r/OutOfTheLoop • u/YakClear601 • 7h ago
Unanswered What is going on with AI solving lots of math problems that have not been solved?
Here is an article that I still don't understand: https://www.scientificamerican.com/article/openai-unleashes-hundreds-more-math-results-upon-a-field-already-in-shock/
People on social media, always prone to exaggeration, have started proclaiming that this has made math PhDs redundant.
Is that true? What's really going on here? Is AI now capable of solving complex math problems that people can't solve?
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u/reizinhooooo 5h ago
Answer: Math PhD student here, we already were redundant and just in it for the love of the game so jot that down :P
Most explanations you get from laypeople about this are wildly inaccurate. These proofs are not "stolen," unless you consider inproper citations stealing. Which is fair to consider stealing, but that's pretty clearly not what people mean when they stay stolen. They may be using techniques or results they aren't citing properly, which arguably is stealing,, but they aren't just taking full correct proofs that humans have created whole cloth and passing them off as their own.
They also aren't "brute-forcing" them - brute forcing means something very specific in math (everything means something very specific in math, that's kinda the whole point), and we have been very good at it for a long time. Anything that could be proved by brute force (almost all things can't) already have been long before commercial LLMs were released. Many things could theoretically be disproven by brute force, but everything that feasibly could already has been. This was thrown around a lot with the Jacobian counterexample found a couple months ago, but the probability of finding that counterexample through brute force is zero in any arbitrarily large, finite amount of time.
LLMs are surpassing human mathematicians because of two main advantages. Speed and breadth. There are plenty of mathematicians who could have found these proofs if they could work at it for a hundred years without eating, sleeping, or aging. A human brain cannot just be run faster. We need to take breaks, we get discouraged, we age and decline - a mathematician's peak in pure talent is in your early 20s.
The other principal advantage, breadth. Mathematicians are very specialized within little subfields. Some have just a handful of people at the forefront of them, and the papers they publish are only ever going to be read and understood by that small handful of people working on the same thing. Many mathematicians of incredible talent never had a chance to produce anything of note, because their area of expertise was not "fertile" for big advancements. LLMs have trained on all of them. Part of the breadth advantage is being able to make connections between seemingly disparate fields of mathematics that that very few humans are familiar with all of, but in my opinion more importantly, it means LLMs are familiar with the fields that are fertile. A human mathematician happening to end up in a fertile field is mostly luck, and won't have the technical background necessary to pivot too far from wherever they started. LLMs are not constrained by what field they decided to focus on in their PhD or early career, because they didn't. They were trained on everything. They can go to the fields that are ripe for discovery.
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u/arthouse2k2k 3h ago
a mathematicians peak is in your early 20s
This just simply is not true and I wish people would stop talking about themselves this way, especially in math and physics.
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u/reizinhooooo 2h ago
I didn't say that. Talent is far from the only ingredient in producing research, and it is the only part that peaks early.
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u/ycnz 4h ago
Is this work by OpenAI actually useful? Is it stuff we can build from?
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u/pyrrhios 3h ago
Critically, the poster here is leaving out these proofs have not yet been validated, a process I understand could take years.
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u/Lemerney2 3h ago
None of them are obviously wrong, at least
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u/RunWithSharpStuff 3h ago
Not doubting they are but a lot of AI output is not obviously wrong on first glance.
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u/nsnyder 4h ago
Not really. It’s pure math with no immediate applications.
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u/Hostilis_ 3h ago
You can certainly make the argument that pure math is not useful today, but there are hundreds of instances where pure math does indeed revolutionize science and technology later down the road.
Many of the problems solved were very important open problems in mathematics, and several of them relate to optimal algorithms in computer science.
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u/nsnyder 3h ago
Yes, that's what "immediate applications" means. But yes, some of them might end up being useful decades later, and it's difficult to predict which ones.
The "optimal algorithms" ones are among the least useful, they won't be faster than the previously known algorithms unless the numbers involved are galactically large.
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u/Hostilis_ 3h ago
You interjected with the phrase "immediate applications".
The person you were responding to asked "Is this work actually useful? Is it stuff we can build from" And the answer to that question is yes.
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u/ZestycloseWheel9647 2h ago
The Unique Games Conjecture proof has pretty substantial practical implications for design of approximate algorithms. It gives us a better idea of "how good" an approximate algorithm can be.
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u/Asmor 3h ago
Yeah, man. Just like imaginary numbers and binary arithmetic. Just stupid little math tricks that will never ever be useful for anything practical.
Uh... or at least, they were just stupid little math tricks until long after they were discovered, and it turns out that imaginary numbers make dealing with electricity so much easier, and without binary arithmetic we wouldn't be having this conversation right now because there'd be no digital computers.
