Illustration beyond Proof

Posted 11 October 2026 on Tao’s blog. Tao’s note: “This is a guest post by Kate Stange and Edmund Harriss. This blog post was initially written in a different file format and converted using AI.” The authors report on a January 2026 workshop at the Institut Henri Poincaré on what it would mean “for an illustration to be rigorous” and present their article ‘Mathematical Illustration: Proof, Intuition and AI’ (arXiv 2610.02655), which they say is “now accepted in the Notices”. They place it next to earlier pieces by Bryna Kra, De Toffoli and Duede, Matilde Marcolli and Grant Sanderson. On LLMs: their code generation makes illustration more accessible, but “by vibecoding, we are now two steps from knowledge”. On “digestion” of machine proofs they cite Chair44: prompted by Ioannis Tsiokos, GPT-6 Astra found the first three-dimensional aperiodic monotile (61-page paper, arXiv 2609.19214), and Chaim Goodman-Strauss distilled the argument into eight pages (arXiv 2609.24779) built around a diagram. They propose calling an illustration’s “affordances” the properties that a proof certifies as accurate, and borrow the art-school “crit” as a way to assess illustrations. They ask for support for existing work (Illustrating Mathematics, Geometry Labs United, the philosophy of mathematical practice). The page had 6 comments when read on 2026-10-13.