Will 10 previously unsolved Erdős problems be resolved by AI in 2026?
Delphi’s forecast
- Yesyour pick80.5%$0.81
- No19.5%$0.20
We could not pin down how this would settle, so there is no market to trade. The odds stand.
Forecast reasoning
OpenAI released 722 manuscripts on October 8 with 17 claimed complete solutions to previously unsolved Erdős problems, 12 verified with formal proofs, while Google DeepMind's AlphaProof solved 9 more including problems open 56 years. The 81% reflects these October breakthroughs plus earlier 2026 resolutions by Tao-verified AI systems, though independent validation of all 17 OpenAI claims remains pending through January 1.
Settlement
Resolution criteria: - "Yes": Wins if at least 10 distinct problems catalogued on erdosproblems.com (Thomas Bloom's Erdős problems database) that were listed as unsolved as of 2026-01-01T00:00:00Z are each confirmed resolved — by a published proof, disproof, or formal verification accepted by the mathematical community — through a solution developed with material AI assistance, strictly after 2026-01-01T00:00:00Z and at or before 2027-01-01T00:00:00Z. - "No": Wins if, at or before 2027-01-01T00:00:00Z, fewer than 10 such problems meet all of the above conditions within the same window. Clarifications: - A problem counts as "resolved by AI" only if: (1) it was listed as unsolved on erdosproblems.com as of 2026-01-01T00:00:00Z; (2) a solution (proof, disproof, or formal verification) was published or formally announced strictly after 2026-01-01T00:00:00Z and at or before 2027-01-01T00:00:00Z; and (3) the solution was developed with material AI assistance, as acknowledged in the publication, announcement, or by the solving team. - Each distinct problem number on erdosproblems.com counts as one problem; a single result resolving multiple problems counts as one per problem explicitly addressed.
Jan 1, 2027, 12:00 AM UTC