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Matteo Capucci@mc@mathstodon.xyz (2026-09-20 18:30:16)
Grant Sanderson wrote a guest post on Tao's blog:
> If math is more than proof, we need to better celebrate the rest of it https://terrytao.wordpress.com/2026/09/18/if-math-is-more-than-proof-we-need-to-better-celebrate-the-rest-of-it/

It's really nice! My fav kind of essay about math's existential crisis are those the put the accent on the inadequacies of current mathematical institutions and socio-scientific practices (prize culture & big problem fetish).

Sanderson also mentions Chow's notion of an 'open exposition problem', which he defined as follows:
> Solving an open exposition problem means explaining a mathematical subject in a way that renders it totally perspicuous. Every step should be motivated and clear; ideally, students should feel that they could have arrived at the results themselves.

This reminds me of Leinster's extended definition of 'category theory', from one of my favourite essays
> https://golem.ph.utexas.edu/category/2010/03/a_perspective_on_higher_catego.html

Leinster doesn't give a tweetable definition of what the calls the 'second meaning' of category theory, so one might summarize it as 'leveraging abstraction to reach clarity'; or 'making the trivial trivially trivial', as some used to say.

After a couple of years in applied category theory, I started accepting that CT was unlikely to make me prove striking results in mature areas of math, and that we should really embrace it's *clarifying* power as the real value of the categorical approach. This means embracing it in teaching and in exposition, and hopefully one day even in papers and grant applications (current AI turmoil might have the effect of making this much much easier).
---Reply---
John Carlos Baez@johncarlosbaez@mathstodon.xyz (2026-09-20 19:28:04)
@mc - The focus on big prizes and big problems is strongest in the self-proclaimed upper echelons of mathematics.  Most of us working mathematicians have long ago decided not to work on those big problems, and don't have a chance of getting those big prizes.   Some working mathematicians admire and respect the upper echelons, others watch them with jaded cynicism or resentment - and still others mostly ignore them because they're having too much fun doing their own math!

It's interesting to see how the rise of LLM proofs is taken differently by different kinds of mathematicians.   But the media attention naturally focuses on people in the upper echelons, like Tsimerman, Tao and Gowers.   So it gets a warped view of what most mathematicians think.