AI solved open mathematical problems. But the biggest surprise came afterwards. A team at Google DeepMind has used AI to resolve 9 open Erdő…

AI solved open mathematical problems. But the biggest surprise came afterwards. A team at Google DeepMind has used AI to resolve 9 open Erdős problems, including questions that had remained unsolved for 56 years. The system also proved 44 previously open conjectures about integer sequences. These are genuine mathematical results, not benchmark exercises. Tsoukalas and coauthors built an agent that generates mathematical proofs in Lean, where every logical step must pass a formal checker. When a proof fails, the model receives feedback and tries again. The original system combined several sophisticated search mechanisms. But then the researchers tested something simpler: an LLM repeatedly generating proofs and checking them with Lean. It solved all nine Erdős problems too. That does not mean the elaborate system was unnecessary. It performed better on some particularly difficult problems, and the comparison was conducted after the original discoveries. Still, the result raises an interesting possibility. As language models become more capable, much of the progress in autonomous mathematical research may come from connecting them to reliable verification tools, rather than continually adding complexity to the agents themselves. And mathematics has a particular advantage here: a proof can be checked with extraordinary rigor. The challenge for the rest of AI for Science is finding equally reliable ways to test what our models discover. Paper: Tsoukalas et al., Science (2026), journal license | https://doi.org/10.1126/science.aej2213

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Source: Yohei Nakajima (X) | 2026-10-10