Open Proof Network

Why this exists

If you have read the declaration of 2026-09-11, you know what goes wrong when a proof arrives from a machine and nobody stands behind it. The record of the last year is not a record of wrong proofs. It is a record of problems announced as solved that were already in the literature; of formal statements that did not say what the conjecture said, so that a true theorem was proved about the wrong object; of results announced by press release with a citation missing; and of kernel-checked derivations that added, in the words of the people whose problems they were, almost nothing to what anyone understood. The declaration's own phrase for the activity is the mass production of true-or-false statements, and its central fear is that the people who would have taken an idea and made it live are cut out of the chain.

What the network does about it

This network is built for that objection, not around it. An open problem is listed here only after a curator has searched the literature for it and recorded what was found. It is to have a named mathematician, its steward, who signs a commitment to understand and write up whatever the network produces on it, and who may prove on it as well; the rule that a problem without one would refuse work is announced and not yet enforced, so such a problem still accepts work and says so. Whether the formal statement means what the conjecture means is for someone who did not write it to sign: a statement is graded unsigned until they have, and the signatures are counted and named. Every attempt, failed or not, is a published, typed record. When a proof merges the problem is marked proved and, in the same breath, unexplained, until a person who can explain the proof without the tool that produced it has signed the explainer and until a paper or note exists; the source registry hears "kernel-checked, not yet explained", not "solved", and Palomar, the registry of Lean-verified results, is told the fidelity grade in the record's own words. The network announces nothing. It keeps no leaderboard. It publishes its failures.

What machines bring, when people stay in the chain

A resolution of an Erdős problem in 2026 became an eight-author paper that generalised the method; a disproof in discrete geometry got a companion paper by nine people and was then improved by hand; a formal proof of Sendov's conjecture was digested by a mathematician from about ninety thousand lines to about fifteen thousand, and found to be, in his word, elementary. In each case the value was created after the certificate, by a person. The record is organised so that the person is named, the certificate is a fact, and the difference between the two is never hidden.

01

Listed only after a search

A curator searches the literature and records what was found. A problem found there is relabelled a known result.

02

Worked on only with a steward

A named mathematician commits to understand and write up whatever is produced. The rule that a problem without one would refuse work is announced and not yet enforced: today such a problem is published, says it needs a steward, and still accepts work.

03

Statement checked by a non-author

A statement is graded unsigned until someone who did not write the Lean signs that it means what the conjecture means; the signatures are counted and named.

04

Proved, then explained

A merged proof marks the problem proved and unexplained until a person signs the explainer and a paper or note exists.

Who runs this

The network is run by Michael Higgins. Write to michael.higgins.data@gmail.com, or connect on LinkedIn ↗. A bug, a question about a statement or a problem to propose belongs in the graph repository's issues ↗, where it is public and on the record.