Jacob Tsimerman, who won the Fields Medal this year, thinks mathematics will soon rest on proofs no one understands. He says it’s already true of many of his own theorems, which build on accepted results whose proofs he doesn’t know. Full episode:

“Do I understand it from first principles? — No”… So we were long gone, even before AI…

Some mathematicians are like authors. I get it. They wrote most of the story but struggle with how it ends. Then an LLM comes along and finishes it in a thrilling way they never expected and get all the credit. They’re upset. Fair! But not all is lost!

Almost all of human progress rests on pushing forward things we do not "understand."

All this means is that math is going to be more like programming. We all stand on the shoulders of giants.

Seems like a reasonable and intelligent mathematician, as opposed to some other big names we won't mention.

Jacob needs to be like @rperezmarco . Jacob is cool but his style sucks. @rperezmarco please teach Jacob.

Yeah but SOMEbody knows

Shouldn't open Ai have won the field medal? 🤣

So in addition to treating an LLM like God, we are now being told we will need to rely on faith in this God It's all so textbook, predictable, and sad

Another bought medal by the tribe.

this i have respect for

There will be layers of mathematics. The accepted, organized and puplished results. Then there will be the wild west of machine proven results. This should also be organized and translated and in time published, once a human has understood them. Value of organizing goes up.

@snezanalawrence #AbolishTenure

@sama probably did a big mistake destabilizing mathematics. among many of the mistakes billionaires do thinking they know everything @elonmusk . but i feel no compassion for them because they could have asked to automate medicine. yet they did not. thought only anout themselves

Admirably honest and self reflected. This is true in many areas, especially the old ones. Acceleration has been true since 1900. 1920 had people pretty much on top of physics and maths (von Neumann for instance).

July 2026: Tsimerman announced that he would take leave from the University of Toronto to work on AI safety at OpenAI, while remaining a faculty member.

AI is a catalyst for the usefulness of pure theorems, not an obstruction to human understanding.

Brilliant minds will always seek new challenges. Has mathematics been lost to AI? Or has humanity simply invented a new way to play the game? Perhaps the greatest achievement isn’t solving the next impossible problem, but creating an intelligence that can take us beyond the limits of our own. Is that surrender—or evolution?

Thanks for posting this. As a layman, I have a basic question: we now know that AI is solving complex math problems at maybe a 100X rate than mathematicans, but can AI also on its own think of entirely new problems to solve, problems that have never occurred to any mathematician?

Should have a convo and not just emotionless scripted questions

Proofs which no one understands have no difference from hallucinations!!!! We all hope that all this will work on practice, but it is barely possible, like say, p-np is not equal. Proof is here, no practice result, no difference from hallucinations:(

Nice. I fully support mathematicians gently redirection their field and colleagues away from Luddite rebellion. There is going to be need for a LOT of that in the coming years.

Appreciate ppl like this

This is actually quite normal. As math branches out more, no one can keep up with all the existing proofs.

You know what the solution is? Genetically engineering branches of humanity to be optimized to the extreme in specific areas, even transcending the human species, though not necessarily the genus Homo. And it has to happen this century.

Why is that a problem? It’s not like better AI models won’t understand those proofs. Humans are not required to advance our civilization.

...wise man, truly

I love his candid account.

@rperezmarco i could never use theorems i didn’t completely understand, so i never got off the ground mathematically, and am a failed mathematician. thats why i was interested when you asked Alpoge if he understood NS proof

can you maintain a system if you don't understand it?

A mathematical proof that no one can understand would qualify as not being a proof afterall, right?

uh... someone understood each subsystem of the train and someone understood how subsystems can be combined in robust ways. This is an insane thing to say.

Math solved by math - or linear algebra for that matter. Which means math dominates everything. A science solving it's own mysteries. Shouldn't this be a happy day for mathematics? 😅