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Google DeepMind's AI solved 9 open Erdős maths problems, with every proof computer-checked

Milestone

AlphaProof Nexus also settled 44 of 492 conjectures about number sequences, for a few hundred dollars each. It failed on most it tried.

9 of 353open Erdős problems solved with computer-checked proofs (about 2.5%)

Erdős problems with a computer-checked solution

Problems in the community Erdős problems database whose solution has been formalized in the Lean proof checker, at the end of each month.

What this measures: Paul Erdős left behind more than a thousand math problems. This counts how many have a solution that the Lean proof checker has verified step by step, whether the proof came from a human or an AI.

01002003004002026

Counts solutions from any source, human or AI, so this is not a count of AI solutions. Early growth partly reflects the database being built. The sources don't explain the August 2026 jump. Since 6 October 2026 erdosproblems.com no longer shows solved counts, and the 12 FrontierMath Erdős problems Epoch AI credits to OpenAI's 6 October release are not yet included. Each point is the last row of its month in the database's statistics_history.csv.

Sources: Erdős problems community database (Tao et al.), Erdős problems community databaseData as of 9 Nov 2026
Show data table and sources
DateLabelValue
30 Sept 20253 problems
31 Dec 202538 problems
31 Jan 202669 problems
28 Feb 2026110 problems
31 Mar 2026124 problems
30 Apr 2026167 problems
31 May 2026186 problems
30 Jun 2026199 problems
31 Jul 2026207 problems
31 Aug 2026292 problems
28 Sept 2026317 problems
29 Oct 2026318 problems
6 Nov 2026318 problems

A Google DeepMind paper posted on 21 May 2026 (arXiv 2605.22763, first author George Tsoukalas) reports the first large-scale test of AI proof search on open maths problems. The AI writes its proofs in Lean, a language in which a computer checks every step, so nobody has to take the AI’s word for it.

The best agent resolved 9 of 353 open Erdős problems (questions posed by the mathematician Paul Erdős) at a few hundred dollars each. It also proved 44 of 492 conjectures from the OEIS, a large online database of whole-number sequences. A simpler generate-and-check agent matched the Erdős results but cost more on the hardest problems. Aarhus University, one of whose mathematicians co-authored the paper, says two of the solved problems had been open since 1970. The Lean proofs are public on GitHub.

According to The Decoder, the system is built on Gemini 3.1 Pro, can call DeepMind’s AlphaProof system, and the work was later published in the journal Science. Separately, DeepMind’s AI co-mathematician system (arXiv 2605.06651) reported 48% on FrontierMath Tier 4, a set of very hard maths problems, which its authors call a new high.

What it means

AI can now settle some open maths questions cheaply, with proofs a computer has checked, so the results do not rest on trusting the AI. It still fails on almost all of them: it solved about 2.5% of the Erdős problems it tried. It helps pick off some open questions, while most remain out of reach.

Caveats

  • The success rate is low: about 2.5% of the Erdős problems attempted.
  • The cost figures leave out the work of picking problems that looked solvable.
  • The Science publication (reported 12 October 2026) comes from The Decoder; we could not open the journal page to confirm it.
  • The 48% FrontierMath Tier 4 score is reported by the system’s own authors.
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