In my recent ICM talk in https://teorth.github.io/tao-web/slides/age-of-ai-icm-2026.pdf, I highlighted the five stages of proof development and maturation: proof generation, proof verification, proof exposition, proof publication, and proof canonicalization. This developmental cycle is somewhat analogous to the developmental cycle of a living being, from an infant, to a child, to an adolescent, and finally to an adult; cf. Cedric Villani's popular book "Birth of a Theorem". As mentioned in those slides, it is the final "adult" stage of having canonical, textbook proofs that is the most valuable for applications (and for generating further proof methods).

To continue this analogy, the authors of a proof have traditionally played a role somewhat similar to that of parents or caretakers, first bringing a proof into the world, and then investing significant effort into growing and improving that proof in various dimensions, such as readability, conceptual clarity, or insightfulness. The acclaim that mathematicians have historically received for creating a difficult new proof is based in part on this expectation of continued investment in the development of that proof, and its surrounding ideas and theory. (1/2)