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

201–210 of 292 posts

Re: Mathematics in the age of AI

#201

Post by qsera »

frozenseven wrote: post #188
qsera wrote: post #144

Earlier quoted context omitted.

> 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.

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

Not sure what this has to do with what I said. A lot of things have been called "AI" in various times. None of them including the current crop of LLMs are not really AI. But people use AI term loosly and that is fine. But it is a problem when a some thought leader does it.

>troll.

Tell me you have run out of arguments without saying you have run out of arguments...

Re: Mathematics in the age of AI

#202

Post by enriquto »

js8 wrote: post #200
HWR_14 wrote: post #164

Earlier quoted context omitted.

If a magic oracle tells you p=np, that's useless. How would that change anything?

Oh it would change a lot. It would be an enormous psychological boost for everyone to find a practical algorithm. In any case, I think it's better to read PP as somebody would find a practical, albeit incomprehensible, algorithm for solving NP complete problems. Although I probably disagree with PP, because even a candidate algorithm that mysteriously works without proof would have practical value, so this case is no…

> a practical, albeit incomprehensible, algorithm for solving NP complete problems.

It would not not necessarily be practical, even if it ran in polynomial time. It may have cost O(n^c), with a totally out of order exponent like c=A(5,5) or whatever.

Re: Mathematics in the age of AI

#203

Post by sothatsit »

Scarblac wrote: post #156
d4v3 wrote: post #119

Earlier quoted context omitted.

> Without persuading other people of the “truths” that you discover, there is no real mathematics. Why? If I sat around and studied math by myself and discovered something true yet not yet known but didn't share it, it's still true. Are you saying I didn't "do math" because I didn't share the result? Math exists on another plane and it has 'truths' that we haven't discovered, yet are still 'true', no?

Sure, but just that some random statement is true isn't interesting. It's interesting if it helps understand some abstract structure better.

It could also be interesting by having a practical use.

Re: Mathematics in the age of AI

#204

Post by ipdashc »

highfrequency wrote: post #7

Terence Tao's quote about AI's math proofs is relatable outside of pure math: "the writing very often dwells at length on trivialities while passing briefly through — or even actively obscuring — the most interesting and novel portions of the argument."

Someone just brought up this point to me a few days ago on here, I'm definitely increasingly convinced that it's one of the main reasons (maybe even the main reason?) AI prose is so annoying to read through, and so rarely seems able to convey true understanding. It assigns the same narrative importance and dramatic tone to everything (the load bearing whatever, the crucial insight, the smoking gun) even when it's trivial.

Re: Mathematics in the age of AI

#205

Post by amoss »

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.

If you place an LLM into a harness, alongside evaluation, feedback and problem decomposition / solution integration - it is still an LLM?

There is an LLM acting as a component in a larger system. But that larger system is not an LLM. Calling it an "AI" is indeed an act of marketing as there is no learning / adjustment as we would expect from an intelligence, but calling it an LLM seems to be inaccurate. So what is it?

Re: Mathematics in the age of AI

#206

Post by visarga »

esafak wrote: post #75
auggierose wrote: post #67

Earlier quoted context omitted.

Whose requirements?

The employer's, whose salary affords your subsistence.

If AI is so great it can do your job it is good enough to provide for your needs directly by automation. Just buy a robot and a plot of land and you don't have to worry about jobs.

Re: Mathematics in the age of AI

#207

Post by leonidasrup »

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.

The goals of Chess and Math may be different, but they follow the same principle of exploration large search space according to fixed rules. In case of Chess these are chess rules, in case of Math these rules of mathematical logic.

Memorized proof patterns have value because they lead you to a final proof.

Re: Mathematics in the age of AI

#208

Post by i_am_a_peasant »

ivansavz wrote: post #16
sonicrocketman wrote: post #3

Anyone else print their white papers before reading? (At least the short ones)

Absolutely. I feel I gain at least 10 IQ points when reading something on paper. This is also the strategy I use for editing drafts of my books. I bring a printed draft to someplace nice (e.g. coffee shop or park) and read it all carefully, then I transfer the edits back to the .tex sources. I do several passes of this, until I feel the text + explanations are solid. Reading on screen just isn't the same...

Oh hey I was thinking of buying your stats book! I'll do that right away.

Re: Mathematics in the age of AI

#209

Post by js8 »

enriquto wrote: post #202
js8 wrote: post #200

Earlier quoted context omitted.

Oh it would change a lot. It would be an enormous psychological boost for everyone to find a practical algorithm. In any case, I think it's better to read PP as somebody would find a practical, albeit incomprehensible, algorithm for solving NP complete problems. Although I probably disagree with PP, because even a candidate algorithm that mysteriously works without proof would have practical value, so this case is no…

> a practical, albeit incomprehensible, algorithm for solving NP complete problems. It would not not necessarily be practical, even if it ran in polynomial time. It may have cost O(n^c), with a totally out of order exponent like c=A(5,5) or whatever.

I know, the goal was to strongman the argument.

Re: Mathematics in the age of AI

#210

Post by Otterly99 »

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.

I was thinking about that too.

I am probably being too optimistic, but wouldn't it solve the problem if peer-review had a pre-screening phase where you give a presentation about your work? Similarly to how a PhD presentation is given. It could give back the publishing power to the expert, rather than the journals.

Once you have validated that the knowledge you want to publish is yours and that you actually understand and own the work, then it doesn't matter if the paper is written by a LLM or if the LLM assisted you in doing the work.

Post reply on HN