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Ten advances in mathematics and theoretical computer science

openai.com

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Re: Ten advances in mathematics and theoretical computer science

#91

Post by energy123 »

einpoklum wrote: post #14
aabhay wrote: post #6

My main gripe here is the lack of transparency around the total experiment and construction. I doubt that they simply pointed their model at these ten specific problems alone and gave the model one shot; therefore the $2000 number could be completely misleading, similar to P-value hacking by not disclosing the total experimental setup. I want to know: 1. How many total problems were given to the model, and what perce…

Also, have there been examples of researchers not affiliated with OpenAI (or another LLM creator), who have done something similar? Another question I have is whether or not OpenAI 'simply' hired capable combinatorics researchers to work on problems, and they have, and the use of the model is incidental / secondary to their work.

Many less important Erdos problems have been solved by amateurs prompting ChatGPT 5.{3,4,5,6} Pro using their $200 subscription.

Re: Ten advances in mathematics and theoretical computer science

#92

Post by [deleted] »

asdewqqwer wrote: post #88
traes wrote: post #39

Earlier quoted context omitted.

Not much point to pure math being kept secret, in all honesty. There isn't really industrial value, its only purpose (to them) is showing off their model's capabilities. More realistically they'll just stop paying for it. Edit: Oh, are you suggesting they just use it to privately improve their models? I imagine a few more correct proofs would have a very marginal benefit, if any. Also, they'll probably just get extra…

At this stage. No doubt calculus had plenty industrial benefit.

[deleted]

Re: Ten advances in mathematics and theoretical computer science

#93

Post by don_esteban »

mathisfun123 wrote: post #66
raincole wrote: post #32

Earlier quoted context omitted.

Sorry, OpenAI's take is correct here. If you're not convinced, here is how they prompted LLM: https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98... [0] A slightly smarter highschooler could write these. I could write these. It's clear as day that the LLM, not the human, did the heavy lift. It'd be ridiculous to give full credit to whoever wrote the prompt. [0]: Not one of the proofs in the linked article, b…

I don't disagree with you but there's no need for exaggeration; ain't no high school student writing this: > In particular, proofs for special graph classes, constructions of cycle covers with some edges covered other than twice, bounded-length or prescribed-cycle variants, reductions to another unproved conjecture, computational verification through any fixed graph size, and candidate counterexamples without a compl…

the fact that such things have to be explicitly in the prompt points to the fact that the underlying system is still far from where it needs to be (basically, lacks basic understanding what a proof is)

Re: Ten advances in mathematics and theoretical computer science

#95

Post by dist-epoch »

aabhay wrote: post #6

My main gripe here is the lack of transparency around the total experiment and construction. I doubt that they simply pointed their model at these ten specific problems alone and gave the model one shot; therefore the $2000 number could be completely misleading, similar to P-value hacking by not disclosing the total experimental setup. I want to know: 1. How many total problems were given to the model, and what perce…

I don't think you want to bring cost into this argument.

Even if the cost was $1 mil for these 10 problems, that's maybe 10-20 math researchers for a year.

Do you really think that if you paid that to humans, they will deliver the same results?

Re: Ten advances in mathematics and theoretical computer science

#96

Post by DrBazza »

Replace philosophers for mathematicians and Douglas Adams was spot on again.

Whilst current models can't 'intuit' and come up with conjectures, they can certainly disprove some of them very quickly through the kind of grind that humans can't do. I suppose there really are some mathematicians out there today, whose last few years of study, have just been up-ended by this.

--

"Yes we are," insisted Majikthise. "We are quite definitely here as representatives of the Amalgamated Union of Philosophers, Sages, Luminaries and Other Thinking Persons, and we want this machine off, and we want it off now!"

"What's the problem?" said Lunkwill.

"I'll tell you what the problem is mate," said Majikthise, "demarcation, that's the problem!"

"We demand," yelled Vroomfondel, "that demarcation may or may not be the problem!"

"You just let the machines get on with the adding up," warned Majikthise, "and we'll take care of the eternal verities thank you very much. You want to check your legal position you do mate. Under law the Quest for Ultimate Truth is quite clearly the inalienable prerogative of your working thinkers. Any bloody machine goes and actually finds it and we're straight out of a job aren't we? I mean what's the use of our sitting up half the night arguing that there may or may not be a God if this machine only goes and gives us his bleeding phone number the next morning?"

Re: Ten advances in mathematics and theoretical computer science

#97

Post by schleck8 »

robinhouston wrote: post #87

In a way the most remarkable thing about this is that it isn't even at the top of the HN homepage. Even if this is a step up from what we've seen before, we're no longer astonished by the idea that AI can make significant advances in mathematics and computer science.

This is one of the most impactful mathematical publications in history by all accounts

I think we've now hit a point where 99.9% of the population gloss over these types of AI advancements because of human competence being insufficient

No human could have published this because it requires paradigm shifts (e. g. Section 5) in multiple mathematical domains. Mastering one of them to this degree is rare, mastering 3+ pretty much non existent for humans.

Re: Ten advances in mathematics and theoretical computer science

#98

Post by dist-epoch »

esperent wrote: post #70
simianwords wrote: post #59

Earlier quoted context omitted.

Yeah fair I concede that this is somewhat crucial information. The parent seems to write it in a tone that suggests deliberate misleading “lack of transparency” etc.

> deliberate misleading “lack of transparency” etc It's a marketing post from a huge company. Only the naive would view it uncritically without assuming it's been written carefully to present the results in the best possible light while skirting the boundaries of outright lying.

The results speak for themselves.

Imagine 2 years from now: "yes, GPT solved the Riemann Hypothesis, but cmon, it's just a marketing stunt to hype their stuff, it was probably Terence Tao doing the work but he's so obsessed with hyping AI that he doesn't want to take credit"

Re: Ten advances in mathematics and theoretical computer science

#99

Post by kingstnap »

It's remarkable how you can manage to get these models to produce remarkable breakthroughs like an explicit construction of a non-sofic group.

And yet this is the exact same company that has screwed up their android app so bad that the latex N^3 rendering problem makes it so having it explain it to me crashes the app.

Truly jagged beyond belief.

Re: Ten advances in mathematics and theoretical computer science

#100

Post by antirez »

robinhouston wrote: post #87

In a way the most remarkable thing about this is that it isn't even at the top of the HN homepage. Even if this is a step up from what we've seen before, we're no longer astonished by the idea that AI can make significant advances in mathematics and computer science.

This is not at the top as it is actively flagged by people that can't psychologically cope with the advances of AI. Hacker News is no longer a web site of an elite.
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