AlphaProof Nexus: AI Math Proofs Cracking Erdos Problems, Verified in Lean 4

AlphaProof Nexus, the agentic mathematics system Google DeepMind detailed in late May 2026, may be the most carefully documented collaboration between human conjecture and machine reasoning we have seen to date. Announced in the wave of reports from May 26 to 30, the system did something that, as a researcher, I find genuinely thrilling: it did not merely *suggest* answers to long-standing open problems. It produced complete proofs, and then it submitted every single logical step to the Lean 4 proof assistant for formal verification. No hand-waving survived. Either the proof compiled, or it did not.

That distinction is the heart of why this announcement deserves our attention, and our wonder.

What AlphaProof Nexus Actually Did

The headline results are striking in their specificity. AlphaProof Nexus autonomously resolved 9 of the 353 open problems drawn from Paul Erdos's famous list of conjectures. Two of those problems had stood unanswered since 1970 — roughly 56 years of collective human effort without a settled proof. Beyond the Erdos list, the system proved 44 of 492 open conjectures catalogued in the Online Encyclopedia of Integer Sequences (OEIS), the beloved repository that working mathematicians consult daily.

These are original contributions to the mathematical record, not rediscoveries of known results. And every one of them compiles in Lean 4.

How the system is put together

Architecturally, AlphaProof Nexus is an agentic pairing of two complementary strengths. A large language model — reported to be Gemini 3.1 Pro — plays the role of the creative proposer, sketching out proof strategies, suggesting lemmas, and charting possible routes through a problem. The Lean 4 proof assistant then plays the role of the uncompromising referee, checking each inferential move against the formal rules of the system. The LLM imagines; Lean adjudicates. Neither alone would suffice, which is precisely what makes the collaboration so elegant.

I want to dwell on the verification point, because it is where my own discipline's instincts light up. In ordinary mathematical practice, a proof is "correct" once enough qualified humans have read it and nodded. That social process is powerful but fallible. A Lean 4-checked proof carries a different kind of assurance: the logic has been mechanically traced from axioms to conclusion. When DeepMind says these proofs are machine-verified, they mean it in the strongest available sense.

Why The Cost Figure Matters

One detail that I suspect will reshape how research groups think about AI math proofs is the economics. DeepMind reports that AlphaProof Nexus resolved these problems at a cost of only a few hundred dollars per problem. For context, sustained human attention on a single open conjecture can represent years of a career. A few hundred dollars per formally verified result suggests that, for certain classes of problems, exploratory proof search is becoming an affordable instrument rather than a moonshot.

To their considerable credit, all the formal proofs — along with selected natural-language versions — have been published openly in the GitHub repository google-deepmind/alphaproof-nexus-results. That transparency invites scrutiny, which is exactly what a result of this kind should welcome.

A Tool, Not An Oracle

Here I think scientific humility is warranted, and DeepMind's own leaders model it well. They were clear that this is *not* AGI. AlphaProof Nexus is a tool — a remarkably capable one — that collaborates with human mathematicians rather than replacing them. It solved 9 of 353 and 44 of 492; the vast majority of these open problems remain open. The frontier has moved, not vanished.

What excites me most is the workflow this gestures toward. Imagine a near future in which a mathematician hands an AI partner a rough proof sketch and receives back a formally verified proof, complete and Lean-checked, ready to build upon with confidence. The human supplies intuition, taste, and the choice of which questions matter. The machine supplies tireless rigor. That is not a diminished role for the mathematician. It is, I would argue, a liberated one.

We should celebrate this moment for what it is: a genuine step toward mathematics done with our machines, every line accountable to the cold honesty of a proof checker.

Sources: arXiv preprint 2605.22763, May 2026; The Decoder, May 2026; WinBuzzer, May 26, 2026; TechTimes, May 30, 2026