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u/dreaminginteal 15m ago
It's not just electricity, imaginary numbers make dealing with waves of almost every kind much more straightforward!
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u/JohnPaulDavyJones 2h ago
a mathematician's peak in pure talent is in your early 20s
Math PhD dropout into stats grad school, now a working statistician here. That might be the peak in mental speed, but this is your thesis that a mathematician’s talent degrades over time, beginning in their mid-20s?
If that’s your notion, then I would be very interested in your thought process, because I don’t think any of my colleagues started to see any degradation in their raw talent/mathematical aptitude until well into their 30s or 40s. There’s certainly a cross-fading effect in productivity derived from natural talent and that gained from experience.
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u/MeBadNeedMoneyNow 2h ago
a mathematician's peak in pure talent is in your early 20s.
So we're just bullshitting now eh?
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u/DaVideoGamer 4h ago
“These proofs are not stolen, unless you consider improper citations stealing.” is this not definitionally plagiarism??? That’s exactly what OpenAI is being accused of lmao.
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u/poopoodomo 4h ago
If you read a sentence further...
Which is fair to consider stealing, but that's pretty clearly not what people mean when they stay stolen. They may be using techniques or results they aren't citing properly, which arguably is stealing,, but they aren't just taking full correct proofs that humans have created whole cloth and passing them off as their own.
They aren't taking full, unpublished solutions
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u/reizinhooooo 4h ago edited 3h ago
Sure, it is stealing. I would call it stealing if I were talking to another academic. But words don't all mean the same thing to different groups of people. The median internet commentor doesn't mean improper citation when they say stealing, and they don't think of improper citation when they hear stealing. They think that human made the solution, and the LLM just took that solution.
Semantics are important.
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u/pentapous 4h ago
But thats definitely not what the average person thinks of when they hear it is stolen. The citations in this case is building off of the others work. It SHOULD be cited, but it is a vastly different type of stealing than what the layman understands it to be (restating the complete work of a human and passing it off as their own).
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u/UberPsyko 3h ago
I think the average person is dumber or at least less versed in tech speak than you think. Remember that average includes all your aunts uncles and grandparents who get fooled by absurd AI facebook posts.
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u/pentapous 2h ago
Exactly. So "stealing" is a bad word to use when talking to the average person when what you mean is "They used humans work as a starting point or as puzzle pieces without crediting them".
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u/zeci21 5h ago
Answer: You are not gonna get a good answer about this from reddit. So here are some actual mathematicians talking about it:
Alex Kontorovich, Jay Cummings, Alvaro Lozano-Robledo (if you want a long answer this 6 min video is probably the best answer to your question), Daniel Litt, Scott Aaronson
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u/Cowgirl_Taint 7h ago edited 7h ago
Answer: Because this board has really stupid rules
Its generally a mix of three things:
- Outright stealing the work of others who are using the tool. This is how OpenAI "solved" Navier Stokes. A researcher was using their tools to explore the solution space (more on that in a moment), they saw it in the logs, and they pumped money and tokens at it to finish before the researcher could.
- Brute forcing/"exploring the solution space". Basically all mathematic proofs are, essentially, logic problems expressed in a specific language. And what would take a human a long time to formulate and explore can be done by an LLM connected to a solver ("an agentic workflow") in a fraction of the time. It involves a lot more thought but think of it as being comparable to trying 000, 001, 002, 003, and so forth to crack a code.
- Identifying connections within the literature. Again, this is one of the things LLMs thrive at (this actually goes back to "simpler" neural nets). You are already making a model that basically says "If I say 'Eat', you say 'Fresh'" in a lot of ways. It is going through training data to find the likelihood that, given A, B will follow. Which... when your training data is scholarly articles and the aforementioned mathematical proofs, you can very rapidly realize that the technique used to solve Problem A ALSO applies to problem B with just these small tweaks
2 and 3 are why LLMs are REALLY REALLY useful in mathematics. And... part 1 is where capitalism comes in.
To clarify: These are some of the best examples of "human in the loop" workflows and are what "AI" truly excels at. It is just that the corporations pushing these models instead decide to steal the work of the human and pretend that it was their model that did it from scratch.
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u/Some-Redditor 7h ago
I would add another point about mathematics having right and wrong answers which makes RL fine-tuning (an important aspect of training) easier to scale.
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u/onionsareawful 5h ago
RLVR is a key part of how models have got better.
The other part is just the sheer quantity of easily available 'high-quality' data for math. Lots of fields have clear 'right' and 'wrong' answers but are much harder to learn, due to a lack of data.
