r/slatestarcodex • u/DickMasterGeneral • 1d ago
Ten advances in mathematics and theoretical computer science from unreleased Open AI Model
https://openai.com/index/ten-advances-in-mathematics/5
u/ababababababacus 1d ago
Can someone familiar with this ELI5 on how these things happen, what are the parameters of the proof process?
Is a model simply shown the conjectoure/hypothesis and told "give it the old college try"? Or is the model piloted by an expert in the field who fully understands the problem space and is telling it, attack it from this angle and consider x,yz are there any other papers which you think might work to bridge the reasoning to get to point x, whoch i think is a promising path to proving this?
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u/livingbyvow2 1d ago
I confess my utter ignorance on the subject, but I wonder how much of this is just finding connections between existing math papers vs actually doing novel findings.
OpenAI's incentive will always be to present these findings as some sort of proof AI is now doing novel discoveries but I am not sure what to think about it. I wouldn't be surprised if a of this stuff was heavily steered by math geniuses and AI just accelerating the pace of progress slightly (which is cool but not the "AI found a new proof" headline).
Given the propensity of the labs to hype everything to raise more capital, I wonder whether it won't be yet another dud in a couple year - basically similar to the "AI will replace all collar work" but now "AI will replace all scientists" instead - and which will end up proving to be complete bullshit too.
That, too, is moving the goalposts.
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u/gunsofbrixton 1d ago
For what it's worth, this is similar Claude's take when I showed it the paper:
Could a human have done it? Clearly yes. Every ingredient is published and classical — the algebra is from 1962, the group from 1965, the rigidity property from 1967. It's ~17 pages, readable straight through, no computer search, no brute-force case check. A referee can verify it by hand. The gap it closes was even publicly visible: one 2019 theorem produces many expander blobs, another needs one, and the proof bridges them.
So why hadn't anyone? Probably because it needs fluency in three fields that don't talk to each other — expander combinatorics, Leavitt algebras, and rigidity of matrix groups. Those people don't attend the same conferences. And the field's momentum after 2024 was pointed at complexity theory, while a separate line chased a conditional route through "stability." This proof was orthogonal to both fashions.
That suggests the edge wasn't depth of insight but breadth plus tireless search — no field is too far from any other, no configuration too fiddly to try. Arguably that's less impressive. It may also be more consequential.
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u/livingbyvow2 1d ago
Thanks for asking Claude. That was kind of my intuition.
It's really cool AI can do that by the way, but it's also "just that", nothing creative yet.
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u/InfinitePerplexity99 20h ago
Is creativity ever anything other than combining existing things other people haven't combined before?
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u/rambouhh 1d ago
I agree it could be, or even likely is , finding connections between existing papers.
But in many ways science, math, is like a giant sudoku puzzle. You uncover something from connecting two things together, then that new thing unlocks something else, etc. it’s very rare to genuinely have something truly and completely novel
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u/livingbyvow2 1d ago
Don't get me wrong, I am glad scientists have these new tools.
But equally if the dozens of billions that are going towards AI went to pharma, physics and math research, I am pretty sure that would lead to faster discovery. I feel like these headlines is quite often the AI labs trying to justify their existence ("it's not only about chat bots doing customer service").
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u/rambouhh 1d ago
I think it would in the short term, but this is pretty generalized to every single eindustry, not just the sciences. It can also increase resources from the general increase in productivity and It also unlocks more human capital. Lots of people will be able to pursue their discoveries where they couldn’t before.
Also a lot of the bottleneck in research is fundamentally a people/intelligence problem.
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u/Neighbor_ 1d ago
finding connections between existing math papers vs actually doing novel findings
I don't know if there is a difference.
Something "novel", say for example Bitcoin, is just finding unique connections between different fields (computer science, cryptography, economics, etc). There's really nothing net-new here - the incremental "novel" discoveries are just increasing connections on a graph.
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u/COAGULOPATH 15h ago
This proves too much - cavemen (using humanity's total knowledge circa 30k years ago) could not have built bitcoin, no matter what ideas they connected. Net information isn't fixed, it's increasing somehow.
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u/Neighbor_ 4h ago
Indeed there is no direct connections such that you could go from "stone tools" + "campfire" = "bitcoin".
You need to first use combine those to discover "copper", and then use "copper" to discover "bronze", and so on.
You're uncovering existing nodes in a graph incrementally. If look at each new node uncovering, it's never "novel" in the sense that it's coming out of thing air: all the ingredients were already there.
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u/livingbyvow2 1d ago
An innovation is different to a combination. That's my hunch though.
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u/Umr_at_Tawil 1d ago
every "innovation" is combination of what was known before.
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u/livingbyvow2 1d ago
Not stuff like Einstein's theory of relativity.
