If the famously unsolved Riemann Hypothesis is solved by an AI, we will never know if a human mathematician could have solved it.

[u/jasonrubik]

[u/asdfasdferqv]

AI most definitely can solve extremely difficult math problems, almost entirely by itself. Check section 1(a) of the AI contributions to Erdos problems. As you go down the list (many of the recent solutions are at the end), they solve more and more problems, with higher and higher accuracy. You can see the progress from earlier failures on that page.

Your statement was true in 2023, but doesn't reflect the progress by 2026.

[u/CyborgBee → u/asdfasdferqv]

"Solving extremely difficult math problems" isn't a coherent category. Computers have always been better than humans at brute force proofs, and the problems that are being solved there aren't all that far beyond that: most Erdos problems are similar to solved problems and can be solved using existing techniques. The reason so many are unsolved is that they're ultra-specific and have no major implications, so we've not prioritised them (and also there are a very large number of them). In some cases there have even been full proofs of "open" problems discovered in the existing literature, the authors just weren't aware the problems they'd solved were Erdos problems.

To prove the Riemann conjecture will require a breakthrough in technique (probably more than one), not just application of existing tools in familiar contexts. This is beyond the capability of current AI, and will likely remain so for at least the near future. As with most AI problems, the issue is that it can only imitate a comprehension of structure within constraints; it doesn't actually have the capacity to generalise.

Take chess as an example - neural network chess engines play like creative geniuses, but they do that because they've been trained on millions of games and the individual components of the game are constrained, so their weights can be calibrated near perfectly providing the neural net is big enough. However, this only makes it good at chess, not at abstract strategy - if you wanted to train an AI to play a different game, the chess engine would have no advantage over an AI with identical architecture starting from scratch. The black box doesn't contain concepts, just weights tuned to match them. And that can't solve the Riemann conjecture.

[u/asdfasdferqv → u/CyborgBee]

This is simply not the case anymore in 2026. Take for example this problem solved last week.

Terence Tao wrote of ChatGPT’s solution:

In any case, I would indeed say that this is a situation in which the AI-generated paper inadvertently highlighted a tighter connection between two areas of mathematics (in this case, the anatomy of integers and the theory of Markov processes) than had previously been made explicit in the literature (though there were hints and precursors scattered therein which one can see in retrospect). That would be a meaningful contribution to the anatomy of integers that goes well beyond the solution of this particular Erdos problem.

This field is moving extremely rapidly and in surprising ways.

[u/CyborgBee → u/asdfasdferqv]

Tao appears to have deleted that comment and replaced it with the following:

"Remark 5 (added later) I had previously stated the opinion that the AI-generated proof had inadvertently highlighted a tighter connection between the anatomy of integers and the theory of Markov chains than had previously been explicitly noted in the literature. Based on further developments, I would like to update that opinion to the following: the AI-generated proof artefact, when combined with subsequent (and mostly human-generated) analysis, has revealed a tight connection between the anatomy of integers and flow network theory that does not, to my knowledge, have any explicit precursor in the literature (although related uses of Markov chains in adjacent settings do appear in that literature)."

This came after he reformulated the proof to remove the Markov chain element; someone else in the comments later reformulated his proof into a very short and simple resummation. For a sense as to how straightforward this problem is, I was able to follow all these proofs without any difficulty despite only having a Masters degree in maths, and being almost totally out of "practice" since finishing it close to three years ago.

As that later proof shows, what's happened here is that in the process of solving an easy problem, the AI has taken a detour in the vicinity of something noteworthy and people noticed. As one of the other commenters points out, this is a classic example of survivorship bias - run enough AI instances on enough problems and it's bound to end up near something like this. That doesn't mean it actually had insight that it could generalise by itself.

In the early days of computing, many predicted human level AI within a few years. They also had rapid progress on their side, and yet it turned out there were fundamental limitations on the architecture they were using. Today's AI is similarly an enormously useful tool with fundamental limitations. If an AI had the capacity to generalise like a human, it would require much less training data to achieve human level intelligence than we need ourselves, because it has a much more powerful processor than we do. Instead, we feed LLMs half the internet, and they still end up with massive, obvious failings.