tang @Vieta__jumping]

@NarkajR sure

[QC @QiaochuYuan]

okay so. when a mathematician proves a random conjecture you are supposed to politely clap. this is because it would be rude and embarrass the mathematician to point out that most conjectures are not that important or meaningful

when an LLM proves a random conjecture mathematicians are caught in a funny position where they want to say "these are not very important or meaningful conjectures and having magic proofs or counterexamples come out of nowhere is not particularly interesting or useful to anybody, except possibly the person who proposed the conjecture and some of their colleagues" but saying that puts them in an awkward position - why didn't they say that when humans were doing it? was nearly all mathematics actually pointless this whole time and mathematicians were just politely avoiding ever pointing this out so they could all still have jobs?

if the best defense you can come up with of mathematics as a human endeavor is, effectively, "it's really fun for us to come up with these baroque puzzles and then solve them, don't screw this up for us," you are completely abdicating your responsibility as a public endeavor that taxpayers fund. i have occasionally argued that pure mathematics lost the plot decades ago and gave up on having any kind of meaningful relationship to the rest of the human quest to understand reality. this was a slow-burning tragedy, and mathematicians have been able to hide this state of affairs from everybody else because nobody else knows enough mathematics to critique what mathematicians are doing

i saw a famous professor point out a few years ago that the machine learning that underpins AI is powered by 18th or maybe 19th century mathematics, you don't need much more than multivariable calculus, linear algebra, a bit of probability. he said this as if it was a dunk on ML and AI; imo it's a much bigger dunk on mathematics. you're telling me the most important scientific revolution of our lifetimes doesn't involve any of the math that mathematicians have been working on over the last century or two? you see how that's worse, right?

(tbc i'm not saying that stuff is all useless, you need a bunch of stuff from the first half of the 20th century to do physics, e.g. functional analysis, lie theory, representation theory all feed into the standard model. after 1950 or so things get more dicey)

if mathematicians still want to have jobs they are going to have to do a better job than they have for the last few decades convincing the public they do something that actually matters, and figuring out what that actually is or should be. this is an opportunity for the field to do some very serious soul-searching, as serious or more serious than the foundational crisis from a century ago. this kind of whining is absolutely not going to cut it