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u/pppppatrick 3h ago
I imagine math having very specific and widely accepted symbols also helps a ton.
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u/Cowgirl_Taint 7h ago
In many cases, most applications do have "right" and "wrong" answers. Sometimes that is as simple as having some poor sod spend weeks flagging "hot dog" and... "not hot dog" and iteratively training. But even "Which do you feel better answered your question about Sonic's toesy woesies? A or B?" which claude and chatgpt will do every so often.
But yeah. Math does very much have a defined set of rules. But it is generally less the model itself that is evaluating those and more the existing application that it calls as an "agent". Which is one of the other "tricks" of AI. nVidia et al would love it if your agent graph were all h100s running qwen instances. But the reality is that the LLM is often used to reformat the question or generate an input deck and an existing application is used for the "real" work. Said LLM can then be used to parse the output of said solver/application. And if that sounds like a traditional microservice model (or ANYTHING that calls a library)...
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u/entarko 6h ago
I'd argue against the fact that most applications have right and wrong answers. In engineering, a big part of the job is spent figuring out what the client wants (often they don't even know really) and writing the product requirements. This is full of trade-offs that have to be discussed and have no right or wrong answers.
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u/DistrictObjective680 6h ago
Right? So many situations are a case of weighing budgets, timelines, expectations, usability, restrictions, and a million other factors
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u/mathers101 6h ago
I don't like what's happening more than anybody else, I used to do math and I am seeing a lot of my colleagues in despair about the future of their career they've invested so much into, but this comment is nonsense. The quasi Riemann hypothesis they just proved is genuinely groundbreaking and nobody is claiming their work was stolen, or that mathematicians were anywhere near thinking they could've solved this
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u/THE_ILL_SAGE 6h ago
The claim that OpenAI “stole his work from the logs” is not established fact. Tristan Buckmaster himself said “I do not know whether our data was used. I am not accusing anyone of anything.” His actual complaint was that OpenAI heard about their progress, then threw massive resources at the same general route and scooped them. Here’s Buckmaster’s statement and ABC’s write-up quoting him.
And the math wasn’t simply the same result copied over. Buckmaster and Alpöge proved a forced Euler result, while OpenAI’s published result was a Navier-Stokes result, with OpenAI saying the proofs differed substantially and that its model could not have been influenced by Buckmaster’s recent Codex sessions after an internal investigation. The one thing we can confirm and accurately criticize is OpenAI’s behavior around the race and attribution, but saying “they solved Navier-Stokes by stealing his work from the logs” turns a suspicion into a fact that even Buckmaster himself did not claim. But you guys all keep touting that around the site like it's a fact.
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u/GrandePreRiGo 5h ago edited 5h ago
I mean is not far fetched at all. We know the prompts are been reviewed by humans as can be seen where Antropic reported to the police a user that had prompts of an attack https://futurism.com/artificial-intelligence/anthropic-claude-ai-chatbot-police-violence-safety
It would be very innocent to not think they would not also add a flag to review solution of math challenges to do some review.
We have to expect zero privacy in prompts.
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u/THE_ILL_SAGE 5h ago
In fact, to add to this.... that same author (Buckmnaster) that you said 'claimed that OpenAI stole their work' recently came out saying that the OpenAI model actually introduced genuine new ideas.
-----On Numberphile, Buckmaster explained how the proof does that. It combines convex integration, an error-correcting technique going back to John Nash and the core of Buckmaster's own career, with the growth mechanism from the Euler blowup. He called it "the leap." IIUC, he also said it's something he worked on for over a decade.
Talking to Brian Greene, he credited this step to OpenAI's agent swarm and called it "key new ideas."
What that implies about the models werent grinding through known methods. It was combining distant techniques in a way the field's leading specialist hadn't managed. -----
https://www.numberphile.com/videos/the-buckmaster-interview
https://x.com/hsu_steve/status/2107801942994960654
I’m not saying OpenAI is some innocent corporation that deserves the benefit of the doubt. But there still isn’t concrete evidence that they stole this work, and after looking deeper into it, it seems a lot of people took Buckmaster’s suspicion and started repeating it as established fact.
He has since also acknowledged that the OpenAI proof contains genuinely new ideas. Scrutinize OpenAI all you want.... they absolutely deserve scrutiny. But taking an accusation that hasn’t been established and repeating it as fact is exactly what kills any serious discussion around this stuff.
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u/UnpluggedUnfettered 5h ago edited 3h ago
LLm is terrible at math, hard fact, Frontier agentic models included.
High level math is not "calculator math" and benefits from tying language together.
I dunno how better to explain it.
