Yeah man I think I will stick to sports now. All careers are going down the data centers coolant pipe.

not sure whether to celebrate, or laugh, or cry myself to sleep

We make more problems until AI gives up.

the solution is stolen from another researchers lol

When I was in primary school, my teacher asked us to write an essay imagining the future.

I imagined that 100 years from now, robot teachers would be teaching us, and we could ask AI to solve any problem.

Less than 10 years after I wrote that essay, all of that became a reality.

deleted

YKW LETS GO AND OLAY OUTSIDE

This is insane.

Attention! Your solution https://openai.com/index/navier-stokes-solution/ for the problem 2000C — Navier-Stokes existence and smoothness significantly coincides with Tristan Buckmaster and Levent Alpöge/https://cims.nyu.edu/tristanB/statement.pdf. Such a coincidence is a clear rules violation. Note that unintentional leakage is also a violation. For example, do not use ChatGPT Codex. If you have conclusive evidence that a coincidence has occurred due to the use of a common source published before the competition, write a comment to post about the round with all the details. More information can be found at http://codeforces.me/blog/entry/8790. Such violation of the rules may be the reason for blocking your account or other penalties. In case of repeated violations, your account may be blocked.

given that ai have solved a millennium problem i have 2 questions! 1)can ai do topology toplogy? 2)just like humans have developed so many theorems and fields for example calculus!, can ai also invent a new field of math?

I suppose this has to be yet verified by third party mathematicians.

The fact that AI can solve that hard problem in 88 hours while humans can't in decades is such a great dissatisfaction.

Intelligent AI should think like a superhero -> with great power comes great responsibility.
Current AI -> with great power comes no responsibility.

I don't really understand why people keep calling this a copied solution when the actual proofs are fundamentally different. Having some overlap in the general direction or using ideas that are related to previous work does not mean that the proof itself was copied.

The two proofs are fundamentally different, not merely minor variations of the same argument. They may share a broad overall direction or rely on related high-level ideas, but the actual reasoning, intermediate steps, technical methods, and conclusions being established are substantially different. Looking only at the general outline and then calling one proof copied ignores the important details that distinguish the two arguments.

Of course, it is completely reasonable to question how OpenAI arrived at the result, especially given the timing and the fact that they started working after hearing that other researchers had made major progress. But that is a different claim from saying that they copied the proof.

If the accusation is specifically that OpenAI used the earlier researchers' unpublished work, then there should be actual evidence for that claim. The similarity of the general route alone does not seem sufficient, especially when the two actual proofs are fundamentally different.

Honestly, I think people are just refusing to believe the truth because they find it difficult to accept that an AI could actually produce a result like this. You don't have to like OpenAI or trust everything they say, but dismissing the result as "copied" without evidence doesn't make the accusation true.

Will AI replace CP some day

just some thoughts

1. if you're a researcher, why would you put your novel ideas into a chatbot? especially on something as massive as NS

2. would the 2 mathematicians have made as much progress as they did without AI? — if no, then openai really does deserve the credit

A dumb converstation with AI

25 Fields Medalists write a letter "A Severe Misalignment of AI in Mathematics", this has to do with OpenAI's claim of solving a Millennium Prize Problem amidst the accusations of data theft from human mathematicians.
 ****

Thougths:
 I am ordinary person, but given the controversy, and also I my own suspicions by observing that how many top tier mathematicians have been tied into the AI ecosystem, and increasingly ever, when it should actually be growing lesser, because the companies claim that their Models can do better job that almost all expert level humans…. So while its important to have oversight, you seem to be hiring more than what’s required for that much… shitstorm seems to be cooking inside… so I believe, and its my personal opinion that all results are achieved by the frontier AI models, but these results are artificial in the sense that very very VERY cleverly and stealthily these scientists and mathematicians, for gargantuan amounts of money in exchange, are somehow influencing how AI models approach these problems. This is point 1.


