Google DeepMind's AlphaProof Nexus proves 9 open Erdős problems and 44 integer-sequence conjectures for a few hundred dollars each
AlphaProof Nexus autonomously solved 9 of 353 open Erdős problems and 44 of 492 open integer-sequence conjectures by having Gemini 3.1 Pro propose Lean proof steps and letting the compiler reject incorrect ones — machine-verified proofs, not informal reasoning chains. The key finding is that even the simplest single-model variant confirmed all nine solutions, pointing to compiler feedback as the core driver: formal-proof automation over open research-level math is now an engineering cost problem, not an architecture research problem.
Source: the-decoder.com ↗
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.
AlphaProof Nexus research paper
Why this matters
- → AI systems now autonomously prove decades-old open math problems at scale, shifting formal-proof automation from research challenge to engineering cost problem.
- → Compiler feedback grounding LLM reasoning achieves this without requiring specialized trained architectures—simple agentic loops with language models suffice.
- → Formal verification becomes a practical filter for research, even when proofs fail, deepening human understanding and catching flawed formalizations in literature.
Compiler feedback wins