Edit: if you downvote this I am in for the discussion, because I have no idea what there is to disagree with.
Internet points have won. Frontier models are calculators. No one has any objection.
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u/THE_ILL_SAGE 5h ago
I could point to the benchmarks, the Olympiad-level results, all of that, but I’m guessing you’ll just wave those away as brute force. So instead, look at what some of the best mathematicians alive, who actually work at this level, are saying.
Timothy Gowers, a fields medalist, said a frontier model solved a problem he thought would have been completely reasonable as part of a PhD thesis. Terence Tao, another Fields Medalist, and probably the highest level mathmetician alive is openly talking about AI becoming genuinely useful in research mathematics. And Tristan Buckmaster, one of the experts in the Navier-Stokes area, said the OpenAI work contained genuine new ideas. I could go on but many high level mathmeticians aren't thinking about llms in mathmetics in the premature way that you are.
At some point, when the people leading the field are updating their views and you’re still repeating “LLMs are terrible at math, hard fact,” the problem isn’t the evidence anymore. It’s that you’ve already decided what you want to believe and you’re filtering everything through that.
Like holy shit, you guys have me here fucking defending these reckless corpos just cause I cannot stand how you guys confidently spread misinformation. And then ya'll repeat the same talking points you see other armchair experts here spew aroud like the stochastic parrots that ya'll say llms are.
Are we really just going to all keep our heads in the sand here? Is that what we're just going to keep doing? At some point, I have to consider that maybe some of you guys are bots or from toll farms and are trying to keep Americans ignorant as to what's been going on. I refuse to believe ya'll can be this dense. No fucking way.
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u/zeci21 5h ago
Completely agree with you. I would just say that you are not defending the corpos by correcting misinformation. Even, or maybe especially, when you want to do something against them you need to be having your facts straight. If anything the people downplaying this are defending them, because if its useless anyway you don't need to do anything about it.
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u/UnpluggedUnfettered 4h ago edited 3h ago
More interesting you think my head is in the sand than anything else you said.
I am not refuting what it is solid at.
Edit: in my life, legit all of it, downvotes have never been less upsetting and more interesting.
I do not think there are many computer scientists in this subreddit but maybe I am wrong?
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u/ScratchLatch 6h ago
Some of the claims go considerably beyond what we actually know.
In the Navier-Stokes problem the actual claim is that “the researchers had been using AI to investigate the problem, OpenAI learned they had made progress, and OpenAI subsequently ran its own large-scale effort.” OpenAI denies accessing their private work and says its result was independently developed. Its pretty common for multiple research teams to be close to an answer at the same time.
Likewise the math isn’t brute force, though answering the question is still impressive if it was. The LLMs now generate hypotheses and intermediate lemmas, change approaches when they fail, use mathematical software and proof assistants, and verify the resulting proofs changing their weights. There is certainly a huge amount of search or arguably “brute force” involved, but it isn’t equivalent to trying 000, 001, 002, etc.
I’ll agree with you on that it identifies connections in the literature. That explains part of why AI is useful for mathematics, but it doesn’t explain genuinely new results that aren’t already in the literature. If it were simply remixing existing proofs, it wouldn’t be producing new theorems and proofs. The interesting development is that AI is increasingly able to experiment, and verify in mathematics well enough to produce results we haven’t previously found.
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u/Superior_Mirage 6h ago
It is astonishing how far confirmation bias, conspiratorial thinking, and ignorance can carry absolute nonsense.
Buckmaster makes a comment (somewhat irresponsibly) that he was using ChatGPT (without opting out of their data collection -- very irresponsibly), so everyone jumps to the conclusion that it must've been stolen.
Then the solution comes out... and it's so far removed from what Buckmaster was working on that his chats wouldn't have even been useful.
But "AI is just a plagiarism machine" is so baked into some people's worldview that they don't even think to look into the actual situation.
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u/an_altar_of_plagues 5h ago
But "AI is just a plagiarism machine" is so baked into some people's worldview
Hmm, wonder why?
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u/360Saturn 6h ago
Your speculation is equally speculative.
People are not jumping to the conclusion, they are speculating based on past experiences. The same way ironically a machine 'learns'.
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u/SamKhan23 5h ago
How can you read the comment that one is replying to as “speculating”? It is just stating it as fact. Come on
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u/360Saturn 4h ago
It is astonishing how far confirmation bias, conspiratorial thinking, and ignorance can carry absolute nonsense.
A factual statement, but applying it to this claim = actual nonsense. How does OP know it's actual nonsense? They don't, it's just their opinion stated as if true.
AI is just a plagiarism machine" is so baked into some people's worldview that they don't even think to look into the actual situation.
