Grant Sanderson · 2026-09-18 · notable
Grant Sanderson — give math credit for explaining, not just proving
Grant Sanderson argues mathematics should give academic credit to "motivated explanations" — work showing how you would have found a result — now that AI can produce proofs without understanding. The guest post ran on Terence Tao's blog.
Grant Sanderson wants open exposition problems treated as seriously as open research problems.
What is it?
"If math is more than proof, we need to better celebrate the rest of it" is a guest post Grant Sanderson published on Terence Tao's blog on 18 September 2026. Sanderson proposes defining a category of work called a "motivated explanation" and giving it academic credit similar to what solving an open problem has had historically. His starting point is that proofs were always a proxy for human understanding, and machines can now generate proofs without it.
How does it work?
A motivated explanation is defined by where the definitions sit. In a proof they come first; in a motivated explanation they arrive in the middle, once the problem they address has been made clear, and an idea that is not quite right but has relatable origins is allowed. Sanderson admits the test is not binary — "there will never be Lean for motivated explanations" — and offers his own working question instead: for each new idea, is it clear where that idea came from? He points to Part IV of the Princeton Companion to Mathematics, Bill Thurston's essay "On Proof and Progress in Mathematics", the sphere-eversion film Outside In, and Timothy Chow's "A beginner's guide to forcing" as work that already does this.
Why does it matter?
Every AI-generated proof is "born an unsolved exposition problem", the post argues, and the next few years will bring a flood of them. The worked example is Erdős Problem 1196: Liam Price got a solution out of GPT-5.4 Pro in April 2026, but understanding only moved once Nat Sothanaphan and Jared Lichtman turned it into a human-readable proof and a May paper by Alexeev, Lichtman, Tao and others expanded the key idea to neighbouring problems. Sanderson's practical suggestions include PhD deliverables presented as talks rather than write-ups, a Millennium-Prize-style list of open exposition problems, and more hiring and tenure weight for textbooks and expositions.
Who is it for?
mathematicians and anyone watching AI move into proof