What's this about?
A paper on AI's role in mathematics, whose Terence Tao quotations did most of the travelling. On AI-generated proofs: "the writing very often dwells at length on trivialities while passing briefly through — or even actively obscuring — the most interesting and novel portions of the argument." And his proposed publication standard: if the authors cannot convincingly demonstrate they can give a clear, expert-level talk on their own results — correct and properly attributed — the result should not be published. Tao's broader claim is that explanation and understanding become the new bottleneck in mathematical research.
What exactly is the problem with a correct proof nobody understands?
Mathematics doesn't only certify statements as true; it produces understanding that gets reused. A proof's value is partly the techniques it introduces and the connections it exposes, which is why mathematicians care how a result is proved rather than only whether it is. A machine-generated proof that is verifiably correct but opaque delivers the certificate without the understanding — you learn that the statement holds, and nothing transferable. Tao's talk test is an elegant operationalization: if you can't explain your own result to experts, you probably don't have the understanding that made it worth publishing.
What's the community saying?
- Tao's rule of thumb was the thread's centrepiece, with several noting it applies just as well to software: if you can't explain the change you're shipping, you shouldn't ship it.
- The most-quoted observation generalizes beyond mathematics — AI writing dwelling on trivialities while rushing the novel part is a complaint people recognized from code reviews and documentation.
- The sharpest dissent challenges the premise. Understanding was the bottleneck when only humans could make progress; if humans stop being necessary for progress, is it still the bottleneck, or just something we want?
- The practical constraint nobody expected: a commenter noted that with a fixed token budget — say $10,000 — choosing *which* problems to attack becomes the real skill, because you cannot afford to point it at everything.
- "If the title had said 'in the age of LLMs' I might have given it a try" — the persistent objection to "AI" as a category label.