This article reminds me of this: https://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf I especially like the Atiyah quote.
For those like me who have bookmarked this to read later but are curious what the Atiyah quote is: MINIO: How do you select a problem to study? ATIYAH: I think that presupposes an answer. I don’t think that’s the way I work at all. Some people may sit back and say, “I want to solve this problem” and they sit down and say, “How do I solve this problem?” I don’t. I just move around in the mathematical waters, thinking…
Thanks! I was feeling lazy. The context of the quote is a discussion of whether one solves problems to understand mathematics, or builds general theory (my paraphrasing) to be able to solve specific problems. I read Atiyah's response as "neither."