Paul Erdos left behind several hundred problems with small cash prizes attached. They are a useful benchmark for mathematical reasoning because they are genuinely open, genuinely varied, and short enough to state precisely.
On 21 May 2026, Google DeepMind posted a paper, Advancing Mathematics Research with AI-Driven Formal Proof Search, reporting that a system called AlphaProof Nexus had autonomously solved nine of them. The proofs are in Lean 4, which means they are not arguments a referee has to read and judge. They are objects a compiler either accepts or rejects.
The numbers
The system was pointed at 353 Erdos problems that had been formalised in Lean, and it closed nine. It was also pointed at 492 conjectures from the Online Encyclopedia of Integer Sequences and proved 44 of those. DeepMind put the cost at a few hundred dollars per solved problem. The Lean proofs were published to a public repository, so the claims are checkable by anyone who installs Lean.
Nine out of 353 is about two and a half per cent. That is the number worth holding onto, and it cuts both ways. It is a low hit rate, and anybody describing the system as having solved mathematics is not reading the paper. It is also nine problems that were open before, including ones that had stood for decades, closed by a process that ran unattended.
Why formal proof changes the argument
The usual objection to a machine-produced proof is that checking it is as much work as writing it. A hundred pages of dense argument from an unreliable source is a burden, not a contribution, and mathematicians have limited patience for refereeing.
Lean removes that objection. A formal proof is checked mechanically against the axioms, in seconds, with no judgement involved. If it compiles, it is correct. The reviewer's job shifts entirely from "is this argument sound" to "is this the statement I meant", which is a much smaller and more tractable question.
That shift is the real content of the result. It means the volume of machine-generated mathematics can grow without the verification burden growing with it, and it is why the formal-methods route looks more durable than impressive-but-unverified output.
The catch
Formalising a problem statement in Lean is itself hard, and it is where the ambiguity goes. An informal problem can be loose about edge cases in a way a formal statement cannot, and the act of pinning it down is a mathematical judgement that a human still makes. A proof that compiles tells you the formal statement is true. Whether the formal statement is the problem Erdos posed is a separate question, and the only defence is that the formalisations are public and can be argued with.
There is no calculator attached to this piece, because there is nothing to compute. The result is about the economics of verification, not about a quantity. For the problems in the same year that do have something to compute, see Erdos problem 728 and the unit distance conjecture.