Seven problems were designated in 2000, each carrying a prize of one million dollars. In twenty-six years, only one has been solved — and its author refused the prize. That ratio says two things: these questions are extraordinarily difficult, and the process that decides whether a proof holds is long and demanding.
This morning we reported an announcement concerning one of these problems. Here is the context that allows it to be read correctly.
What these problems are
They were chosen for a common reason: they are questions that block entire fields. Solving them would not merely yield a result, it would unlock methods.
They cover very different domains: number theory, theoretical computer science, geometry, mathematical physics. The one concerning fluids, which we discussed this morning, relates to equations used daily in engineering without anyone knowing how to prove that they always behave well.
The only one solved to date, in 2003, concerned a question of topology. It took the community four years to validate the proof, and its author subsequently refused both the Fields Medal and the million dollars.
How a proof becomes accepted
Here is the point that current events suddenly make concrete, and it is poorly understood.
Publication. The prize rules require publication in a peer-reviewed journal. This assumes that several specialists, chosen by the editor and generally anonymous, examine the proof line by line. This process takes months, sometimes years.
The two-year delay. After publication, the rules impose a period of general acceptance by the community. The idea is simple: a proof can pass peer review and turn out to be false when a third-party specialist takes it up from a different angle.
Review by a committee. Only then does a commission rule.
In concrete terms, this means that an announcement made in September 2026 could not produce an award before 2029 at the earliest, whatever the quality of the work.
The history of mathematics is full of proofs announced, published, then invalidated years later. The most famous case is that of Fermat's Last Theorem: the first version presented in 1993 contained a gap, discovered during peer review, and it took another year to fill it. The proof was right in its architecture and wrong in one link. This is exactly the kind of error that a quick review does not detect, and it is why the process is slow.
What formal verification changes
This is where current events become interesting.
We explained in our article on proof assistants that a formalised proof is checked mechanically, step by step. The kind of error that delayed Fermat for a year — a missing link in a correct architecture — is precisely what a verifier detects immediately.
This could considerably shorten the technical review phase. What it does not shorten is the verification that the formalised statement corresponds to the question asked. This step remains human, it is short, and it is where attention will focus.
It is an interesting division of labour: the machine verifies the proof, the human verifies the question.
What to take away
The process of accepting a proof is not an administrative formality: it is what distinguishes a mathematical result from a claim.
We wrote in our article on what a proof is that a result is established only when someone has been able to challenge it and has failed. The two-year delay in the rules is the exact institutional translation of that principle.
This invites a certain patience in the face of announcements. A claim is not a result, a formalisation is not a validation, and twenty-six years for a single solved problem suggests that caution has historically been right.