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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

#141

Post by simianwords »

esperent wrote: post #127
dist-epoch wrote: post #98

Earlier quoted context omitted.

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"

Nobody is claiming the results are false. We're saying look critically at the claims for how it was done, that it only cost $2000, etc. it would be extremely easy to run 100 sessions that failed, each costing ~$2000, and then just publishing an article about the one that succeeded, for example. This goes double since it's an internal secret model (Astra) so nobody else can verify the results.

Would this be your reaction if OpenAI also solved millennium problems? The point we are trying to make is that the significance of this news is much larger than the skepticism you are providing.

Re: Ten advances in mathematics and theoretical computer science

#142

Post by foobar10000 »

utopiah wrote: post #130
xyzsparetimexyz wrote: post #104

Any implication of any of these findings? They seem like unimportant nerd snipes to me. If you want to do something actually relevant, get chatgpt to write a simulation of graphene nanotube construction and figure out how to do it at scale.

Very marketable nerd snipes indeed.

One - and I do not mean to be snarky - you can literally ask Gpt 5.6 Sol this - and if you want to see cool stuff - Fable running in their app (not website) has a view thinking button that is actually a good way to explore the adjacent fields, etc.

The non-sofic group one is definitely a big deal - would have been a Fields medal if discovered by a human.

Re: Ten advances in mathematics and theoretical computer science

#143

Post by kzrdude »

piker wrote: post #2

I don’t feel the existential dread of mathematicians is correct. It seems to me in fact these results are bringing math mainstream. I now personally look forward to the interpretations and discussions of the significance of such results by human mathematicians. Now I understand that it’s mostly the super stars benefitting from the increased attention. Folks who are less established don’t share in that glory. But on t…

Do mathematicians have the right to say "no AI PRs please, the volume is too much" just like how some open source maintainers do it? I guess they feel a loss of control, there is no way to turn the hose off.

Thinking of this a little bit with the perspective of every new proof as a burden, dumped for review by actual mathematicians.

Re: Ten advances in mathematics and theoretical computer science

#144

Post by kevinwang »

dist-epoch wrote: post #95
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?

It would still provide better context to see the numbers that the parent proposes, though.

Re: Ten advances in mathematics and theoretical computer science

#145

Post by frenzyguy »

This is both awesome and terrifying for mathematicians, however some ideas can be generated and the field as whole expanded with the attention!

However, I was looking at the proofs and reason explanation and openAI should be more explicit in how the work has flown. I find the models have jumped hoops in some places of the proofs, that can be hard to track. In fact, when a paper is published you usually get a review and if no reviewer understands they ask you to further explain the thought process. It will be fun to see if this happens here.

Re: Ten advances in mathematics and theoretical computer science

#146

Post by woeirua »

Delk wrote: post #77
naasking wrote: post #19

Earlier quoted context omitted.

> AI has no self-awareness What is your mechanistic model of self awareness that yields this conclusion? > It's a tool Does your model suggest that tools can't have self awareness?

I honestly don't think a language model is enough for self-awareness, regardless of the exact model of awareness. A language model (or an image model or whatever) cannot even be sentient, and I think sentience is a prerequisite for awareness. Even if we express a lot of our subjective experience with words, the language is just a symbolic representation of those experiences. The qualia themselves, even those that are…

So… your model is 100% vibes based. Got it.

Re: Ten advances in mathematics and theoretical computer science

#147

Post by saithound »

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.

I don't think that's it. Multiple or my friends from the target audience (academic mathematicians) admitted to scrolling past because the title made it sound like a review of last month's contributions, instead of 10 new ones.

Re: Ten advances in mathematics and theoretical computer science

#149

Post by robotpepi »

dist-epoch wrote: post #95
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?

it's still important. not everyone has access to 1 million USD. saying it "only" coat 2000 USD is highly misleading for the discussion and future. the concentration of power is a huge problem with AI.

Re: Ten advances in mathematics and theoretical computer science

#150

Post by woeirua »

ultimatefan1 wrote: post #118

one of the early premises of how ai takeoff would go was that a system that could solve open problems in advanced mathematics would also discover novel advances in math and computer science that directly unlock drastically better software performance. we are seeing frontier level math breakthroughs (ie performance that would put it in the top 100 or 1000 mathematicians in the world if it were a human, meaning top .00…

This makes no sense. To believe this you have to think that the models are somehow being overfit explicitly on academic mathematics and it doesn’t carry over at all to more practical software engineering. I wouldn’t make that bet.
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