Wolfram argues against handing pure math research to AI, citing the 1988 Mathematica parallel

Past experience arguments only go so far. Mathematica in 1988 isn't the same situation as LLMs now, and you can't just map one onto the other.

The real question is whether the gains keep coming. The AI labs could run out of human trainers good enough to refine the models further, or we could be sitting right at real superintelligence. Nobody knows which.

The TL;DR I wanted is that AI can do the proofs and calculations, but deciding why we do math and which problems to solve stays with humans. As a non-mathematician that reads like a weak, slightly bizarre argument.

If the training data is purely historical, how does the model look forward? And if human mathematicians stop producing new results, the AI is eating its own seed corn, just at scale.

I worry about keeping a critical mass of people who actually understand frontier math. In five or ten years the only ones working at the frontier might be AIs, and deep understanding gets replaced by broad-strokes grasp plus machine verification.

Journal submissions are way up and rejections are up with them. Frontier models still stumble on small conjectures despite all the hype, and it depends a lot on the prompt and the problem type. AI makes it easier to produce papers, not easier to publish them.

AI is basically a compressed database of human knowledge you can query, not a thinking machine. Generating useful math is a much more exacting task than generating language, and LLMs are chatbots, not mathbots.

That database framing is outdated. Reasoning models actually think and can solve novel problems, even hard ones. The whole reason we're having this conversation is that an AI solved a Millennium Prize problem no human had an answer to.

I like Wolfram's posts, but he clearly wants Mathematica to be central to math as a field and it's proprietary. If the company ever dissolves there's no guarantee a proof formalized in it can be checked again. Pin a Lean version and you can check that proof forever.

His strongest point is that math aims at human understanding. Turn loose a near infinite proof search on today's definitions and it could produce a valid proof so long and mechanical that no lineage of humans until the end of the universe could finish reading it. That's computation, not mathematics.

The human understanding line begs the question. What does the rest of humanity get from a small group holding something called understanding, especially when that group is historically terrible at communicating it and most people can't learn it anyway? I nearly finished a math PhD and I still don't see why the rest of us should fund it, barring something like UBI.

There are two assumptions in the core argument and both are shaky. AI may end up deciding which math is useful, not just proving it. And human understandability may be an interim trust mechanism rather than the end goal. The article may hold for today but not two years from now.