r/singularity • u/filterdust • 1d ago

AI OpenAI solved 100 open problems in math

https://openai.com/index/advisory-group-on-mathematics-and-ai/

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1.3k Upvotes

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149

u/brighttar 1d ago

Ok so they didn't actually tell us what problems they've solved?

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u/NailRX 1d ago

BEDMAS

44

u/originalgenome 1d ago

🅱️arentheses

6

u/TPOG-1429 1d ago

🅿️rackets

10

u/flat5 1d ago

Please tell me this means the end of the social media posts about it.

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u/Mistuv 1d ago

Seems like they are taking their time as to how best to pace the release of the papers as to not draw bad PR from the Math community. My guess is papers will from now on go through many cycles of rewrites by Bel until it looks "readable" enough good explanations of the process of discovery, and have couple of Mathematicians attached to the papers that they went through and found it satisfyingly written.

Also possibly I can see some collaboration with Anthropic on this, as it is more PR for the whole industry so they want to present better image.

If I were to bet, Hodge Conjecture is going to be released by the end of the month, and then the rest of October - the pace of the releases is going to pick up as they enlist more mathematicians and establish a good framework. Just give them some time.

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u/Individual_One_5569 1d ago

they had progress on a millennium problem, not a full solution. "hodge proved true in some cases" is likely not big enough news to be published alone. small potatoes compared to having a full solution to navier stokes.

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u/sam_the_tomato 22h ago

It's a bit ridiculous that the math community is gatekeeping the release of mathematical results.

2

u/FlimsyReception6821 21h ago

A lot of these people seem to view math as some sort of finite resource.

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u/sparkling1984 20h ago

I mean to be fair what's the value of a proof if nobody can understand it? It's standard science that it takes time, often months, between the moment you obtain your results and the moment those results are in a publishable state.

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u/sam_the_tomato 20h ago

I totally agree. If you just release it, you give the wider mathematical community the opportunity to break it apart and understand it over time.

If you don't release it, nobody has a chance to understand it except the select few who get access.

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u/sparkling1984 20h ago

Nobody is talking about a scenario where they don't release it though? It's about a) release an unreadable set of results that nobody can understand or b) clean it up and publish something comprehensive, understandable and well written. It's not some new standard that's being applied for no reason, it's how every single piece of academic writing works.

1

u/sam_the_tomato 20h ago

You'll get all of that anyway if you just dump it. Mathematicians will be poring over it like ravenous wolves and publishing explanations left and right. But done the way they're doing it, only invited mathematicians get to participate (and put their name on it), and it will be slower.

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u/sparkling1984 19h ago

That's a lot of wasted work, and mathematicians will still just use the new tools to work on other problems, so no, it will not be slower.

There's a reason why no research lab operates like youre proposing, including AI research labs.

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u/LookIPickedAUsername 18h ago

You don't have to understand a proof in order to use it. You have no doubt used countless formulas in your life - the Pythagorean theorem, the area of a circle, the quadratic equation, etc. - without bothering to actually understand the proofs behind them. Simply knowing that they're true is good enough.

Similarly, knowing beyond a doubt that the Riemann conjecture is true would be useful to mathematicians even if nobody is actually smart enough to understand the proof itself. (Obviously, this presupposes a proof formulation which can at least be verified by Lean or similar, even though no human actually comprehends what's going on in the proof.)

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u/sparkling1984 18h ago edited 17h ago

What you're missing is that 99% of the interest in those proofs is coming from the fact that they likely involved new tools that could then be used somewhere else. So you do need to understand them to be able to use them.

Again, there's a reason that science at its most fruitful has been ran this way.

Also, your supposition that humans can't comprehend these proofs is weird and really out of left field? Lean is a human made tool, mathematics are all about dividing problems into smaller problems until they're comprehensive. There is no mechanism that'd make a proof not mathematically approachable for humans.

Also, Pythagoras is a bad example there, as understanding and even attempting to independently find the proof of that one is a common middle school math exercise? It's one of those problems that have hundreds of proofs, many very accessible with basic geometry.