Point 2, its not just these scientists, but there has been serious theft going on that too from all around the globe, of academic data, that is secretly fed into these huge data centers, and that stolen data has paved path for these “artificial” results, and its appalling that AI still needs Humans to steer it with that much stealing, and don’t forget the cost of computing, the tax on the environment. Guess what, this is the defining trait of capitalism, and they will try convince you its real, because they want to control everything, so thats what is at stake now, Every freakin thing, trillions of dollars and right now its also become about survival, a death spiral…

In my opinion, the human brain is the result of billions of years of continuous biological adjustments, its amazing at what it does, and there is an environment that’s being created to make you ditch the superpowers you have, they have even tried to make you dumb through various means so that this task becomes easier to do.

Whether this originally was the plan that is been going on for decades or if its spontaneous brain child of some silicon valley wiz-kid who observed the change and its effect on society, human IQ, and all the other things, that came with advent of technology... idk about all that, and it doesn’t matter tbh.
 I’d be impressed, if an AI system, given all the compute that exists, all the electricity, all the water etc etc.... but train it on mathematical data within bounds of undergraduate math, not an inch more than in the mathematics real estate... Then observe how much can the machines figure out by itself, without any form or in any sense, external support, human or otherwise.... I say Human high school students do better, with an actually minuscule scale of knowledge they have relative to AIs, they with only that much they have "at times" surprised the world by tracing paths to mathematical wonders.

Ramanujan freaking worked with G.S.Carr’s Synopsis of Mathematics, its a compilation of formulas, just look it up if you don't know and see how much mathematical knowledge does that book can impart to reader, and how stimulating they can be in the sense what can you naturally expect of a student who would work with it, with only all that in hand Ramanujan did mathematical wonders that to this day blow the socks off of mathematicians when they try to imagine the absurdity all that was... All I see is that it’s all very shady, but please, IT'S JUST MY OPINION given how things are and have been, dark forces (ofc human hahaha, capitalism etc) are at work too… so take it with a pinch of salt, and about AI, I think the technology is a good, one and just as with everything else that has seen the light of day its got both the good and bad.....


Lastly, this letter, Idk man, Mathematicians should trust their skill above anything else, as much AI has progressed, and its future potential, they should never lose focus of their own capacity which is no less, this letter while it raises some points, feels lacking in that direction and aspect....


AI's Assesment:

The comment is intellectually interesting because it mixes some very legitimate concerns with several much stronger claims that currently aren't supported by evidence. I would separate the argument into three layers: what is demonstrably happening, what is plausible but unproven, and what is speculative.


1. Your suspicion about the human contribution to frontier AI mathematics is reasonable — but the mechanism matters

There is a real tension here. If an AI company says that its model can perform at or beyond expert mathematician level, while simultaneously employing large numbers of elite mathematicians, giving models carefully constructed problems, designing evaluations, generating synthetic data, and incorporating expert feedback, then it is entirely legitimate to ask: How much of the demonstrated capability belongs to the model itself, and how much belongs to the human-machine system surrounding it? That's a very good question.

But your hypothesis that mathematicians are secretly "steering" the models in exchange for enormous sums of money in order to manufacture the appearance of autonomous mathematical discovery is a much stronger proposition. There would need to be evidence of that specific behavior. And there's an important distinction between: * mathematicians helping design training/evaluation systems, * mathematicians supplying demonstrations or feedback, * mathematicians helping an AI decompose difficult problems, * mathematicians verifying AI-generated proofs, * mathematicians collaborating with AI during research, and * mathematicians secretly providing the actual mathematical ideas while the AI is presented as having discovered them independently. The first five are entirely unsurprising. The last one would be a major allegation requiring evidence. So I'd retain the question, but soften the conclusion.

