Fields Medalist Timothy Gowers: "when we solve maths problems ourselves, we understand exactly what we're doing. when we one-shot a maths problem with ChatGPT, we don't — we just stuck it in a machine" How can AI find such long, complex proofs? What algorithm is operating inside the LLM?... That question remains unansweredshow more

Nothing is preventing them from studying the AI results until they understand it, if they can. Progress cannot wait for them to understand. We don’t understand how 90% of things work.

LLMs are great at explaining things. Hook it to Blender, ask for explanation videos.

nobody asked the calculator how it works either

No. The fact that mathematicians aren’t getting it tells us a lot.

Wasn't Riverside who said that "one doesn't need to understand digestion in order to appreciate a good dinner!" ?

then we ask the machine to explain 😂

bro is envious

I don’t care the exact details of how warp drive works - as long as it works - nerds can take hundreds of years to refine our understanding while we go explore the stars

@grok what algorithms had been deployed to generate the candidates solutions and verify via LEAN and feedback verification results and improve and generate new candidates solutions?

Long proofs aren't a search algorithm. They're learned representations under pressure

New talk from Terence Tao yesterday:

at least in math you can check every step

All these Fields medalists so-called great mathematicians are revealing themselves hopelessly clueless in front of AI. They have no idea about how&why it works. They don't know how to use it. They don't know what to do next. They look pathetic.

Verification being trivial while proof discovery feels uninterpretable is classic math.

It really won’t matter we don’t understand how it did it. The future will be AI building on top of AI without humans in the loop.

When he states his assumptions, it is categorically incorrect to use the word "we." It would be correct to use the pronoun "I." Just because he doesn't understand, it doesn't mean that no one else understands!

I am a mathematician and for many years I have been saying that these "geniuses" are the dumbest people in the world. Finally, the world can see it with its own eyes.

These guys act like humans didn’t use fire before understanding it. Or oxygen. Or gravity.

Prompt an AI reasoning model for help with understanding.

does the machine show its steps, or only the finished proof?

Tim is the goat 🐐.

Some of the math papers contain math that is SI thinking 'outside the box'. That is the point, SI is discovering new 'alien' maths as solutions. Mathematicians would do well to try to learn it. It will help them grow in math comprehension. Posing the problems is still the job.

does the full talk say which of the summer proofs he went through line by line himself? the clip makes it sound like even he is taking some of them on trust

By making shit up and it being proclaimed in an impossible-to-review manner of a huge dump like a lawyer trying to hide evidence in bulk frivolous shit

@haider1 the harder question is what happens when the machine gives you a proof that looks complete but has a subtle flaw. how do you catch it without understanding each step?

The same when reading the proof of transcendance of Pi by Lindemann ..

Sounds like a good job for mathematicians!

Software devs went through the same phase. The gains come when you realize that you should be driving the AI and not the other way around. Until then, he's right. You're just creating slop.

People like him will only become more irrelevant as time passes and the models improve even more.

2 diff Qs: - why did an LLM produce a proof - why does it work? fThe irst remains open. We pin sources/assumptions, replay certificates & check Lean 4; then use interpolation, counterexamples, premise ablation and proof-transfer maps to investigate why proofs work or fail.

大脑如何工作，这个问题也未解决。DNN和大脑都属于复杂结构的范畴。

Is not an algorithm, is just picking strings of may-be-related text and refining it. It cannot understsnd the proof it writes.

More than that, when a LLM tells us "your proof is wrong", it doesn't understand. It's not checking all the reasoning. So it's fumbling. Not quite hallucinating, but not understanding. When you prove something, you have that intricate understanding.