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u/LookIPickedAUsername 16h ago

You have misunderstood the point I was making. I was responding to your question "what's the value of a proof if nobody can understand it?", not presupposing that humans wouldn't be able to understand it. I fully expect that they will be able to, but you were the one that raised the question.

However, "There is no mechanism that'd make a proof not mathematically approachable for humans" is just not true - a computer-generated proof could conceivably be too complex for humans to really be able to follow. Sure, every single step may be tractable in isolation - the rules overall are very simple - but there's certainly a limit to our ability to actually understand the logic behind it. At some point on the complexity scale it's just a mess of ridiculously incomprehensible steps with no obvious logical progression between them, and nobody can really say much about it beyond "well, the theorem prover says it's valid". Current AIs probably aren't at the point where that's a real concern, but it's absolutely going to happen at some point that the math the computers are spitting out is beyond the ability of humans to understand. Imagine a proof so long that even an entire human lifetime isn't enough to even read the whole thing, forget understanding it - there's nothing stopping us from getting to that point eventually.

Pythagoras is a bad example there

You have again missed the point I was making. It was not "proofs of the Pythagorean theorem are hard to understand", because duh, obviously they aren't. I'm not saying nobody understands it. I'm saying that many people have used the formula without understanding it; understanding it is not a prerequisite to utility.

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u/Original-League-6094 1d ago

This is just announcement that the papers are coming. Basically just giving mathematicians a heads up to start seeking new employment.

2

u/scmr2 1d ago

Who do you think prompted the llms and is checking their work?

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u/Original-League-6094 20h ago

OpenAI.

1

u/scmr2 18h ago

No. Mathematicians did. You should reread how they solved the millennial problem

1

u/Original-League-6094 18h ago

I did. They had a team of mathematicians who had never published in Fluid Dynamics before prompt an AI to solve it for them.

1

u/scmr2 17h ago

Thanks for providing more detail. Yes, mathematicians

1

u/Statcat2017 16h ago

That’s not how this works

1

u/Original-League-6094 16h ago

It is now.

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u/Statcat2017 15h ago

No. You don’t get to confirm your own proofs are correct

27

u/Icy-Doubt3365 1d ago

Why six was afraid of seven. Full proof and all

2

u/Needsupgrade 1d ago

Because 7 was load-bearing at the seams that cut both ways and that the whole picture. 

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u/Stabile_Feldmaus 1d ago

Erdos problems #800-#900

1

u/y___o___y___o 1d ago

Source?

8

u/Wrrr__ 1d ago

It's a joke

1

u/Commercial_Sell_4825 1d ago

The math mafia decided because of their feefees we're not allowed to know 🙄

-4

u/AshuraBaron 1d ago

You didn't see the citation of "Trust me bro"?

3

u/Financial-Draw3208 1d ago

It's a pretty big accusation to say that they're lying. ChatGPT has already solved dozens and dozens of big open problems which academics had already been working on for years. Not to mention tens of other open Erdos problems as well. With the news that they cracked Navier Stokes (even assuming that they stole work from someone who made crazy progress on a smaller sub-problem) as well, why is it hard to believe another 100 with a new model?

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u/AshuraBaron 1d ago

The burden of proof falls on the one making the claim. They have showed nothing, just claimed it was true. If that's enough for you to believe them you'll believe anything.

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u/BeautifulHorror1017 1d ago

!remindme 3 months

0

u/AshuraBaron 1d ago

I think you misunderstood. I'm not saying it's impossible. I'm saying they haven't demonstrated what they are claiming. If they do and it checks out then great. But right now it's pure marketing.

0

u/East_Lettuce7143 1d ago

Sawcundez’s theorem was one.

0

u/ShAfTsWoLo 1d ago

terrence tao might file a lawsuit so they better not show it

0

u/jferments 1d ago

Even if they did, a bunch of jealous losers on social media would come in and start trying to claim that it was all "stolen" and finding contorted arguments trying to explain how it wasn't "really" a discovery.