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Mathematics in the age of AI

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Re: Mathematics in the age of AI

#141

Post by copemaxxxing »

a2ff6eeb0 wrote: post #41
TSiege wrote: post #37

Earlier quoted context omitted.

I’m not anti AI but thinking the human brain is obsolete and using it will become a hobby is a dystopian view of the future where no one has any agency anymore. By your logic since our brains provide no value why not just shoot ourselves in the head while we’re at?

What's wrong with sitting on the beach with a bottle of wine for eternity, with no need to do anything, knowing that all your needs and desires will be automatically taken care of? I don't think you can be coherently pro-AI without thinking that the human brain will be obsolete, unless you believe in some inherent magic that the brain is imbued with. The only other option is that you haven't thought through the long…

That's not gonna happen. What's gonna happen is you'll be in forever slavery. You think those in power will let you enjoy your life?

Re: Mathematics in the age of AI

#142

Post by chongli »

nilkn wrote: post #107
skybrian wrote: post #49

Earlier quoted context omitted.

Maybe that will be true when it's math with practical applications, but most theoretical math isn't like that. If it's not practical and it's not for mathematians to understand, what good is it?

We have thousands of years of precedent that suggests that breakthroughs in mathematics tend to accumulate into broader technology breakthroughs in other domains. Why does this tend to be the case, even when some of the smartest people in the world have historically predicted incorrectly that certain branches of math would forever be useless (e.g., number theory)? I can only offer my own theory on that, but my guess…

We have thousands of years of precedent that suggests that breakthroughs in mathematics tend to accumulate into broader technology breakthroughs in other domains.

That's a misconception. Only a tiny percentage of mathematics has seen any applications whatsoever. There are vast libraries full of mathematics no one (in this discussion, anyway) has ever heard of that no one reads anymore and has never been applied to anything.

This idea of trying to "prove all the math" with AI makes as much sense to me as using chess engines to try to "solve chess."

Re: Mathematics in the age of AI

#143

Post by thatjoeoverthr »

zahlman wrote: post #83
kriro wrote: post #35

Earlier quoted context omitted.

The counterpoint to this comes from chess. High level engines "prove" certain lines correct (not in the mathematical sense) but those "engine lines" are really hard to explain to humans, even by GMs. They can sort of explain that something is a good line but not why. Engines crush GMs and are considered ground truth even if noone really understands what is happening. Would it be a nightmare if math was the same, not…

I don't think this is a valid counterpoint at all. Math is cooperative, and comprehension is the point : the proof has value exactly because (and only to that extent) it empowers humans to understand an abstract truth. Chess is competitive: the memorized line has value because it makes you incrementally more likely to defeat your opponent.

Yes, this. Comprehension is the point. We could map this to something like physics. If a man on a horse can shoot another man with a bow, empirically he makes correct predictions on gravity, wind and relative motion. But he can’t explain it. It’s not any different if your model has some “embodied” or demonstrable understanding; the model is not part of the discourse.

Re: Mathematics in the age of AI

#144

Post by qsera »

frozenseven wrote: post #122
qsera wrote: post #100

Earlier quoted context omitted.

>This is obviously no longer the case today. Advancement in capability does not mean the mechanism is the different. The LLM name denotes a very specific mechanism..

>The LLM name denotes a very specific mechanism.. No, not really. This is just the term that stuck around. The "large" is now up to five orders of magnitude larger and "language model" has gone far beyond any simple notion of modeling a singular natural language. And anything you'd cite about transformers, or tokens, or autoregression, etc., is more of a factoid about what works best and happens to be the most conven…

> The "large" is now up to five orders of magnitude larger and "language model" has gone far beyond any simple notion of modeling a singular natural language.

Does not matter. It is still an LLM.

And I am not the one who is playing word games. You and your idols are, for sake of marketing.

Re: Mathematics in the age of AI

#145

Post by Jblx2 »

rowanG077 wrote: post #105
Jblx2 wrote: post #65

Earlier quoted context omitted.

