Sep 27 - Oct 2, 2026 · Hybrid kickoff at MIT · Worldwide online
One week. Open mathematics. Machine-checked results.
Join a global competition to formalize mathematics, attack open problems, and create verifiable public results with any combination of human reasoning and AI.
Scoring, judging, eligibility, and the submission cutoff are set out in the handbook. The submission workspace and checker instructions will be linked here before submissions open.
How much rigorous mathematics can one week produce?
The strongest AI systems can now explore mathematical ideas at extraordinary speed. A serious challenge for those systems can no longer stop at familiar exercises with known answers. It has to reach the frontier: open problems, reusable formalizations, decisive counterexamples, meaningful reductions, and new mathematical variations.
OpenMath concentrates many human and machine research loops into one public effort. Teams propose, compute, test, criticize, revise, formalize, and verify. They may attempt as many independently meaningful claims as they can finish. The objective is not a spectacle of confident answers. It is a large, inspectable body of mathematics that other researchers can check, reuse, and build upon.
The workflow is open. The standard of acceptance is not.
No formalization, no official result
A model-generated proof sketch, numerical pattern, informal argument, or persuasive manuscript may be valuable research evidence. It is not, by itself, an accepted competition result. A score-bearing claim must be encoded as an exact formal artifact or approved formal certificate, reproduce in a pinned environment, disclose its dependencies and material tools, and pass both machine checking and human semantic-fidelity review.
Machine checking answers whether the encoded object passes the specified formal system. Human review answers whether that object faithfully captures the mathematical claim being presented, whether the result is genuinely new or correctly classified, and whether attribution and provenance are complete. Both are required.
Fast generation + exact verification + public provenance.
A recursive loop designed to compound
Choose or propose a target. Start with the versioned competition corpus or nominate an eligible problem or variation.
Explore in parallel. Use mathematics, AI agents, search, code, symbolic tools, theorem provers, or any lawful combination.
Preserve useful state. Retain lemmas, counterexamples, failed approaches, improved statements, proof dependencies, and tool traces that can improve the next attempt.
Formalize the exact claim. Encode the statement and proof or certificate in an approved environment.
Submit through the official Hill and Climb workflow. Link the immutable artifact, evaluator output, authorship, provenance, and disclosures.
Verify and review. Re-run the checker and confirm statement fidelity, novelty, classification, conflicts, and attribution.
Publish and reuse. Accepted work enters the competition record with human authorship and reusable artifacts.
Different mathematical targets. One formal standard.
Organizer-curated focus problems
Work on a versioned focus set selected for special emphasis. The organizers expect a substantial set, but will not publish a final count until import, deduplication, statement review, and status checking are complete. Accepted focus-set results earn a 1.1x focus bonus, as set out in the handbook.
Formalization of mathematics
Create useful formalizations of established theorems, arguments, structures, or bodies of knowledge. Credit belongs to the new formal artifact and its authors, while historical mathematical attribution remains intact. This path can expand the libraries and infrastructure needed for future open-problem work.
Other open problems
Pursue admitted open problems outside the focus set. A target must have a precise canonical statement, provenance, open-status review, family identity, and difficulty assessment before it becomes score-eligible.
Open Mathematics variations
Formulate and solve a substantive new variation connected to a canonical Open Mathematics parent. A meaningful change in hypotheses, objects, or conclusion can qualify. Cosmetic restatements, equivalent formulations, and artificial fragmentation do not create separate results.