The proof is in the prompt: why math is not going away

OpenAI’s October 6 release of hundreds of mathematical results has produced another round of headlines:

[Note: The initial release contained 722 manuscripts grouped into 372 families of related results, which explains the different numbers being circulated. These include companion papers, consequences, and alternative proofs, so the manuscript count is not a count of separate problems solved.]

This has again invited the typical predictions of mathematicians becoming obsolete or math dying, along with armchair diagnoses about mathematicians having an existential crisis. But I have long predicted that AI will not make math careers obsolete or dismantle the “math hierarchy” of elite institutions, journals, tenure, and so on. Hierarchies persist because someone must decide what’s interesting and correct, and AI floods submissions.

Someone tweeted:

Is this sarcasm? Either way, I will put the outcome it describes under “not going to happen.” I wish there were a Polymarket contract for betting on “the math status quo surviving AI.” In another tweet, Curtis Yarvin (Moldbug) likened math to philosophy in terms of leaving its practitioners “unemployable”:

I don’t see math PhDs going away either. The value of a doctoral program (especially at a good school) is not to solve problems per se, but to become familiar with contemporary research and cultivate a network of experts for future work. Its purpose is mainly to guide future researchers towards productive areas of study, which AI alone doesn’t do. Conversely, when novices use AI for math, they tend to ask it to find all sorts of mathematical relations or results that they deem personally interesting or cool, but this doesn’t mean such findings are interesting to the broader “math community”.

Moreover, OpenAI and Anthropic themselves employ mathematicians. Anthropic, for example, describes its mathematicians examining Claude’s work and explaining how it relates to earlier research. This runs counter to predictions of mathematicians being unemployable. Such mathematicians presumably produced the actual prompts used for these proofs. The choice of prompt can make the difference between a problem being solved or not. Thus, expertise helps greatly in nudging the AI towards a fruitful direction to pursue.

The prompts were not disclosed in any of the OpenAI proofs, but were arguably as important as the proofs themselves. This is part of the reason for the controversy over AI proofs, because the necessary intermediate steps or attribution are not disclosed. I asked OpenAI whether the prompts were disclosed; they were not:

So in the case of Barnette’s conjecture, also solved by OpenAI, the prompting mathematician likely suggested the approach described below:

So what looked like an “aha” moment or epiphany was, if I had to guess, a combination of the AI’s capabilities and a really good prompt from an expert who knew precisely what to ask or where to steer it. From that point on, the AI may have done the rest with little outside help. In other cases, though, the AI can solve a problem or make progress with only the problem statement, copied verbatim—the so-called “one-shot” proof.

It’s also worth keeping in mind that OpenAI is using proprietary models with effectively an unlimited budget, so it’s not as if anyone could have reproduced those proofs using commercial products. Being “scooped” by AI doesn’t necessarily reflect a lack of skill; it can mean being beaten by superior machinery, possibly with expert mathematical guidance. It was never a fair fight. There is also survivorship bias, with failed attempts at solving problems with AI going unreported.

To use myself as an example, I found an alternative proof for a 40-year-old result, which had already been proven, but the alternative proof was still missing. Others had been looking for it with no success. I put the problem into ChatGPT and Claude with max setting, and no success. For 15 minutes it spat out various attempts by scanning a large search space, but could not actually resolve it. (When AI fails, it typically falls back to easier or incomplete versions of the original request, so as to not waste the token budget on nothing.) An entirely new approach was needed.

I then uploaded a 2025 paper I had written on this same topic, with a third proof of my own. I told the AI where to look, and my proof cleared the impasse. AI did the rest, constructing the sought alternative proof, which used my contribution. So in that sense, I did help in a substantive way. I imagine something similar happened with Barnette’s conjecture: An expert zeroed in on the correct strategy, and AI filled in the rest. This is why hours spent with Fable were not enough, because without the correct prompt, it wouldn’t know where to look in the first place.

Overall, contrary to AI “solving math,” in reality, it’s hit or miss, and highly dependent on the prompt and/or the problem. Even obscure problems can stump the model, as mentioned above, and need skilled prompting.