It will be interesting to see the evolution of journals in the next ten years for sure. Have they outlived their usefulness? Maybe everyone will just upload papers to arXiv, along with a copy of the formal proof.

Just package the proof as a library and put it in some source code repository like github.

Apparently, it is Palomar:

https://terrytao.wordpress.com/2026/08/18/palomar-a-registry...

Re: Mathematics in the age of AI

#146

Post by Paracompact »

GPerson wrote: post #136
thechao wrote: post #95

Earlier quoted context omitted.

I hope I'm remembering this right: a mathematician claims to have a proof for the ABC conjecture, but can't conceive any other mathematician it's right — it's "too weird", so the proof is rejected?

Some of the best mathematicians in the world tried to study his work, found flaws he did not address, and somehow there’s someone every week suggesting there’s a conspiracy against this guy. It’s really baffling. AI will probably help him move on by lean verifying his proof is wrong…

By this point, he is very much nutso enough that a Lean certified counterexample to his theories would not dissuade him. His response would be either that the formalization is incorrect (with no coherent insights on how to fix it), or worse, Lean itself is a tool of Western imperialism and incapable of properly explicating his ideas. He has, in the past, ranted against such things as monotheism and English grammar as being the reason for his theories' lack of popularity.

IIRC he has expressed support in the past for attempts to formalize IUT in Lean, but we'll see where that really goes, because he's absolutely not clearheaded enough to lead such a project himself.

Re: Mathematics in the age of AI

#147

Post by efavdb »

one thought: AI can often help us solve a problem once posed. E.g., try to prove that X is True. But formulating good conjectures is something altogether different. right now we have a backlog of interesting / good conjectures that ai can grind on. but once those are done, will we still need people to sniff out interesting new ones?

Re: Mathematics in the age of AI

#148

Post by [deleted] »

frozenseven wrote: post #123
qsera wrote: post #102

Earlier quoted context omitted.

Then it has always been the age of "AI"...So the article title is inaccurate!

We can meaningfully talk about (1) the existence of a field and (2) the said field hitting its stride. The title of Tao's article denotes the latter. And oh, what a stride it is: https://vibemathed.com/stats

[deleted]

Re: Mathematics in the age of AI

#149

Post by nilkn »

chongli wrote: post #142
nilkn wrote: post #107

Earlier quoted context omitted.

We have thousands of years of precedent that suggests that breakthroughs in mathematics tend to accumulate into broader technology breakthroughs in other domains. Why does this tend to be the case, even when some of the smartest people in the world have historically predicted incorrectly that certain branches of math would forever be useless (e.g., number theory)? I can only offer my own theory on that, but my guess…

We have thousands of years of precedent that suggests that breakthroughs in mathematics tend to accumulate into broader technology breakthroughs in other domains. That's a misconception. Only a tiny percentage of mathematics has seen any applications whatsoever. There are vast libraries full of mathematics no one (in this discussion, anyway) has ever heard of that no one reads anymore and has never been applied to an…

> There are vast libraries full of mathematics no one (in this discussion, anyway) has ever heard of that no one reads anymore and has never been applied to anything.

And that's an issue why? It would seem to me that producing that also produced the mathematics that revolutionized the world repeatedly for centuries. I would go further and claim that, if you want the mathematics that revolutionizes the world, there's no way to get it without advancing mathematics as a field broadly. Those are not two separate activities, and thinking that they are is indeed a misconception.

> This idea of trying to "prove all the math" with AI makes as much sense to me as using chess engines to try to "solve chess."

You're right: "prove all the math" does not make sense on any level, and nobody serious would phrase any of this in that way. I certainly didn't.

Re: Mathematics in the age of AI

#150

Post by [deleted] »

sonicrocketman wrote: post #8

Tao's Rule of Thumb (which applies very well to software): > My own suggested rule of thumb: if the authors cannot convincingly demonstrate that they are able to give a clear, expert-level talk on their results, one that is correct and properly attributed, then the result should not be published. A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified.

[deleted]
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