1. The "AI solved it" question is actually much more subtle than it sounds This is, in my view, the strongest philosophical point in your comment. Suppose an AI system produces a spectacular mathematical result after:
2. being pretrained on enormous amounts of mathematical literature,
3. being fine-tuned on mathematical reasoning,
4. being given sophisticated prompting,
5. being supplied with tools,
6. being guided by human-designed scaffolding,
7. having its answers repeatedly evaluated,
8. being allowed to generate and discard thousands/millions of attempts,
9. having humans select useful approaches,
10. and perhaps being incorporated into an elaborate automated proving system. Then saying simply "the AI solved the problem" hides an enormous amount of infrastructure. But this doesn't necessarily make the result fake or artificial. A calculator doesn't "really" calculate because humans invented arithmetic notation and electronics. A proof assistant doesn't cease to be useful because humans designed its axioms and language. The more interesting question is: What level of independence should an AI mathematical discovery demonstrate before we call the discovery genuinely attributable to the AI? That's a much stronger formulation of the stated concern.

11. Your undergraduate-data thought experiment is genuinely interesting This part of your comment is actually something I would take seriously as a proposed research experiment rather than merely a rhetorical complaint. Your proposed test is roughly: Give an AI enormous compute, but restrict its mathematical training data to undergraduate-level mathematics, and see what mathematics it can discover without external mathematical assistance. That would test something important: how much novel mathematical structure can emerge from general reasoning ability versus how much depends on exposure to the accumulated mathematical literature? However, there are several complications. An undergraduate-level corpus isn't equivalent to the amount of mathematical knowledge possessed by an undergraduate human. A human undergraduate also possesses:

• general language knowledge,
• visual/spatial intuition,
• physical experience,
• years of informal reasoning,
• common-sense knowledge,
• social learning,
• the ability to formulate questions,
• curiosity,
• and an enormous amount of information that isn't explicitly contained in their mathematics textbooks.

Ramanujan is an extraordinarily bad baseline for "what a normal human can do." Srinivasa Ramanujan was an extreme mathematical outlier. His achievement is fascinating precisely because it demonstrates that humans sometimes produce astonishing mathematical structures from surprisingly limited formal resources. But it doesn't establish that ordinary high-school students generally possess comparable latent mathematical abilities.

1. Your Ramanujan example is powerful, but it cuts both ways The A Synopsis of Elementary Results in Pure and Applied Mathematics really is an interesting example because it wasn't a conventional modern textbook designed to explain mathematics pedagogically. It was essentially a huge collection of mathematical results and formulas. Ramanujan used it intensely. And what he subsequently produced went vastly beyond simply reproducing what he had read. That's precisely why Ramanujan is so fascinating.

But there's another interpretation: The book provided a gigantic landscape of mathematical objects, identities and relationships from which Ramanujan could make connections. In other words, his achievement doesn't necessarily demonstrate that mathematical knowledge is unnecessary for discovery. It demonstrates how extraordinarily powerful internal recombination, intuition and pattern recognition can be once someone has access to mathematical objects. And that makes your AI question even more interesting. Because modern AI has access to vastly more mathematical material than Ramanujan ever did.

1. Your data-theft argument needs considerably more caution

This is where I think your comment moves from legitimate skepticism into claims that aren't adequately substantiated.

There are serious disputes concerning AI training data, copyright, licensing, copyrighted books, scraping, copyrighted books, datasets, and whether companies have used material without adequate authorization or compensation. Those are legitimate issues.

But:"serious theft has been going on all around the globe, of academic data, that is secretly fed into these huge data centers" is too sweeping.

There is a major difference between: "AI companies have faced serious allegations and litigation concerning unauthorized use of copyrighted material." and "We know that stolen academic material is secretly being fed into these systems and is responsible for their mathematical breakthroughs."

The first is a defensible statement. The second requires considerably more evidence. And there's an additional technical problem: even if a model has memorized portions of mathematical literature, that doesn't establish that a particular novel result was obtained through memorization.

