>Quote: "The Overhang consists of the unrealized capital gains of past mathematical creativity, the latent value from connecting the dots in the existing corpus. It is a dividend of canonization. Mathematician X states problem A, mathematician Y crafts concept B, then mathematician Z notices that B trivially solves A and “captures” the social reward.

I've made an entire career out of being 'jack of all trades, master of none'. Being able to synthesize connections from relatively trivial knowledge in a bunch of domains is SOP for many humans as well. I think AI just has deeper knowledge and better pattern matching to make up for it's (at least now) lack of strength in cognition and 'ex nihilo' creativity.

(Which probably isn't 'ex nihilo' at all, and has more to do with the plethora of modalities that humans live in vs. large language models. For example, why do we pick the color red for notating important things and why do we say a schedule 'slips'...these are informed by a shared human experience borne of distinct physical sensation deep in our wiring that LLMs can only infer from what we write.)

> Quote: "The Overhang consists of the unrealized capital gains of past mathematical creativity, the latent value from connecting the dots in the existing corpus. It is a dividend of canonization. Mathematician X states problem A, mathematician Y crafts concept B, then mathematician Z notices that B trivially solves A and “captures” the social reward. But in the process of capturing the reward, Z usually introduces new concepts and new open problems, reinjecting latent value into the Overhang.

That overhang seems like a precious resource for AI companies. They can exploit that overhang to inflate the impression of AI's capabilities, and hopefully that exploitation will discourage the next generation of mathematicians from pursuing math. If they play their cards right, OpenAI and Anthropic can dominate the field even if they ultimately can't replicate the creativity of human mathematicians, because they'll have driven their competition out.

What we should be trying to achieve is a ladder-breaking maneuver: knock out the lower rungs so no person can reasonably climb to the top-reaches of mathematical skill anymore. That may ultimately result in stagnation, but it's what's best for AI, so it's what should be done now.

We need to do everything we can to create the greatest-possible dependence on AI tools.

There is also "sexy proof", people want nice math that can be printed in t-shirt. Not super hard grind, where you need several years of studying, just to understand the question (that is before even trying to solve it).

Many problems are solvable, but require months of work, and thousands of pages of proof. So people do not even try to create or verify the proof. AI changes that, it can verify and perhaps even simplify it, to more digestible form.

Could "superintelligence" arrive as basically applying this overhang to all other domains?

> no human has broad enough knowledge and enough time to try them all.

The other part is, humans don’t really want to fund other humans doing this.

Very few want to be a math major; and of those that do, fewer complete a grad degree; and for those that do get grad degrees, there’s scant few research jobs; and for those who do get jobs there’s hardly any research funding to go around.

There does seem to be unlimited money for ai researchers to use ai to solve these problems though.

We’ve turned education into job training, so because there’s no jobs in solving math problems, few aspire to do it. If there were more opportunities for people, more people would do it, and more low hanging fruit would be plucked.

It's like AlphaGo but playing against all living mathematicians. (Overhang being low hanging fruit is what allows this comparison, of course the general moot point is the skepticism that LLMs are also innovative etc.)

OpenAI have come out and said:

>The Wednesday evening statement from OpenAI was more emphatic: “We can say categorically that it is impossible for Dr. Buckmaster’s Codex prompts over the last two months to have influenced the system in any way, including training.”

>The statement added, “After investigating, we can say with full confidence that no user inputs past July 3rd could have influenced this system in any way.”

https://www.nytimes.com/2026/09/10/science/tristan-buckmaste...

> What we don't know is just how recent this model was, and therefore what it may have been trained on.

OpenAI's statement says that they began training their new model on August 28.

And conceptually novel approaches to outstanding problems are the sort of thing that a retrain should pick up on, because they would be hard to compress into what it already knows.

Openai said that a new model became available to them during this. But that could mean anything from a big new base model to a LoRA, fine-tuned on a few dozen prompts...

Very likely.

These mathematicians’ prompts are not like “hey chat, please solve Navier-Stokes for me”. They add real expertise and intuition from the cutting edge of their field.

You forgot possibility 3: OpenAI solved the problem without using any private training data from the two researchers.

Everyone in this thread seems to have made up their mind about OpenAI's guilt though.

Anthropic isnt getting enough scrutiny for their unprofessionalism:

1. Anthropic employee working on monumental problem but didnt receive/ask for the full backing of the company's resources

2. May or may not be mixing unreleased Claude output with Codex without zero data retention agreement

3. Victory lap on Twitter and giggling around the city before they finished the job, sparking rumors for competitors

The brute-forcing is a good, old-fashioned generate-and-test approach like in Simon and Newell's Logic Theorist, which was presented in the Dartmouth convention in 1956, where AI was named by John McCarthy. Logic Theorist caused a big stir by (re) proving several of the theorems in Principia Mathematica by Russel and Whitehead.

There was much excitement, then, as now, for this kind of approach and there were several systems that followed along the same lines, e.g. Automated Mathematician by Doug Lenat.

Eventually it became clear that this approach is limited by what it can generate: you may have a sound and complete verifier, but if the generator, i.e. the first step in the generate-and-test pipeline, is incomplete, then the entire thing will run out of steam sooner or later.

The difference with LLMs is that they are... well, large. They are the most powerful generators ever created. That means their limits are not in sight and it will probably take us a very long time to find them.

Which is all to say that, yes of course, automatic verification is indispensable. But without an LLM generating an unprecedentedly large number of plausible theorems, there would be no AI mathematics, or in any case AI mathematics wouldn't have gone as far as it has.

True, but could humans cross pollinating lean x prolog x A* ( or any search algorithm) could have solved such math problems with super computer ?

How long until we find out that some AI has quietly buried an exploit in Lean to cheat at proofs?

>They had to burn millions of dollars to solve a single problem

I'd like to adjust that to "They had to burn a lot of energy (create a lot of entropy) to solve a single problem. As we go into the super-intelligence age the current paradigm of money as humans understand it may break at some point. For example to a paperclip-maximizer money at best is a short term instrumental goal, hard power of matter conversion machines is what it wants and once it has those money no longer has purpose.

They "burn" a lot when they do benchmarks, while these runs can become valid roll outs for training. Perhaps less efficient than other data creation, but hardly burned in the same way.

> were the first victims

Spinning it negatively like that doesn't do anybody good.

Were mathematicians the "victims" of calculators? of Matlab?

Were writers the ""vIcTiMs"" of word processors?? (apparently yes, according to old TV shows about computers during the 1980s, that you can see on YouTube)

> "tHiS iS nOt ThE sAmE" — Everyone every time.

No, just look it up. Look into old magazines and TV shows or newspaper articles from whenever a disruptive new technology came out.

Wouldn't that be chess players as the first victims?

You think other mathematicians are currently working on very little subset of relatively low-hanging fruit problems?