jay (invariant)

A postdoctoral researcher in Number theory. He/him.

[Bartosz Naskręcki @nasqret]

I have my own theory here: many mathematicians have started using top-tier models and agentic systems. The effect is that they are finishing up very old projects that were left untouched for years. They realized that they had all the required ideas and tools but did not have a person to wrap things up. I think this "vacuum cleaner effect" will last for the next few years and will end up with a complete stall in most areas of mathematics. What will remain are very hard questions, and possibly some new ones. But once a question is within reach of the agent, it will get published almost automatically. People will remember this period of civilization as the "great purge of ideas". The outcome will be a vast intellectual startup where everyone is at ground zero, and the occasional genius will pop up to scale their ideas and drain it again until the thread dies.

[Balázs Pozsgay @pozsgaybalazs]

Can I publish a proof that I don't understand? Should I? .... I never thought I would reach this dilemma so soon, but I did. In the last 2 days I played around with ChatGPT 5.5, I reconsidered one of my old problems. It was always too difficult for me, technically. Now AI claims it solved it...

This is a problem in stochastic dynamics, probability theory. It needs special skills that I do not have. There is a stochastic system which is complicated. Particles hopping on a 1D lattice, with some special rules. The model is physically interesting, and in good variables it becomes much simpler. One needs to connect the quantities along multiple coordinate transformations, non-local maps, eventually arriving at the desired result.

I knew what could be an initial strategy towards a proof. In fact we have the required coordinate transformations in a published paper. But I was never enough to do the full rigorous proof. Now the AI claims it did it for me. It supplied another connection to existing literature, a connection I wouldn't have been able to make. And now the proof seems to be complete.

Now I have a manuscript, which is >30 pages long. I worked a lot on the introductory Sections, which explain the strategy. This takes up 10 pages approx. Then comes the grinding, for 20 pages.

What did I learn from this? What does the community learn? Should I put this to the arxiv? Or to my blog? Should at least announce the result in a conference or somewhere? Or just tell people in person?

Eventually we could try to formalize it in Lean. But I am not sure whether we would learn anything from it. OK then people could say they believe it.

If I send this to a journal, the referee will not work through 20 pages of hard grinding. They can give it to an AI if they want to. Then we have the future, where AI referees the work of an AI.

In any case, I understand the problem and the proof strategy. Maybe that is actually enough in this case. I honestly don't know.

[Slava Naprienko @SlavaNaprienko]

Now I have my own "the drowning number theorist" result:

log log log log n / log log log n

https://t.co/75GMMD1xOa

[jay (invariant) @jay196884]

Feynman wrote down : “what is the general problem solving strategy?”
Feynman thought very, very hard.
And then Feynman wrote down:

[gabe @gabekahen_]

@mathemetica

[jay (invariant) @jay196884]

Hmm i realized that that was the second talk actually

[jay (invariant) @jay196884]

I gave this year’s the first talk today

[Shital Shah @sytelus]

Current LLM architecture is so inefficient that most people don’t realize how fast GPUs are.

A *single* token generation for 1T model spends same number of flops as

- simulating 2hr weather for small city
- chess engine playing half game
- multiplying two 255000 digit numbers

We are basically brute forcing our way to AGI.

[jay (invariant) @jay196884]

@hanuljeon95 귀국 및 졸업 취직 등 축하드립니다!

[jay (invariant) @jay196884]

Why did i say condition when i had to say opinion

[jay (invariant) @jay196884]

(possibly) unpopular condition
best tool for drawing directed acyclic graph (or, partially ordered set) is Google Presentation (or MS Powerpoint)

[jay (invariant) @jay196884]

the y⁴ term in this random-looking function somehow vanishes (by a coincidence). (y+sinh(y))/2 = y + y³/12 +..., ln(cosh(y)) = y²/2 - y⁴/12 +...

(Yes, I brought yet another Taylor series expansion.) [4/4]

[jay (invariant) @jay196884]

One observation:

Recall cos(x/2)² = (1 + cos x)/2, so we are comparing
cos((x + sin x)/2))² and exp(-x²), or (by taking sqrt)
cos(( x + sin x)/2) and exp(-x²/2).

Let x = iy then we are comparing
cosh((y + sinh y)/2) and exp(y²/2). [1/4]

[いちごじゃむ @1strawberry_jam]

どうやら y=cos(sinx+x) のグラフは 正規分布のグラフにめちゃくちゃ近いっぽく、何か背景があれば教えてください...

[jay (invariant) @jay196884]

Recall again that we are comparing
cosh((y+sinh(y))/2) and exp(y²/2).
Let A = (y+sinh(y)/2), then what we are asking is that: is ln(cosh((y+sinh(y))/2)) close to y²/2? (given that exp is smooth.)

yes, kind of, as
ln(cosh((y+sinh(y))/2)) = y²/2 + y⁶/480 - y⁸/20160 + ... [3/4]

[Agustin Lebron @AgustinLebron3]

Turns out Paul Erdos's biggest contribution to humanity was as an eval creator.

[jay (invariant) @jay196884]

the question is that to which rail i will be tied

[jay (invariant) @jay196884]

I’ve just come up with yet another trolley problem.

If you press the button, everyone who has ever devised a trolley problem will die. If you refrain from pressing it, every victim who has appeared in any trolley problem ever proposed will die. What would you do?

[jay (invariant) @jay196884]

I think djt is a very strong candidate for the ig nobel peace prize 2026

[Physical Review A @PhysRevA]

PRA Letter: Hamiltonian with energy levels corresponding to Riemann zeros https://t.co/8QlnCiL30O

[jay (invariant) @jay196884]

It seems like "§ 3.1" with a non-breakable spacing is the standard way when it comes to the legal document. maybe the standard would also apply for the general section numbers; Maybe I should use \S~3.1 or \S~\ref{section: example}

Actually my preference is Section~3.1 though..

[jay (invariant) @jay196884]

Which is appropriate?

A. \S 3.1
B. others e.g. \S3.1, \S~3.1, etc

\S 3.1 gives the result "§3.1" without breaking. It seems like \S is sticky, i.e. § and the following string `3.1' (without space) won't part at the end of the line (which is my concern) Is it correct to use A?