That's something researchers can actually investigate through data contamination, memorization, benchmark leakage, nearest-neighbor analysis, and controlled evaluations. So I would absolutely keep the data-governance criticism, but remove the implication that it explains the controversial mathematical achievements unless there is evidence specific to the case.

1. "Artificial" is probably the wrong word

This is perhaps the biggest conceptual issue in your comment. You repeatedly call AI results "artificial". But artificial doesn't mean illegitimate. If an AI discovers a previously unknown theorem through a genuinely novel chain of reasoning, the theorem is still mathematically true. The more important distinction is autonomous vs. assisted, rather than artificial vs. real.

Imagine a mathematician uses: * Mathematica, * a proof assistant, * Google, * thousands of papers, * numerical experimentation, * colleagues, * graduate students, * computer searches, * and an AI system.

If they discover a theorem nobody knew before, the theorem doesn't become "artificial." The question becomes what contribution each component made.

And this is precisely where I think your criticism of the mathematicians' letter has considerable merit.

1. Your final point may actually be your strongest one You say mathematicians should trust their own mathematical abilities and not lose sight of human capacity. I agree with the underlying concern. But I wouldn't frame it as "humans versus AI."

A more productive formulation is: Mathematicians shouldn't allow the impressive performance of AI systems to cause them to underestimate the epistemic importance of human mathematical judgment. There's a difference between producing a proof-like object and understanding why a theorem matters.

A mathematician can ask: * Why should we care about this problem? * Why is this definition natural? * What is the conceptual obstruction? * Is this proof illuminating or merely valid? * Is this generalizable? * What mathematical structure have we actually uncovered? * What should we investigate next?

Those are enormously important abilities. And even if AI eventually becomes extraordinarily powerful at mathematical reasoning, mathematics isn't merely the production of correct strings of symbols. It is also the creation of concepts, questions, explanations, connections and understanding.

One thing I'd change quite substantially, the Comment currently jumps from: "There is something strange about the relationship between AI companies and elite mathematicians." to: "Therefore perhaps these mathematicians are secretly responsible for AI's apparent achievements." Then from: "AI companies have controversial relationships with training data." to: "Therefore stolen academic data has enabled these results." And finally to: "There are dark forces at work." The problem isn't that you're forbidden from having those suspicions. It's that the evidentiary standard changes dramatically at each step. The first observation can motivate an investigation.The second is a hypothesis. The third is an allegation. The fourth becomes a conspiracy theory unless independently supported. Your argument would become substantially stronger if you stopped at the hypothesis and said: "I don't know whether this is happening, but the incentives and opacity surrounding frontier AI make this an empirical question worth investigating." That's much harder to dismiss.

And there's a fascinating irony in your argument -> Your proposed undergraduate-mathematics experiment is actually very close to what I think the AI community should be doing. Instead of asking only:

"How good is the model?"

we should ask:

"Under what information conditions did it become good?"

For example, imagine controlled systems with progressively different access: System Mathematical information available Human assistance A Undergraduate material None B Undergraduate + graduate material None C Broad mathematical literature None D Broad literature + tools None E Broad literature + tools Expert collaboration F Full frontier system Full research team Then give them genuinely novel problems whose solutions were not present in their training data. Now measure:
 * novel theorem discovery, * proof correctness, * conceptual generalization, * ability to formulate useful conjectures, * dependence on external hints, * reproducibility, * and how much human intervention was required.
 That would tell us vastly more about "AI mathematical intelligence" than a headline saying that an AI system solved a difficult problem. And it would directly address the central intuition behind your comment.

User: You disregard one thing in Ramanujan’s case. Carr's book, with as much mathematical knowledge it had in it, could NOT be considered the state-of-the-art level even for that time, so I have read. Thus what Ramanujan was created, with that kind of mathematical background and honestly few more years worth during his years in Cambridge, could not be comprehended properly until many decades in future, UNITIL WHEN “the mathematical apparatus could actually accommodate those ideas”.