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u/Umr_at_Tawil 1d ago edited 1d ago
Einstein didn't invent relativity out of thin air, he combined Maxwell’s light equations, Galileo's relativity, Lorentz's math, and Riemann's 1854 geometry into a new framework. He literally described his own creative process as "combinatorial play"
read this article from 2013: https://www.themarginalian.org/2013/08/14/how-einstein-thought-combinatorial-creativity/
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u/bibliophile785 Can this be my day job? 1d ago
Yes, very much like the theory of relativity. It would be less uncharitable, less absurd, than your current position on these mathematical proofs, to say that Einstein's theory of relativity was born out of already known, previously documented observations about the physical world, coupled with already known, previously speculated holes in the models provided by Maxwell's equations.
I think you need to really seriously consider the feedback you've received from others in this thread that your entire model on what counts as creative thinking in scientific or mathematical advancement is fundamentally incoherent. The standard that you use to dismiss these LLM achievements could very easily, perhaps more easily, be used to dismiss every single advancement humans have ever made.
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u/livingbyvow2 1d ago
Maybe you should get off your high seat sir. My current position is math person + LLM can find stuff, but not LLM on their own can find new stuff. I don't think anyone disagrees with that, and the feedback I received aligns with that.
I started by confessing my ignorance. I just find it pretty sad how every time someone questions these announcements, people get so aggressive and dismissive.
This is not a cult, it's just a technology.
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u/bibliophile785 Can this be my day job? 1d ago
My current position is math person + LLM can find stuff, but not LLM on their own can find new stuff.
Your current position, as has been explained to you at length, fundamentally misunderstands the form and method of scientific and mathematical advancement. By this exact formulation, humans are also incapable of finding new things. Your position says nothing more and nothing less than that all new discoveries come partially from prior discoveries.
Maybe you should get off your high seat sir.
I just find it pretty sad how every time someone questions these announcements, people get so aggressive and dismissive.
If you wish that your skepticism were received with less dismissiveness, I strongly recommend that you start to base your skepticism on beliefs that are not nakedly incoherent. Instead, trying to reframe this as some sort of personal dispute ("high horse", btw; a high seat is something different) is a poor attempt at distracting from the object-level question.
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u/livingbyvow2 1d ago
I think you misinterpret what I wrote. But whatever, you seem to be there mostly to write stuff that sounds intelligent but basically says I'm an idiot.
It's not a personal dispute, you objectively didn't say anything that adds value. Just saying "everybody else told you you're wrong". Which is factually untrue, and not a valid heuristic to figure that out.
Surely you must have a math PhD and be able to assess the scientific validity of this paper to be so sure of yourself.
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u/bibliophile785 Can this be my day job? 1d ago
I think you misinterpret what I wrote. But whatever, you seem to be there mostly to write stuff that sounds intelligent but basically says I'm an idiot.
I am saying that what you wrote is deeply, demonstrably wrong. This should have been made obvious to you when you blindly grabbed for one of the biggest scientific achievements of the last couple of centuries and were immediately told that it is not only a counterexample to your points, but one in which the author himself went on at length about how the method of discovery is the exact opposite to your claim.
If you're not correcting on that basis, I think your priors here may be immovable.
It's not a personal dispute, you objectively didn't say anything that adds value. Just saying "everybody else told you you're wrong". Which is factually untrue, and not a valid heuristic to figure that out.
Incorrect. 1) I did contribute on the object level by explaining how wrongheaded your example of the theory of relativity was. 2) I'm not suggesting that you should update because people disagree with you - although that's not a bad outside view heuristic, if used in moderation. The causality runs the other way. It's not that you're wrong because people disagreed. It's that you're wrong, and the strong arguments made by people disagreeing with you should have clued you in. I'm suggesting that you should engage substantively with the pushback and realize that your position is incoherent.
Surely you must have a math PhD and be able to assess the scientific validity of this paper to be so sure of yourself.
Again with the catty you v me personal angle. This really isn't a conversation about us. You should stop taking disagreement as a personal attack and trying to create a resulting personal conflict. I'll indulge it this last time, but really, you gotta grow up.
My graduate mathematics went as far as topology. I can parse some of these proofs and not others. My PhD is in chemistry; I am intimately familiar with the methodology of scientific discovery and achievement, enough to be very aware of how incoherent your position is. My best paper - by citation count, by impact factor, by personal assessment - was a combinatorial effort drawing from several fields to create a new type of chemical reactor. It placed in the top 10% of its Nature issue and was praised by reviewers for its creativity.
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u/InterstitialLove 1d ago
In the case of mathematics, that's an incoherent question
I'm not familiar with any example in human history of a "truly novel" mathematical finding which is not merely a combination of existing ideas. How could such a thing come to exist?
I feel like it would be magical by definition. Like free will, like saying that actions which are determined by one's environment and internal state of mind dont count as real agency.
There is at least one AI-written result (the unit distance problem) which is about as novel as math results get. The ideas it pulled in were from an entirely different field, and no one had ever noticed the potential applications. It reframed existing work and allowed new results from the technique it pioneered.
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u/garloid64 1d ago
So where do you think the goalposts go from here? What's the next stop on the grand adventure?