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Jacob Zelko (Jan 03 2025 at 13:13):Hi folks,
It is an exciting place to be situated in these days: I have been able to successfully complete a few graduate maths courses in algebra, analysis, category theory, and beyond. It is quite fun to discuss with other math folks ideas, approaches, and so forth. Along the way, I've also been getting further exposure to philosophical thought that exists across the math spectrum and so am curious: does anyone have any suggested resources (books, blogs, discussions, etc.) for deepening one's own philosophy of mathematics?
I've been introduced by Stewart Shapiro's Thinking about Mathematics which feels like a nice survey of thought. Additionally, looking through Benacerraf's Mathematical Truth to get a stronger sense for ongoing discussions. Particularly, what interests me most at this early stage, from a philosophical perspective, is centered around the broad and vague question of "what does mathematics represent?" especially in relation to phenomena outside of mathematics. To give a feeling of what "relations" I mean here, as a sort of guidepost, I really like thinking about the John Baez quote, "every sufficiently good analogy is yearning to become a functor."
Morgan Rogers (he/him) (Jan 03 2025 at 13:30):Have you read any philosophical logic? The focus is different from a mathematical/"formalist" approach to logic, so there are some interesting comparisons to be made.
Spencer Breiner (Jan 03 2025 at 14:01):I like a thread of work that goes under the heading philosophy of mathematical practice. There is a book with that title (https://doi.org/10.1093/acprof:oso/9780199296453.001.0001), but also other work in the same area
Peva Blanchard (Jan 03 2025 at 17:11):I added very recently the following paper on my list. It is about the unreasonable ineffectiveness of mathematics in biology. I haven't read it yet, but the title is funny, and could match what you are looking for.
John Baez (Jan 03 2025 at 17:16):I recommend Saunders Mac Lane's Mathematics: Form and Function. He wasn't just one of the founders of category theory: he was a powerful mathematician with a broad and clear outlook on mathematics. This book is quite readable, but full of ideas.
fosco (Jan 03 2025 at 17:33):John Baez said:
I recommend Saunders Mac Lane's Mathematics: Form and Function. He wasn't just one of the founders of mathematics: he was a powerful mathematician with a broad and clear outlook on mathematics. This book is quite readable, but full of ideas.
I appreciate the Freudian slip that before Mac Lane / before category theory mathematics didn't have a foundation....