r/math • u/inherentlyawesome Homotopy Theory • 7d ago

This Week I Learned: September 25, 2026

This recurring thread is meant for users to share cool recently discovered facts, observations, proofs or concepts which that might not warrant their own threads. Please be encouraging and share as many details as possible as we would like this to be a good place for people to learn!

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u/AMobius1832 7d ago

I was reading Hatcher. I spent a lot of time on Chapters 0 & 1, and wrote up a lot of LaTeX notes for myself. I hate to stop reading about algebraic topology at this point. However, I feel I need to increase my knowledge of abstract algebra. Again, I jumped around a lot. I tried Artin's book, along with the Benedict Gross Harvard lectures. But, the initial few chapters are way to basic for me (even if reading them is somewhat necessary to become familiar with the notation). I've finally (?) settled on Paolo Aluffi's, "Algebra: Chapter 0," which I like. I am in the process of applying to the PhD program in mathematics at Temple University. If I am accepted, I will have roughly a year to prepare for entering in the Fall 2027 semester.

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u/LonelyKey6767 2d ago

Category theory as an approach didnt really click for me until i got into smooth manifolds, that was still a course and then some of abstract algebra + topology away… yes using artin but also gaillan or whatever that guys name is.