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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

#531

Post by gowld »

halJordan wrote: post #236
dgacmu wrote: post #184

Earlier quoted context omitted.

This isn't really about delivering - it's more about helping to understand the shape of problems that AI can solve right now. If they took 1000 problems and threw the model at it and it solved these ten, is there something we learn about these ten problems and the kinds of things that current AI is good at? That's very different from picking ten problems _at random_ and solving all of them successfully, which would s…

That's totally disjointed from anything in this thread. The main accusation is that openai is cherrypicking math problems and we should be against these results. As if a mathematical proof stops being provably correct because it was cherry picked And frankly these "concerns" ignore reality. In any research phd course you're actively told to bite off something small and likely to be provable so that you can prove it (…

> In any research phd course you're actively told to bite off something small and likely to be provable so that you can prove it (and publish it).

But that's the start of math research, not the end.

The point is to get practice and experience doing research.

Did ChatGPT learn anything from these proofs, that it can build on?

Part of what's annoying people is that ChatGPT is churning though problems that are meant to be motivating. They are problems that aren't worth the effort of human professionals (usually because they are incredibly computation-hevy, so better suited for a computer than a human), so they are good for students to work on.

Re: Ten advances in mathematics and theoretical computer science

#532

Post by denismenace »

pama wrote: post #512
sdenton4 wrote: post #495

Earlier quoted context omitted.

Some of them... The two places were seeing lots of movement are: * Updates to lower/upper bounds. In many cases, these kinds of problems are the deep-math equivalent of calculating more digits of pi. Yes, if you throw time at it you'll break the record, but it may not be terribly worthwhile. * Finding counter examples which disprove conjectures. This is really useful, and helps offset some positivity bias on the huma…

It is unfair to dismiss contributions to decades old open problems as equivalent to calculating more digits of pi. It missed the mark by a lot—as does the two bucket simplifaction.

How does calculating more digits of pi help us?

Re: Ten advances in mathematics and theoretical computer science

#533

Post by sothatsit »

People argue whether we are at y-5, y, or y+5, meanwhile we seem to be on a y=2^x exponential that keeps delivering more and more impressive results.

The most interesting question to me is what will be consumed by the exponential like math seems to be undergoing, and what won’t. Writing has been quite stubborn, but I’ve noticed Fable to be quite a big step up there. How about politics? Will we develop new ways to let people express their own values in democracies, or will we just get much better at manipulation? How about experiment driven domains like biology?

Re: Ten advances in mathematics and theoretical computer science

#535

Post by vessenes »

cwiz wrote: post #529

I feel increasingly anxious reading this. Machine research shouldn’t be merged into mainline of human knowledge.

When you can formalize it in Lean or some such, why would this be? I can understand the desire to separate out other forms of research from the human corpus. But theoretical math that is decidable/provable, I’m not sure I see the risks.

Re: Ten advances in mathematics and theoretical computer science

#538

Post by paxys »

christofosho wrote: post #134

I would love more time and money put into real-world problems by these companies. Climate, food insecurity, pollution, technology for convenience and/or to help people have a higher quality of life. I'm sure they must do some of this type of work, right?

None of these problems need technology to solve. Step 1 is trying to get different groups of people to cooperate with each other. Good luck with that.

Re: Ten advances in mathematics and theoretical computer science

#540

Post by orangecat »

HarHarVeryFunny wrote: post #471
Chance-Device wrote: post #446

Earlier quoted context omitted.

Asking questions about policy and values and pushing to have those resolved in positive ways is about as far away from denial as you can get. It’s possibly the only useful thing an ordinary person can do. What a lot of people want to do, and I’m not saying that you’re one of them, is to assume that a positive outcome is impossible and either do nothing or loudly yell that the world is ending. Neither is particularly…

The AI companies themselves, who are highly motivated to sell AI as overall positive for society, notwithstanding some security/etc risks, and who have economists on the payroll to think about things like this, do not seem to have found any possible positive outcome to present. Shane Legg (DeepMind co-founder), one of the more intelligent and thoughtful people you'll find in the industry, could only offer "it's a tou…

do not seem to have found any possible positive outcome to present

See "Machines of Loving Grace" by Dario Amodei: https://darioamodei.com/essay/machines-of-loving-grace.

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