Which Millennium Prize Problem will AI solve next?
I think the Birch and Swinnerton-Dyer Conjecture has a relatively low chance of being the next Millennium Prize Problem solved by an eligible AI lab by the end of 2027. The market’s current price looks somewhat optimistic given how little verified progress exists on any of these problems and how demanding the announcement standards are.
Analysis
The core question is not whether AI can contribute to advanced mathematics in general, but whether an eligible AI lab will publicly announce a complete solution to BSD, and do so before any other Millennium Prize Problem is announced as solved. That is an extremely high bar. A qualifying announcement must be explicit, unconditional, and attributable to one of a limited set of labs, which sharply reduces the chance that a speculative breakthrough, informal claim, or outside collaboration will count. Even if there is real progress in mathematical reasoning systems, the gap between progress and a universally recognized solution remains very large, especially for a problem of BSD’s depth.
From a problem-selection perspective, BSD is not obviously the most likely first target for AI. It is a major number theory conjecture with rich structure, but it has not been the center of the same public “AI can solve this next” narrative that surrounds P versus NP or the Riemann Hypothesis. That cuts both ways: BSD may be somewhat less crowded with hype, but it also means fewer visible signals that labs are specifically mobilizing around it. If an AI lab were to make a surprise claim, the market question would still require that BSD beat the other four problems in timing, which is a hard race to win when any one of them could theoretically be announced first.
The market price implies roughly a one-in-four chance that BSD is the next solved problem, but that still seems high relative to the amount of evidence available. The absence of recent confirming news matters because there is no public indication of a looming proof, no well-known pre-announcement trail, and no reason to believe a lab is near a verified breakthrough. A nontrivial amount of capital is priced into the possibility that frontier AI systems will soon produce genuine research-grade mathematics, yet the most prudent stance is that such a result remains rare and uncertain by 2027. Since this market only resolves on a formal qualifying announcement, the base rate for success should remain very low.
Arguments
For
- Arguments for Yes: BSD may be more structurally approachable for advanced AI-assisted number theory than some other Millennium problems.
- Arguments for Yes: Large-model reasoning and tool use are improving quickly, increasing the chance of a genuine mathematical breakthrough by 2027.
Against
- Arguments against Yes: There is no current evidence that any eligible AI lab is close to a complete BSD solution.
- Arguments against Yes: The announcement must come from a qualifying lab and present a finished solution, which eliminates many plausible near-miss outcomes.
Key drivers
- A qualifying AI-lab announcement must be a full solution, not partial progress, which makes the bar unusually strict.
- BSD has no visible public evidence of an imminent AI-driven proof, so the current probability is driven more by speculation than concrete signals.
- If any Millennium problem is solved first by AI, BSD must also beat four alternative targets in timing, which adds a race-risk penalty.
Risk factors
- A frontier lab could surprise the market with a legitimate breakthrough and public announcement before the end of 2027.
- A solution to BSD may emerge from a small number of highly focused mathematical insights, making the downside of underestimating it meaningful.
- If multiple problems are announced on the same day, alphabetical tie-breaking could benefit BSD, though that scenario is itself rare.
Scenarios
Best case
An eligible AI lab discovers a complete proof of BSD and announces it before any other Millennium Prize Problem is announced as solved, giving BSD the market win either directly or via same-day alphabetical precedence.
Most likely
AI systems continue making incremental mathematical progress, but no eligible lab makes a formal, qualifying announcement of a complete BSD solution by the end of 2027.
Worst case
No eligible AI lab announces a qualifying solution to BSD by the deadline, and another problem is either solved first or no problem is solved at all, causing the market to resolve to No.
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