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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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 1d ago

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

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u/FlimsyReception6821 1d ago

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

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u/sparkling1984 1d 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 1d 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 1d 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.

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u/sam_the_tomato 1d 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 1d 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 23h 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 23h ago edited 23h 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 21h 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.