Could AI be a mathematical buddy?

Artificial Intelligence (AI) may not be up for the Fields Medal (mathematics’ Nobel Prize) any time soon, but it may act as an intermediary for mathematicians working on proofs. However, something is lacking for AI to get down to it as Terry Tao explains.

#shorts #science #maths #math #mathematics #stem #ai

[captnmaico]

24/7 live stream of terence tao solving math problems incoming.

[arnaudparan]

That's a very important thing in science. When you find a counterexample of euler's conjecture on sums of like powers, you just give the counterexample. Yet you don't present the whole way you got to that counterexample.

Papers don't account for the scientific thinking, they're a report of the result and hence we don't have data to train models on scientific thinking because what we have is papers.

[Alfakkin]

This genuinely important, a deep concept about approaches in Mathematics. Thank you for speaking about it.

[LeninMcDonalds]

“Professor Terence Tao is something of a rockstar in the world of mathematics…”

[UrAWizard]

The same can be said about life problems too. Often the hardest part is finding the right intermediate step and if you can do that you’ll have the motivation to complete the whole thing

[judo-rob]

Mathematicians perhaps should write in journals about their missteps. Perhaps, abandon the notion that pristine polished proofs are the only ways of advancing knowledge.

[rayrocher]

Great work, you're a good man terance tao.

[opusnumber]

It’s because every math paper an ai is trained on says “the proof is left as an exercise for the reader”. Thanks a lot mathematicians!

[joeynumbers]

Proof is logic and creativity. The AI has that. What the AI can’t do properly (for some insane reason) is do really basic counting reliably. It makes chunks of mistakes. The human element of reflection is still critical to keep the AI checked because it needs to be told it made a mistake to correct course.

[aalok_]

Fundamental problem solving is a field to be worked upon

[trushbetold]

The problem is humans will make abstract thought chains that are not logical, even inaccurate, yet these often lead to accurate discovery. What we currently call "hallucinations" in AI is not much different from an imagination

[DaronKabe]

bro can't cope with being replaced

[marioxerxescastelancastro]

This reminded me of Beth's interpolation theorem, although it does not give the middle step this person refers to regarding how we actually solve problems.

[cajonesalt]

The problem with that is that I write proofs by staring at the wall for 45 minutes, taking a walk, getting home, doing the chores, going to sleep, waking up, going to work, and then seeing a group of pigeons flock together on the way to work and suddenly having an epiphany of how flocking behavior can represent an optimization problem in the right context. The big proofs are always going to come from inspiration. That's a result of incompleteness and undefinability. There are problems we can define that math *cannot* solve, but we can. Until you build an AI that escapes relying on computation to solve the credit assignment problem, AI isn't going to help us besides giving many, many, many related pieces of information we weren't aware of.

[..]

That's the cool thing about reasoning models like DeepSeek, they just train on the output, all those reasoning tokens emerge from unsupervised reinforcement learning.

[folaemmanuel]

What we could do is "VCS for mathematicians", like git, it will store history of their progress, each step they take, mistakes...etc
...and then train ai on that data

[hotman]

That's kinda how I use AI with math, not to solve things but if I get stuck it can get you halfway there and point you in some general direction instead of wandering in the dark. There's textbooks too of course but AI is also useful. Of course this is mostly for elementary math, not any advanced proofs. AI struggles hard with any semblance of a complex problem. But for fairly straightforward rudimentary things, even calculus to some extent, it's useful.

[JordanMetroidManiac]

This is why reinforcement learning algorithms will outperform supervised learning in proof writing advancement.

One idea is to approximate the optimal reward function with an LLM that is sufficiently good at judging whether an intermediate step in a proof is logically coherent with the point A and the point B. Even an approximation of the optimal reward function would yield good results since that’s how RL works.

[eagleholyengel]

THANKS As Always!!.. To Perhaps The Most ASSIDUOUS International Math, No! UNIVERSAL MATHEMATICIAN Today! @Terrence Tao, SUCH An INSPIRATION! ❤❤🎉🎉🎉😊😊😊😊

[More.A-gfrd]

Intresting! Applies not only to math but also life