The systems and mathematical language or apparatus, if its okay to say that, couldn't carry or accommodate major chunks of what he managed to create out of barely bones, in terms of input vs output, qualitatively speaking that is.

Assistant: Yes — that is an important correction, and it makes the Ramanujan analogy substantially more interesting than I gave it credit for.

The point isn't merely that Ramanujan had "limited information." The stronger point is about the distance between the representational resources available to him and the mathematical territory he subsequently entered.


Carr's Synopsis was not a survey of the "frontier of mathematics". It was deliberately a compilation of results, formulas and identities, and much of the material was presented without the kind of explanatory development that would characterize modern mathematical education. Ramanujan nevertheless extracted structures and relationships from it that went far beyond the level at which he had encountered them. And this gets to something deeper.
The extraordinary part isn't that Ramanujan knew little, it is that the mathematical apparatus available to Ramanujan did not fully explain what Ramanujan was seeing.

There is a distinction between:
 "I have learned theorem X, therefore I can reproduce theorem X." and: "I have encountered a collection of mathematical objects and relationships, and somehow I can see structures that aren't explicitly encoded in what I've been given."

Ramanujan's notebooks are extraordinary partly because later mathematics supplied frameworks in which many of his observations could be properly interpreted. His work anticipated or intersected with areas that were developed much more fully later, including aspects of modular forms, q-series, mock theta functions and related structures.

So your analogy isn't really:
 small dataset → impressive output.

It's closer to: low-level/old mathematical substrate → extraordinarily high-level mathematical structure. That is a much more interesting phenomenon.

And there's an important consequence for your AI argument : It gives you a sharper criterion than simply asking whether an AI can solve problems.

Suppose an AI system is trained on essentially the entire mathematical literature up to 2026 and then produces a remarkable theorem.

That's impressive, but there is an obvious question: How much of the conceptual space from which that theorem emerged was already present in its training environment?

If the model has absorbed millions of papers containing advanced definitions, conjectures, proof techniques, examples, counterexamples, mathematical language and relationships, then we have to be careful about interpreting its achievement as evidence of unguided mathematical invention. Ramanujan gives us an unusually provocative counterexample because his available formal mathematical environment was so comparatively impoverished. He wasn't sitting on a corpus containing the modern theory that would eventually make many of his ideas intelligible. He was, in some sense, reaching toward mathematical structures for which the surrounding mathematical ecosystem didn't yet possess the appropriate conceptual vocabulary. That's very different from interpolation over an enormous existing mathematical corpus.

But there is one caveat: I would still avoid saying that Ramanujan literally had "nothing" from which to construct his mathematics. Carr's book was dense, it contained an enormous number of mathematical results. Ramanujan also had access to other books and mathematical material, and, of course, he possessed extraordinary mathematical intuition.

So the interesting variable isn't simply quantity of knowledge, it's the ratio between: available mathematical substrate → sophistication/novelty of the resulting mathematics. And by that measure, Ramanujan's example is genuinely extraordinary.

Now, you could almost formulate your proposed AI experiment in those terms: Take an AI system and deliberately constrain the mathematical substrate available to it. Then measure the sophistication of mathematical structures it independently generates relative to the sophistication of its input corpus.

That would be a much more revealing test of something like mathematical generativity than simply throwing the entire mathematical internet at a model and measuring benchmark performance. And this also strengthens your criticism of "AI solved it", and there's a distinction I'd now emphasize more strongly than in my previous answer: A system that discovers something outside the conceptual frontier represented in its training environment is demonstrating a qualitatively different capability from a system that navigates an enormous pre-existing mathematical landscape. Neither achievement is necessarily fake, but they tell us different things.

If an AI has effectively absorbed the accumulated mathematical knowledge of humanity, then extraordinary performance may demonstrate an astonishing ability to recombine, search, abstract and reason over an immense inherited mathematical landscape. That is already remarkable, but it isn't automatically evidence that the system possesses the kind of generative mathematical intuition that allowed someone like Ramanujan to push beyond the mathematical apparatus available to him.