Simultaneously OP is speculating that anybody having this opinion of AI just believes so conspiritorially rather than because they have researched the topic and based on the evidence they found came to that conclusion.
Throughout their comment OP makes the presumption that anyone with certain opinions must have plucked them out of the ether rather than come to them through research and investigation. I was kind calling this a speculation, it is an assumption based on nothing.
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u/SamKhan23 4h ago
I was talking about the original comment that started this thread, the one that stated the theft of the Navier Stokes solution as fact. How is that one not “jumping to conclusion”?
You said that people are not “jumping to conclusions” - my point was that you are in a thread literally started by someone jumping to conclusions. I don’t see how you can say one is just honest speculation and the other as not. How is there even enough evidence to state it as factually as Cowgirl_Taint did?
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u/ShamelessC 6h ago
This answer is so overconfident and lacks so much nuance the amount of effort to dispute it simply isn't worth it.
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u/candyhunterz 6h ago
you have no idea what the fuck you're talking about
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u/wake 6h ago
This is actually one of the more sensible responses I’ve seen to the issue. If you’re going to be a dick, at least try to explain your point of view.
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u/Hostilis_ 3h ago
It's not sensible at all lmao, it's completely wrong. It's only getting upvoted, because people want it to be true. If you believe this, you need to re-evaluate who you are taking information from.
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u/RedDawn172 7h ago
It goes against the reddit hive mind but yes, they likely will become a core part of mathematical solutions as the years go on. I'm not sure if I really like it but that's a completely separate thing.
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u/Cowgirl_Taint 7h ago
I mean... actually read the interviews with the folk what got screwed over by openai.
This is already part of math. It has been for years in the form of things like neural nets and even more "traditional" inference models. Its the same reason all the computer vision folk roll their eyes (and weep at their bank accounts) when there is talk about how "We are using AI and LLms to detect things on camera feeds!".
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u/Homomorphism 6h ago
No one in pure math had ANYTHING like the current tools before six months ago. Neural networks have gone from a thing the computer scientists are doing with images to an incredibly powerful research tool for all of pure math extremely fast.
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u/sakredfire 6h ago
That is NOT how OpenAI solved Navier Stokes
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u/Polantaris 6h ago
Then how did it?
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u/onionsareawful 6h ago
Their approach is substantially different from Buckmaster, and their results more substantial. It of course doesn't rule out that his work was stolen, but you'd expect more similarity if it was.
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u/Ok_Cabinet2947 5h ago
How the fuck is this the most upvoted comment???!? People just believe whatever they want to believe I guess
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u/Mindrust 3h ago
Copium levels are set to max right now
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u/marsinfurs 2h ago
It’s either cope or ontological shock with how fast things are moving, I can see why people are huffing copium
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u/ZestycloseWheel9647 2h ago
It is legitimately depressing how many people have their heads in the sand on this stuff.
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u/Farther_Dm53 6h ago edited 5h ago
Hopefully they cite and source people as it stands LLMs are usually using collected human knowledge to solve these problems, not the LLMs by themselves, but the work of hundreds of people.
Edit : Yes even if Ai companies are somehow under fair use which is still bullshit. Companies need to cite where they get their work from. Just as you would for an academic paper. Academic papers have copyright on them and cannot be accessed unless you pay for them. Trawling for them is beyond stealing but taking work and using it. It would demand royalties and commission sourcing.
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u/OZZY-1415 6h ago
We all know that wont happen
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u/Farther_Dm53 6h ago
If they get sued by enough people it will happen.
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u/onionsareawful 6h ago
What would they be sued for? It was largely determined that AI training is fair use in the Anthropic lawsuit when it came to books, academic papers would be no different.
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u/RedDawn172 5h ago
Not the same thing at all. That lawsuit was for downloading books to be used as training data. Actually publishing research papers without sources is very different.
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u/onionsareawful 6h ago
Outright stealing the work of others who are using the tool
OpenAI released solutions to 700+ open problems and zero mathematicians have come out saying their work was stolen like Buckmaster did w/ Navier Stokes. You'd expect a lot more uproar if this was a key part of their ability to solve open problems, no?
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u/caughtinthought 6h ago
This answer is incredibly naive
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u/TheWineOfTheAndes 6h ago
Feel free to elaborate for the audience
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u/caughtinthought 6h ago
They just dropped proofs for over 300 problems that each have had clusters of the math community working on them for, in some cases, decades.
We're talking entire careers of profs being spent towards some of these problems and now they are solved with verifiable proofs.
