趋势解读：Google Deepmind's AlphaProof Nexus solves decades-old math problems，聚焦形式化数学

Google Deepmind has developed AlphaProof Nexus, a framework that autonomously solved nine of 353 open mathematical Erdős problems along with other complex conjectures, at an inference cost of just a few hundred dollars per problem. The system relies on the Gemini 3.1 Pro language model to generate proof steps in Lean, a formal programming language used for mathematical verification, enabling rigorous and machine-checkable solutions. While the vast majority of Erdős problems remained beyond the AI's reach, Deepmind researchers see the system as a valuable tool for supporting mathematical research. AlphaProof Nexus combines LLM-driven proof generation with machine verification to crack open math research problems that have stumped mathematicians for decades. Google Deepmind's new framework AlphaProof Nexus has autonomously solved nine out of 353 open Erdős problems it attempted, including two questions that had gone unanswered for 56 years. The system also proved 44 out of 492 open conjectures from the Online Encyclopedia of Integer Sequences (OEIS), settled a 15-year-old question about Hilbert functions in algebraic geometry, and improved a known bound in convex optimization. Inference costs ran just a few hundred dollars per problem, according to the research paper . Ad Unlike (potentially) pure natural-language approaches such as OpenAI's recent solution , the underlying language model in AlphaProof Nexus—in this case Gemini 3.1 Pro—doesn't have to carry the entire logical chain on its own. Ad DEC_D_Incontent-1 Instead, it generates proof steps in Lean's formal language, and the compiler checks each one. Error messages feed directly back into the next attempt. That way, the LLM gets grounded by symbolic feedback, a safety net that offsets the well-known weaknesses of language models when it comes to logical reasoning. Humans only step in at the very end to check the results. The system consists of four agent variants with increasing complexity. The simplest, Agent (A), deploys independent sub-agents running on Gemini 3.1 Pro in loops: the language model generates proof steps, the Lean compiler checks them, and error messages feed back into the next try. Ad Agent (B) adds queries to AlphaProof, Google's reinforcement-learning-based system for olympiad math, which can fill in missing proof segments. Agent (C) introduces an evolutionary component. Inspired by AlphaEvolve , sub-agents share a common population of proof sketches. Rating agents built on Gemini 3.0 Flash score these sketches for plausibility and novelty, then rank them using an Elo system. The fully equipped Agent (D) combines all of these capabilities. Agent (D) was used for the Erdős problems. But a post-hoc analysis turned up a surprise: the simplest Agent (A), which only uses an LLM and compiler feedback, could also prove all nine solved Erdős problems, albeit pricier on the hardest ones. Ad DEC_D_Incontent-2 The researchers attribute the simple agent's success to two factors: rapid improvement in the underlying language models and the "power of compiler feedback in grounding LLM reasoning." The fully equipped agent still holds an edge on the toughest tasks for now, but that lead could shrink as LLMs get better. The researchers say this points to a broader trend, describing "an ongoing shift from specialized trained systems toward simple agentic loops as LLMs become more capable." Ad