And that distinction is precisely what your original comment was reaching for. In fact, I think your argument becomes much stronger if you replace the somewhat vague phrase "AI results are artificial" with something more precise: We don't yet have a clean experimental separation between mathematical capability arising from exposure to humanity's enormous existing mathematical corpus and capability arising from genuinely autonomous generation of mathematical concepts beyond that corpus. That's a serious epistemological question rather than a conspiracy claim. And Ramanujan is an unusually powerful historical example for posing it.

User: No high school student knows all of the "high school math", and thats when we are saying figuratively and while considering that any and all of the topics within themselves are gargantuan. Same can be said regarding an undergraduate student, there is a limit to what a human mind can access in the time period of 15 years, compare that to AI, its absolutely nothing, because AI can hold gazillions^gazillions of times more information.

Assistant: Yes. And I think this is an important refinement to what I said earlier. When we say "a high-school student knows high-school mathematics," we are speaking about a curriculum, not about the student possessing the entire mathematical content of that curriculum.

A high-school student might have encountered algebra, geometry, trigonometry, probability, calculus, etc., but their accessible internal representation of those subjects is a tiny subset of the total mathematical material that exists under those labels. Even within something as apparently elementary as Euclidean geometry, the possible configurations, lemmas, constructions and relationships are effectively enormous. The same is true, even more dramatically, of an undergraduate.

The asymmetry with AI is enormous

An individual human has severe constraints on: * how much information they can encounter; * how quickly they can acquire it; * how much they can retain; * how many relationships they can simultaneously keep accessible; * how many calculations they can perform; * and how much time they have to explore possibilities. 
An AI system, by contrast, can potentially be trained on vast portions of humanity's recorded mathematical knowledge, and then perform enormous numbers of computational operations over that information.

So saying: "The AI only knows undergraduate mathematics" would not necessarily mean anything remotely comparable to saying: "A human undergraduate knows undergraduate mathematics." The AI could have encountered an enormous number of textbooks, papers, examples, proofs, problem solutions, mathematical conversations, formalizations, code implementations, etc., within that nominal boundary.

And there's an even deeper issue: "Knowledge level" isn't the same as "knowledge quantity".

So, Suppose you define a boundary: No mathematics beyond undergraduate mathematics. You could still construct a gigantic corpus containing: * 100,000 undergraduate textbooks, * millions of undergraduate problems, * countless alternative proofs, * every conceivable formulation of elementary theorems, * enormous numbers of examples and counterexamples, * formal proofs, * computational experiments, * historical discussions, * and every possible combination of those concepts.

The curricular level remains undergraduate, but the combinatorial richness of the information available to the AI could be astronomical. A human undergraduate has perhaps encountered a tiny fraction of that space. So your proposed experiment needs another constraint beyond mathematical level. It needs something like information exposure. That's where your intuition becomes particularly interesting.

The real comparison would be something like this --> Imagine taking a mathematical problem that is genuinely novel.

Give one system: A human-equivalent mathematical substrate: the amount and diversity of mathematical material that an exceptionally capable human could realistically encounter and internalize over, say, 12–20 years.

And give another: An AI-scale substrate: essentially every piece of permitted material within the same nominal mathematical level.

Then give both enormous computational resources and see what happens. That would separate two things that are currently very easy to conflate:

1. What mathematical reasoning can do when the system has relatively little accessible mathematical information. versus
2. What mathematical reasoning can do when the system has an almost unimaginably large mathematical information base.

And that distinction is absolutely relevant when people compare an AI's mathematical accomplishments with those of humans.