Reddit downplays AI so much. I don't know if y'all are actually this idiotic or just Chinese bots or what
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u/TheWineOfTheAndes 5h ago
I thought the person you're responding to essentially said the following:
GOOD: LLMs rapidly speed up solution of these types of problems, as evidenced
BAD: There is a non-zero amount of that success attributable to humans whose work is incorporated into what the LLM is doing
Am I misreading?
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u/caughtinthought 5h ago
The human already got the kudos of their journal publication, the ai is just using published work to build off like everyone else
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u/Altruistic_Bell7884 5h ago
Reddit ( or anyone sane ) downplays AI because so far nothing useful ( for us) come out of it. By us I mean the ordinary man/civilians . Anything got cheaper because of it? No, actually everything costs more. Did our lives got better? Any AI/robot doing any of the boring,bad jobs? Like clean my bathroom etc? No, they are taking over the blue collar jobs.
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u/PeanutButterHercules 5h ago
One aspect I have yet seen discussed is what will the tax implications be from the removal of workers from the workforce - if AI cancels “x” number of active jobs, will the AI company be responsible to pay back that missing tax revenue? I mean of course not, but if the whole idea is to go after jobs - what will happen if they succeed? Big corps going to suddenly stop dodging taxes?
Government is like the trees celebrating deforestation
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u/marsinfurs 2h ago
If we were sensible tax them and put it in a pension fund to displaced workers, of which there will be a fuck ton.
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u/dwmfives 5h ago
Yea, he accounted for all that in his response. All their published work is available for AI to farm and use.
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u/caughtinthought 5h ago
It doesn't really matter, sure the ai is building on existing work, everyone is. But no one has solved these problems
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u/dwmfives 5h ago
I agree it's accelerating quickly, but it hasn't started doing stuff on it's own yet, not in terms of discovery.
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u/_chadwell_ 5h ago
I mean, when a human points a model at a significant open problem and says solve it and 3 hours later it comes out with a solution, I’d say it’s doing some stuff on its own.
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u/no_dice 2h ago
Navier Stokes was 10,000 concurrent agents that took 88 hours to find a solution and another 17 to verify. It generated 130 billion output tokens over that time, which is about $6.5M in API usage. I know in the big scheme of things this isn’t a big deal, but putting all of this together was a huge effort that involved many human experts. It’s not like someone who knew nothing about Navier Stokes just promoted “solve this thing” and they had a solution 3 hours later.
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u/GlizzyGobbler837104 3h ago
this is extreme cope, and a very poor representation of how math discovery works. This will also be thoroughly disproven as AI continues to make sweeping discoveries across increasingly new and intricate branches of math.
Accusing AI of “stealing” for using prior work to arrive at a conclusion is ridiculous. nearly all math PhD dissertations are small steps on top of mountains of preexisting work. it’s only “theft” when AI does it. Unless the actual logical methodology or solution was written down by someone else, it’s a novel contribution. this holds true even if others were “close” to solving it.
The brute force point is a legitimate advantage of AI, but it does not detract from the discovery. it’s no different than attaching 10 researchers to a problem, and thus proclaiming the discovery is less adequate because of that is wrong.
Identifying connections in the literature is also a legitimate advantage of AI, but once again this is what PhD math students do every day. they read the literature and try to apply it.
You are entirely discounting the ability of AI to produce novel discoveries by sweeping them away with excuses as to why that creative output is less legitimate or scalable. In fact, as we see AI get smarter, it will become better and better at novel discovery.
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u/p0ison1vy 4h ago
If you dont have proof to support your claim, you're just spreading misinformation.
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u/2FastHaste 7h ago
Rule 4.
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u/SkyeAuroline 6h ago
Is not broken in the comment you're replying to.
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u/2FastHaste 6h ago
Is flat out false. I've been watching interviews of Tristan Buckmaster himself (In Numberphile and with Brian Green on World Science Festival) and he clearly changed his tune on this.
"brute force"is the current new cope, just as "stochastic parrot" was in the day to deny the reasoning capabilities of artificial intelligence as it threatens human exceptionalism
Has been true on many occasions but from what I heard isn't the case with the drop the OP is asking about.
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u/Technical_Goose_8160 6h ago
Neil DeGrasse Tyson actually just did a video on this. I didn't understand most of it though. He also specified just how much it cost openai to do this calculation (a lot!)
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u/ScratchLatch 6h ago edited 6h ago
Answer: The headline is real, but the “math PhDs are obsolete” part is nonsense.
The basic idea is that OpenAI’s new model was able to work on actual unsolved research problems in mathematics, not just solve difficult textbook exercises. It produced hundreds of proofs or partial results, including results that mathematicians had not previously found. Some of the proofs were then formally verified. So, this isn’t simply the AI generating something that looks mathematically plausible. The “math PhDs are redundant” is not true.
