Google DeepMind has introduced a new mathematical framework called AlphaProof Nexus. This system independently solved nine open problems from the list of famous mathematician Paul Erdős. Some of these had remained unsolved for over half a century. The system also proved 44 hypotheses from the Online Encyclopedia of Integer Sequences (OEIS) and solved a 15-year-old problem in algebraic geometry. This was reported by Ixbt.com reports.
The key feature of the AlphaProof Nexus system is the integration of the Gemini 3.1 Pro language model with the Lean formal mathematical verification system. Unlike standard LLMs, this system generates proofs step-by-step in the Lean programming language rather than natural language. Each step is automatically verified by a compiler. If an error occurs, Lean returns a precise message, and the model learns from it for the next attempt. This approach prevents AI from making logical errors (hallucinations).
According to the researchers, the computational cost to solve a single problem amounted to several hundred dollars. The system performed particularly well in areas where the Mathlib library is well-developed, such as combinatorics, number theory, and convex optimization. Nevertheless, only nine of Erdős's 353 open problems have been solved so far, indicating that there is still much work to be done for AI.
DeepMind experts emphasize that AlphaProof Nexus will not replace mathematicians but will become a new research tool. All formal proofs provided by the system have been published on the GitHub platform. This work was carried out against the backdrop of achievements in mathematical research by competitors such as OpenAI. For example, OpenAI previously used its reasoning model to disprove Erdős's distance hypothesis.
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