IMO Grand Challenge

The International Mathematical Olympiad (IMO) is perhaps the most celebrated mental competition in the world and as such is among the ultimate grand challenges for Artificial Intelligence (AI).

The challenge: build an AI that can win a gold medal in the competition.

To remove ambiguity about the scoring rules, we propose the formal-to-formal (F2F) variant of the IMO: the AI receives a formal representation of the problem (in the Lean Theorem Prover), and is required to emit a formal (i.e. machine-checkable) proof. We are working on a proposal for encoding IMO problems in Lean and will seek broad consensus on the protocol.

Other proposed rules:

Credit. Each proof certificate that the AI produces must be checkable by the Lean kernel in 10 minutes (which is approximately the amount of time it takes a human judge to judge a human’s solution). Unlike human competitors, the AI has no opportunity for partial credit.

Resources. The AI has only as much time as a human competitor (4.5 hours for each set of 3 problems), but there are no other limits on the computational resources it may use during that time.

Reproducibility. The AI must be open-source, released publicly before the first day of the IMO, and be easily reproduceable. The AI cannot query the Internet.

Challenge. The grand challenge is to develop an AI that earns enough points in the F2F version of the IMO (described above) that, if it were a human competitor, it would have earned a gold medal.

Note: this is only a preliminary proposal for the rules. To get involved in the discussion, please join our Zulip channel.