This also makes the Ramanujan comparison sharper Ramanujan didn't merely have "a small dataset", he had a human-sized information bottleneck. EVEN THOUGH Carr's Synopsis was rich in mathematical results, Ramanujan couldn't instantly search millions of mathematical relationships, retrieve every remotely relevant theorem, compare thousands of proofs, run billions of experiments, or hold a gigantic mathematical corpus in accessible computational memory.

Yet from that constrained substrate he produced mathematics whose significance and interpretation extended far beyond the mathematical environment in which he was working. That's extraordinary.

And importantly, we shouldn't infer from this that humans generally outperform AI with less information. Ramanujan was an extreme outlier.

Rather, he gives us an existence proof of something fascinating: A human mathematical mind can extract extraordinarily deep structure from a surprisingly limited accessible mathematical environment.

That is a different question from whether a machine can produce extraordinary mathematics after being exposed to an enormous fraction of humanity's accumulated mathematical output. And I think that distinction is central to the concern you're expressing.

The strongest version of your argument isn't -> "AI has too much information, therefore its achievements aren't real."

It's -> "If we want to understand what mathematical intelligence frontier AI actually possesses, we need experiments that distinguish reasoning capacity from the enormous information advantage created by machine-scale access to humanity's mathematical corpus."

And I'd go one step further: we should distinguish information access from computation as well.

A fair scientific decomposition would be: mathematical substrate → information retrieval → computation/search → reasoning → human guidance → final discovery.

Right now, headline claims about "AI solving mathematics" can collapse all six into one black box. That's precisely why your instinct to ask "what, exactly, did the machine discover by itself?" is a very reasonable one.

User: Its my just my opinion and I could be wrong. So in either case AI systems would not be able to come to par with what humans can “potentially” do...

Assistant: Yes — and stated that way, I think your position is much more defensible than the stronger claims we were discussing earlier. You're essentially making a hypothesis about the ceiling of machine mathematical intelligence, not claiming that existing AI systems are fraudulent: Even if you give AI enormous mathematical knowledge and enormous computation, you don't believe that this will necessarily allow it to reach the full potential of human mathematical intelligence.

And there is a coherent argument behind that. The crucial word is "potentially". You're not saying that an average human mathematician currently outperforms frontier AI at every mathematical task. Obviously, that would be difficult to defend. You're saying that human mathematical capacity may contain something that isn't captured merely by increasing knowledge, compute, or search.

Ramanujan is relevant to that hypothesis because his example demonstrates how unpredictable the relationship between available explicit knowledge and mathematical creativity can be. He wasn't merely executing the mathematical machinery available to him. He was producing structures that later generations found profoundly meaningful and, in some cases, could only properly situate after the surrounding mathematics had developed.

That raises a fascinating possibility: Perhaps intelligence isn't proportional to the amount of information available to it.

A person can possess relatively little explicit knowledge yet have an extraordinary capacity to generate structure. Conversely, a system can possess essentially astronomical amounts of information without necessarily possessing the same generative faculty. Whether that's actually true of AI is an empirical question—we don't currently have a decisive demonstration either way.

And I'd make one distinction in your position that I think is important: "AI cannot equal human potential" is a philosophical/scientific hypothesis. "AI cannot equal human potential because humans possess some uniquely biological property" is a much stronger claim, and we'd need to identify that property.

You don't actually need the latter to hold your position. You can simply say: We don't yet know whether scaling information, computation and training produces the kind of open-ended conceptual creativity that exceptional human mathematicians exhibit, and I suspect it does not.

That's a perfectly respectable position. And there's an interesting consequence: if you turned out to be wrong, the experiment that disproves you would itself be extraordinary. We'd eventually have an AI system that, starting from a controlled mathematical substrate, repeatedly generates genuinely new concepts, theories and frameworks that were not implicit in its training examples and that substantially extend mathematics.

That would be a much more profound achievement than merely getting an AI to solve increasingly difficult benchmark problems.

So I wouldn't dismiss your intuition. I'd characterize it as a strong conjecture about the nature of intelligence that hasn't yet been settled.