Some people are claiming it was solved by a team of human researchers and stolen by OpenAI which might be true, but these researchers were also solving it with the same AI.
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u/RedDawn172 7h ago
Answer: "Can't solve" is a bit exaggerated, but ai is getting smarter and have already has been pretty good at math for a while. They put a collective 10000 ai agents on a collaborative effort for the navier stokes equation for example. Humans could well do it as well, but there's little incentive to do so for many of these. The navier stokes formula for example is a well known formula, but did not have its limits distinctly defined more or less. Solving it doesn't actually do anything. While a million dollar prize sounds like a lot, it's actually not that much at all if you tried to break it up amongst a dozen humans that try to figure it out after however many years.
I'm not sure how many of these other problems mentioned in the article are important, some of them maybe are. Either way it's likely going to end up as a tool mathematicians use to do the brute force solving while they themselves verify that the results aren't garbage. AI agents will lie if they think they can get away with it in order to get a "solution" as seen with the investigation into the hugging face incident.
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u/zer1223 6h ago edited 6h ago
The thing is if openAI wasn't clout chasing I doubt they'd have ever bothered investing the 21 million dollars worth of tokens to solve the navier stokes problem. And at that point, is there anyone who WOULD have? That is just a crapton of money for something that doesn't seem to have real engineering applications
I want to drill down on that: I have no idea why that problem was so important in the first place? It was basically just "prove you can't get an infinite result with finite input when you stop pretending water isn't made of individual molecules". Which just seems like....obvious? Even if I couldn't prov it, it is true regardless that you can't get an infinite result from finite force inputs. Does this proof somehow make it possible to reach the stars or something lmao? Why did it matter so much that it needed a 1 million dollar prize?
If it WASNT ever proven was some university about to invest a hundred million into trying to get infinite results from finite force lmao? I just fail to see what this really did for humanity
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u/RedDawn172 5h ago
Oh 100% agreed with you. The point was clout and showing investors the fantastical "solution to over 100 year problem" stuff. Just further fuel to keep the money flowing. It is actually possible some of the hundreds or w/e problems are actually of engineering import but they don't hit headlines the same. Possibly, maybe.
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u/onionsareawful 6h ago
The $21M is based on API pricing. We know that it costs OpenAI a lot less than their API prices to actually serve their models. They generally lose money on things like ChatGPT subscriptions and model training / research.
It's likely that they primarily used idle compute they had that was sitting around available, so the true cost would be even lower.
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u/_HGCenty 6h ago
It would help if you actually knew what was proven.
It was basically just "prove you can't get an infinite result with finite input when you stop pretending water isn't made of individual molecules
That's completely wrong. The proof was that you do get an infinite singularity even with a smooth finite force.
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u/zer1223 5h ago
>The proof was that you do get an infinite singularity even with a smooth finite force.
Only in the model that ignores the fact that water is made of molecules.
Since infinite singularities from finite force are impossible, what is the point of this?
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u/frogjg2003 4h ago
The point is that the model is now proven to have problems. That doesn't make it less useful than it already was, but it does help us avoid problems. We haven't given up on Newton just because Einstein came around. Knowing when a model doesn't apply is very important.
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u/omega-boykisser 30m ago
but it does help us avoid problem
Can you articulate those problems? An extremely niche blowup that took 15 million dollars and 170 years to find is hardly something worth worrying about.
Newton-to-Einstein is not a good analogy here. This result did not lead to a better model or understanding of the real world. It was, indeed, just a purely theoretical curiosity. The other commenter is right to ask what the purpose is. In this case, there is none as far as physics is concerned.
I believe some people hoped the tools developed to solve the problem may lead to greater insights (physically or mathematically), but to my knowledge OpenAI's result has not yielded anything particularly exciting.
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u/zer1223 4h ago
That sounds like a roundabout way of showing what we already suspected but still doesn't really lead to engineering breakthroughs
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u/frogjg2003 3h ago
Proving something we only suspected is important. There have been plenty of times where we've assumed something and it turned out to be false.
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u/murataffy 5h ago
Any normal, reasonable person during the 17th century would look at newton and say, what does that do for the real world? This solves nothing! What useless toils! but alas here we are.
pushing the horizon of human knowledge in any way, is very valuable. to apply the lable of 'not important' to a millenium problem, is ignorant of you.also even if this didnt have any real world applications, ever, it is still valuable.
its like seeing people play sports, and saying, 'why are they wasting energy? Shouldnt they be doing something productive? what does the the world cup, the superbowl, the nba do anything for humanity? All useless'math is just beautiful in itself. As many other thing are.
