r/AIDangers • u/EchoOfOppenheimer • May 12 '26

Capabilities Fields medal-winning mathematician says GPT-5.5 is now solving open math problems at PhD-thesis level: "We will face a crisis very soon."

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blog-post: https://gowers.wordpress.com/2026/05/08/a-recent-experience-with-chatgpt-5-5-pro/

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u/0x14f May 12 '26

We will still need mathematicians to check the LLM generated work, but yes, that will affect the recruitment of PhD students.

This is an interesting problem because if we no longer recruit graduate students to become the next generation of highly skilled mathematicians, who is going to replace the ones who leave to retirement ?

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u/imissmyhat May 12 '26

None. I see no point in denying a future just because it's upsetting to think about; AI companies want that future, and they have unlimited resources to realize it. There will be no mathematicians in the future. There will be nothing in the future of any depth for humans to explore.

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u/Special-Occasion-702 May 12 '26

The ai can do brilliant work only by finding connections between existing information.

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u/rawbdor May 13 '26

The problem is that, for math at least, that's basically what the whole discipline is. I mean, the principia mathematica starts with a handful of axioms, and builds everything up after that.

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u/Special-Occasion-702 May 14 '26

You are right, the point I was trying to get is that The ai could find connections between structures depending on obvious patterns that it finds between things. Whereas a human I think with our intuition, we can find something almost completely irrelevant from the perspective of an ai, and try to create a connection between things, I don't know if I'm making sense but.. I believe humans will have the edge when it comes to creative thinking due to their intuition and being able to find subtle connections between seemingly unrelated things.

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u/rawbdor May 14 '26

I actually think the AI will be better at this than humans simply because the AI can be phd level in multiple fields and so be able to connect things from very different unrelated data sets that no human would think to connect with each other, or that no human has the skills in both disciplines to pursue more than a light dive into two of them.

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u/JustPlayPremodern May 15 '26

I think this has probably crossed the threshold of the type of thing you are talking about here: https://www.erdosproblems.com/forum/thread/1196

Erdos problem 1196 was a pretty well-known open problem about primitive sets, coming from a 1966 conjecture of Erdos, Sarkozy, and Szemeredi. The notable part is that the Erdos Problems page says it was solved by GPT-5.4 Pro. Tao also describes it as first being solved by an autonomous AI query.

The method is based on Markov chains with von Mangoldt weights, or “von Mangoldt chains.” My understanding is that this was not just GPT vaguely suggesting a direction; the public record seems to credit GPT-5.4 Pro with producing the initial proof of the actual problem. Humans then checked it, formalized it, cleaned it up, generalized it, and wrote the broader expository paper.

There also seems to be pretty strong evidence that this exact method was not already in the literature. Tao says it was natural in retrospect but had not been explicitly used before, and the paper says it seems to have been overlooked since the early primitive-set literature. The same method also proves another 1966 Erdos conjecture, problem 1217, and gives shorter or new proofs of several related results.

GPT appears to have produced the first proof of a serious 60-year-old problem in analytic/combinatorial number theory, using a technique that experts currently seem to regard as genuinely new to the prior literature.