DeepMind AI solves 9 of 353 Erdős problems

Google DeepMind's AlphaProof Nexus proved 9 of 353 open Erdős problems, a paper in Science said on the 8th of October 2026. That is about 2.5%, by our arithmetic.

The results first appeared on arXiv on the 21st of May 2026. What is new is peer review, the check by outside experts before a journal prints a paper.

Erdős problems are 1,221 maths puzzles posed by Paul Erdős

The site erdosproblems.com lists 1,221 problems posed by the mathematician Paul Erdős, its home page showed on the 15th of October. An open problem is one nobody has solved yet.

Every step is checked by Lean, a program that tests proofs

Google's Gemini 3.1 Pro writes each proof in Lean, a computer language for maths, The Decoder reported on the 25th of May. Lean checks every step and sends errors back for the next try.

The cost was a few hundred dollars per problem, the arXiv abstract says. Two of the solved problems had been open for 56 years, The Decoder reported.

Below we break down what the 9 of 353 figure counts

The 9 results sit in 9 Lean files on DeepMind's GitHub page. They cover 7 problem numbers, by our count: 12, 26, 125, 138, 152, 741 and 846.

Problems 12 and 741 are split into 2 parts each. Problems 26, 125 and 138 are changed versions of the first question.

The system also proved 44 of 492 open claims from OEIS, an online list of number sequences, the abstract says. That is about 8.9%, by our arithmetic.

What is confirmed: Lean checks the written statement only

Lean proves only the statement as written in Lean, said Josep Curto of the Open University of Catalonia. Science Media Centre Spain quoted him on the 8th of October.

DeepMind and an OpenAI model each showed problem 846 to be false, its erdosproblems.com page says.

Key facts

Published in Science on the 8th of October 2026.

9 of 353 open Erdős problems, about 2.5% by our arithmetic.

44 of 492 OEIS claims, about 8.9% by our arithmetic.

Every proof checked in Lean, a few hundred dollars per problem.