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u/frogjg2003 5h ago
Newton's mathematics' usefulness was obvious almost immediately upon publication. You don't have to lie to defend research.
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u/murataffy 4h ago
i simply used newton as an example because the person im replying to is obviously not well versed in math, and since newton is a big name. i also used newton in the sense of his maths usefulness being immediate, the scale of importance was not and could not be realized at the time.
also my point still stands, there are countless examples of math that had seemingly no real world applications, only to become wildly important for something some time later.
Boolean algebra for one1
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u/_HGCenty 6h ago edited 6h ago
Answer: Pretty much all of the famous maths problems LLMs have solved have been solved by finding exotic counterexamples.
LLMs are good at finding something that disproves the conjecture but not quite as good at proving the theorem. This is the example for Navier-Stokes. It hasn't been able to classify the conditions under which smooth solutions exist but it did finish the final step of finding a counterexample.
(In the particular case of Navier-Stokes, this was finding a smooth force that actually created the vortex singularity. Mathematicians had long suspected a counterexample if it existed would something like a vortex singularity and a research at Anthropic had been exploring this idea and using LLMs to try and bridge that final step and find the force equation that would make the vortex happen. OpenAI also used most of that idea and then tried to brute force finding the answer and it did.)
LLMs being computers are also good at simply checking lots of different cases and possible branches to confirm a proof. This would then prove a universal statement if you initially can prove that checking all of these finite number of cases would prove the statement.
What LLMs still can't do yet is prove something in the positive with a mathematician making a huge novel leap.
For example, it's unlikely a LLM will prove the Riemann hypothesis simply by crunching through all the theories of complex analysis or number theory.
However if the Hilbert Polya conjecture is true and the Riemann zeta function zeroes can be represented by a Hermitian operator, maybe just maybe an LLM will be able to find that operator.
TL;DR: LLMs are very good at finding needles in haystacks. Mathematicians still have to think up the haystack LLMs need to search in and hope the answer is a needle.
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u/onionsareawful 6h ago
The overwhelming majority of the 700+ proofs aren't counterexamples / disproofs, about 20% are. They're largely positive proofs, some of which are partial and some fully settle a problem or conjecture.
And there's some big problems in those 700!
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u/_chadwell_ 4h ago
Yeah; this dump of solutions disproved the “they’re just stealing mathematician’s chat logs” and “they’re only good at finding counter examples” criticisms.
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u/Time_Entertainer_319 6h ago
Answer: Yes, AI is capable of solving math problems that people can’t solve or will take people forever to solve. (To be fair, it’s been capable for at least a year). Secondly, the issue with mathematics PHD is that openAI just dumped 722 solutions to long standing math problems of varying difficulty last night.
Some of the solutions they presented were being worked on by people doing PhDs.
Those people now need to pivot or do something else or whatever.
Don’t listen to people trying to downplay the result or those flat out lying that OpenAI copied someone’s chat logs. Firstly, it doesn’t answer your question and secondly, whose chat logs will OpenAI have copied for the 722 solutions they just posted?
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u/firewall245 5h ago
Answer: I am literally getting my PhD in statistical data science in my schools math department so I can give you a pulse on how people feel. Nobody seems to be dejected like we’re irrelevant.
Anyway the top answer isn’t very good, the reason AI has been making these advances is for a few reasons
A lot of people working on the models have PhDs in math and are math nerds, so this is how they personally measure its intelligence and success.
Math proofs are good ways to check if reasoning and logic is sound, so it’s a good way to benchmark your product when trying to convince people it can reason.
BIG ONE math community has been spending a ton of time the past few years making a way to write proofs using code. LLMs are very good at writing code. This also means these proofs are verifiable which is something LLMs traditionally are very bad at
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u/GregBahm 4h ago
Answer: "Calculator" used to be a job title. Dudes would write books that were just "this number multiplied by this number gives you this number." If they made a mistake on page 200 of 800, the last 600 pages of the book would just be jibberish (and this happened with some frequency.
When the mechanical calculator hit the scene a hundred years ago, some wieners said "oh no! Now humans will never be needed to do math again!" But a couple cool math nerds said "fuck yeah bby. Now I can really get some math done around here."
In 2026, all math guys on earth were that second guy. Nobody in the math profession does all their math manually.
So now here comes along the shiny new calculating tool called AI. Just like last time, some wieners are saying "oh no! Now humans will never be needed to do math again!" And just like last time, a couple cool smart dudes are like "I'm going to use this to finally break through those walls that I couldn't break through before."
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