Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Mathematics in the age of AI

arxiv.org

Post reply on HN
Print view View original

181–190 of 292 posts

Re: Mathematics in the age of AI

#181

Post by ziiinq »

glimshe wrote: post #112
zahlman wrote: post #83

Earlier quoted context omitted.

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.

Math isn't "cooperative". Math is about truths. The length of circumference. The area of a triangle. The formulas for these are true in an objective sense irrespective of whether you understand them. That said, without understanding, Math can't evolve. Comprehension of a proof is very important, but not what Math is fundamentally about. Computer programs are Math. You can use them without understanding how they work.

[dead]

Re: Mathematics in the age of AI

#182

Post by zmgsabst »

thatjoeoverthr wrote: post #143
zahlman wrote: post #83

Earlier quoted context omitted.

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.

I’m not convinced.

In history, we made much more use of hitting things with bows than abstractly comprehending arrow flight.

Re: Mathematics in the age of AI

#183

Post by Jensson »

a2ff6eeb0 wrote: post #178
Jensson wrote: post #174

Earlier quoted context omitted.

p = np doesn't produce any value though, the stuff you learn solving it might but the fact that they are the same wouldn't be valuable at all.

sure, agreed, but once you have a proof, you can probably get AI to reduce other problems to that problem in P.

Why wouldn't you be able to do that without a proof? I don't see the value of the proof here, just ask the AI to solve the problem you want and the proof isn't needed.

Re: Mathematics in the age of AI

#184

Post by zmgsabst »

Paracompact wrote: post #146
GPerson wrote: post #136

Earlier quoted context omitted.

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…

Project LANA ran into the same roadblock as Scholze and Stix, when they attempted to formalize the proof in Lean.

Re: Mathematics in the age of AI

#185

Post by Jensson »

glimshe wrote: post #166
ves wrote: post #153

Earlier quoted context omitted.

This hasn't been a remotely reasonable characterization of math since at least Hilbert's time.

I think Hardy would be very much on the same page with me, as well as Godel and many others. Mathematical truths exist independently from our feelings and processes to discover them. People do and should argue about which truths are interesting to pursue and refine, but all of them are out there to be discovered... or not. Whatever philosophy you prefer, math is about establishing objectively valid logical results, c…

Axioms don't exist independently from our feelings and processes, we pick axioms we feel are good, and axioms defines mathematics.

Mathematicians even argue which axioms we should have, it isn't objective in the slightest, mathematics is therefore very closely linked to our feelings and intuition. Remove that and you just have formal logic, a very different field.

Re: Mathematics in the age of AI

#186

Post by czgov »

HWR_14 wrote: post #177
czgov wrote: post #173

Earlier quoted context omitted.

If it’s an oracle and we know it’s an oracle then it’s not useless. Humans make mistake and there are examples of published results that were widely believed to be correct by experts that later proved to be wrong. Why do you think human verified proofs are better than machine verified proofs? Suppose an oracle tells us the Riemann Hypothesis is correct. There are a vast number of results of the form: If RH is correct…

I asked how would it change anything. What's the next step if an oracle were to tell you p=np that changes anything about the world? We all believe it. It's a magic oracle. Now what?

If it is known that A is provably true then one can study the consequences of A being true. It changes things becuase the body of knowledge has expanded.

Re: Mathematics in the age of AI

#187

Post by czgov »

Jensson wrote: post #176
czgov wrote: post #173

Earlier quoted context omitted.

If it’s an oracle and we know it’s an oracle then it’s not useless. Humans make mistake and there are examples of published results that were widely believed to be correct by experts that later proved to be wrong. Why do you think human verified proofs are better than machine verified proofs? Suppose an oracle tells us the Riemann Hypothesis is correct. There are a vast number of results of the form: If RH is correct…

> It would be very useful to have an oracle tells us whether or not RH is correct. For what? Which product becomes better if it is correct?

You have an unfortunate view of the value of knowledge. The frontiers of science would be static if everyone believed as you do.

Re: Mathematics in the age of AI

#188

Post by frozenseven »

qsera wrote: post #144
frozenseven wrote: post #122

Earlier quoted context omitted.

>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.

>Does not matter. It is still an LLM.

Cool. So now you can accept that "LLMs" are an obvious example of AI.

>You and your idols are, for sake of marketing.

Let's be very clear here. Terence Tao is arguably the greatest mathematician alive. Yet, you are throwing lazy insults and accusations around because you don't like the term "AI". And that's my final comment for you, troll.

Re: Mathematics in the age of AI

#189

Post by [deleted] »

czgov wrote: post #187
Jensson wrote: post #176

Earlier quoted context omitted.

> It would be very useful to have an oracle tells us whether or not RH is correct. For what? Which product becomes better if it is correct?

You have an unfortunate view of the value of knowledge. The frontiers of science would be static if everyone believed as you do.

[deleted]

Re: Mathematics in the age of AI

#190

Post by Jensson »

czgov wrote: post #187
Jensson wrote: post #176

Earlier quoted context omitted.

> It would be very useful to have an oracle tells us whether or not RH is correct. For what? Which product becomes better if it is correct?

You have an unfortunate view of the value of knowledge. The frontiers of science would be static if everyone believed as you do.

The whole point why anyone cares about these proofs is that the things we learn as we make the proof might add value, proving p = np itself isn't interesting, that knowledge has no application and therefore no value in itself.

I have published mathematics so I do value knowledge, but for most of mathematics the value of the knowledge isn't the thing you try to prove it is all the things you learn as you try to prove it. p = np is one such thing.

So the whole interesting bit about it is the proof, not the fact.

Post reply on HN