Gowers on mathematics research and LLMs

Via a recent Bluesky post by Zach Wienersmith, a passage from Gowers on what it feels like to “do math” these days:

So what is the point of struggling with a difficult mathematics problem? One answer is that it can be very satisfying to solve a problem even if the answer is already known, but I don’t think that is a sufficient reason to spend several years of your life on this peculiar activity. A better answer is that by solving hard problems you get an insight into the problem-solving process itself, at least in your area of expertise, in a way that you simply don’t if all you do is read other people’s solutions. One consequence of this is that people who have themselves solved difficult problems are likely to be significantly better at using solving problems with the help of AI, just as very good coders are better at vibe coding than not such good coders, or people who have a solid grasp of how to do basic arithmetic are likely to be more skilled at using calculators (and especially at noticing when an answer feels off). Mathematics is a highly transferable skill, and that applies to research-level mathematics as well. By doing research in mathematics, you may not get the same rewards as your equivalents a generation ago, but there is a good chance that you will be equipping yourself very well for the world we are about to experience.

One of the first things I did, first day I bought a Claude Pro subscription, was to ask for a detailed, academic-style treatment of some random-ass musings I’d done a few years back. I’ve looked over it a few times now, and I like it. There’s a bit more to add, and then I’ll also be posting a cleaned copy here as a “noprint” (since all I did was ask leading questions, and admonish a certain tone of voice).

How does one cite a noprint?