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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

#291

Earlier quoted context omitted.

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?

Grad students on zero pay solve problems like this everyday. What exactly is your point here?

Grad students do not solve problems such as the existence of non-sofic groups every day.

Re: Ten advances in mathematics and theoretical computer science

#292

Earlier quoted context omitted.

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?

Grad students on zero pay solve problems like this everyday. What exactly is your point here?

Zero pay? These would be PhD candidates; surely they have a stipend?

Re: Ten advances in mathematics and theoretical computer science

#293
People weren't their strongest even when most did manual labor. Now that humans are free from mental labor we work on creating and optimizing the best exercises for each mind. Couple that with restructuring transport infrastructure and diets many people will be smarter and fitter than at any time in history. They won't be able to outrun an automobile or out think an autointelligence.

Re: Ten advances in mathematics and theoretical computer science

#294
post #186
post #158

Not being an expert in any of the fields OpenAI has "advanced" I don't want to prematurely downplay the significance of this contribution. However, I am worried that the language they are using in this blog post is exaggerating for the sake of marketing. It is true there hasn't been a reliable computational approach to solving these problems before. But do these proofs contribute new ideas to the mathematical corpus,…

"Breakthrough research" can be defined (in the citation record) as research that both (1) becomes highly cited, and (2) brings together citation chains that were previously not showing up together. Mundane incremental research is cobbled from existing citations that already appear nearby in the record. Basically, innovative research is a measure of bridging thought and domains that were previously not bridged. It's q…

Breakthrough math research is very rarely highly cited. Maybe some combination of pretraining scale, inference speed and orchestration will help, but it's telling that OpenAI is solving random math research problems rather than bedrock algorithms and their implementation. Even as cool as the tech is, there still is very much a clock that they have to outrace before they collapse.

Re: Ten advances in mathematics and theoretical computer science

#295

Any advances in theoretical physics yet? Are there any fundamental obstacles? I would have thought not, but I haven't seen anything reported.

The fundamental obstacle is that we have no conceivable way to produce the energy levels to test the predictions that new theoretical physics would produce. We are like over a dozen orders of magnitude off.

Re: Ten advances in mathematics and theoretical computer science

#296

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.

I like your comments and agree with a lot of your points, including parts of this one. That said, please don't go to this route. A lot of the doomerism comes from financial insecurity fears. Try to remember that a lot of people are subconsciously afraid of losing their homes. I know that it is pretty hard to ignore them, but try to engage with people that do not dismiss 100% of AI accomplishments.

Re: Ten advances in mathematics and theoretical computer science

#297
post #293

People weren't their strongest even when most did manual labor. Now that humans are free from mental labor we work on creating and optimizing the best exercises for each mind. Couple that with restructuring transport infrastructure and diets many people will be smarter and fitter than at any time in history. They won't be able to outrun an automobile or out think an autointelligence.

[dead]

Re: Ten advances in mathematics and theoretical computer science

#298

Earlier quoted context omitted.

Capabilities of this sort have already been demonstrated by independent parties, and models have consistently gotten better at this. Yes, insinuating that mathematicians and scientists are secretly solving decades-old problems on OpenAI's behalf is an insane conspiracy theory.

That's not what is being purported, you're doing a complete misdirect. OpenAI wants to IPO so Altman can potentially capture a trillion dollar bag, with so much money on the line + betting US foreign policy on it as well (pax silica) it's not hard to be overly suspicious of such claims. Especially in the context of a group of people wanting to generate a new decades long cold war in the form of China being the new bi…

Altman has no shares in OpenAI.

Re: Ten advances in mathematics and theoretical computer science

#299
Can anyone comment on the significance of any of these results for their respective fields? Or what impact they might have? Presumably none are quite at the level of the Jacobian conjecture, but some of the results on group theory and sphere packing sound pretty important at first glance.

Re: Ten advances in mathematics and theoretical computer science

#300
post #7

Earlier quoted context omitted.

No, the correctness isn't for the "inside the Lean proofs", but for the translation of "human language math" and its formal Lean variant.

I see. It still feels like a bit of an oddly solemn way of saying "this is the part we admit responsibility for"

Traditionally, a mathematician would be implicitly responsible for all that (if they were to publish Lean code) and also the intellectual work that led to the artifact of the mathematical paper (and code, if part of the contribution). This statement should rather be read as an acknowledgement of limitation of authorship from the implicit, traditional understanding.
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