The Riemann Hypothesis (https://en.m.wikipedia.org/wiki/Riemann_hypothesis) has yet to be proven and is often considered one of the most challenging currently unsolved math problems.
This market only refers to whether an AI will “write” the proof by 2026, not necessarily create the proof itself. Therefore, if a human proves the Riemann Hypothesis before then, and an AI is able to write out that proof when asked, this market would still resolve to Yes.
This refers to any AI model, public or private, that has successfully written the proof, regardless of whether it is a generally available model.
The validity of the proof will be determined by whether or not the Clay Mathematics Institute has deemed it to be a successful solution to meet the requirements of the Millennium Prize Problem of proving the Riemann Hypothesis.
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@yum yep, the AI can use whatever. But proving the Riemann hypothesis has gone unsolved for 160 years, so unless someone cracks it before the deadline, it’s not going to be able to find a proof for it on the internet
@WillSpagnoli Right, but if the AI model can pull information from the internet then it seems like this question is essentially just, “Will the Riemann hypothesis be proven”. The AI model stuff seems like a near certainty if that happens.
@yum to an extent, but the AI model would have to find it on its own, and copy it perfectly without a single error. If someone wrote the proof today, it’d probably be 6 months of peer review and another 6 months of broader expert review before it’d be determined to be a true solution and widely publicized as so. Therefore, if a human solves it next year, and the AI searches the web on Dec 31, all their search results would probably still be claiming that it’s unsolved, and it’d have to decide to keep digging anyways, find the proposed proof somehow, then determine it’s a correct solution. If someone finds a proof in the next 3 months, then yeah it’d probably be trivial for an AI to write it by end of next year, but the chances of that are pretty slim
@AdamKallstenius yes, that would resolve to yes. If a human finally solves it, and that solution makes it into an AI model’s training data and the model can fully reproduce the proof without errors from memory when asked, then that would suffice. Granted, I doubt anyone will be training an LLM just for this manifold market, so there’d likely be a 6-12 month lag time to make it into the training data, meaning a human would likely have to solve it within ~1 year for it to be included in the training cutoff before the market deadline. That scenario a much easier criteria for AI to achieve, but much harder for humans considering how quickly it’d need to be solved.