Terence Tao proposes assigning priority in mathematics based on a complete set of materials
Terence Tao proposes assigning priority in mathematics based on a complete set of materials
On August 6, mathematician Terence Tao described a rule for results produced in the age of AI. Priority should go to the first person to publish both a manuscript and an explanation that other mathematicians can understand. Once formal verification becomes standard practice, it should also be included. Tao proposes treating the package as released when the last of these materials is ready.
When Tao was a graduate student, priority was usually determined by the publication date of a journal article. Later, a public timestamp in the open manuscript repository arXiv allowed authors to establish when their work became available and reduced the risk that a reviewer might publish a similar result first. Tao writes that AI is accelerating this race. Authors can announce an answer on social media before it has been checked or clearly explained, allowing them to secure an earlier timestamp than others.
Previously, a single paper recorded the result, gave colleagues a text they could check, explained the reasoning, and provided a lasting public record of the work. Tao proposes distributing these functions across several materials. The manuscript records the result. A log of the dialogue with AI can show how the solution was found. Lean, a specialized language that allows a computer to check the logical steps of a proof, verifies its formal representation. A lecture or video explains the idea to people.
“Priority would then be assigned to whoever first presented the complete set of materials,” Tao writes.
An early announcement can tell colleagues that the work is still in progress and help competing groups combine their efforts or arrange simultaneous publication. Tao also allows for a cryptographic hash, a computed fingerprint of a file that can later be used to confirm whether the published file matches the version recorded earlier. Under his proposal, priority goes to the first person to release a package that enables another mathematician to check the proof and understand the reasoning.
“The social norm would be to wait until all of these tasks had reached at least the preprint stage,” Tao writes.
In a July lecture, Tao said that AI is increasing the volume of proofs, while mathematicians still have to determine what those proofs mean and how they relate to existing theory. In his August series, he proposed a rule: priority should be tied to the point when the next mathematician can use the work.