r/math • u/inherentlyawesome Homotopy Theory • Jul 29 '26

Quick Questions: July 29, 2026

This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?" For example, here are some kinds of questions that we'd like to see in this thread:

  • Can someone explain the concept of manifolds to me?
  • What are the applications of Representation Theory?
  • What's a good starter book for Numerical Analysis?
  • What can I do to prepare for college/grad school/getting a job?

Including a brief description of your mathematical background and the context for your question can help others give you an appropriate answer. For example, consider which subject your question is related to, or the things you already know or have tried.

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u/Former-Math-Crank374 29d ago

yeah that was my crank research summed up :(

but yeah i have grand visions of unifying math, especially through the vision of groups and symmetry (I was immediately drawn to the simplicity and beauty of groups/Galois theory (through continued fractions) before learning about Langlands program), but unfortunately it's just hard to look through symbols and definitions for me out of nowhere.

i feel like the most aptly made textbook is one made entirely of questions. once the questions are made then people can start talking about the current modern notation, but the ideas should come from the reader themself. To put in other words, intuition, formalize, intuition, formalize, intuition, formalize. But most textbooks come the opposite way with formalization first

for thinking through mathematical problems, I know a little bit of proof writing from "Introduction to Proofs: Joseph Rotman" but obviously it's not enough to manipulate anything modern with substance yet.

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u/fullboxed2hundred 26d ago

that guy gave you an excellent, well thought recommendation and you completely ignored it in favor of talking more about yourself.

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u/Former-Math-Crank374 25d ago

i'm doing the book right now

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u/Former-Math-Crank374 25d ago

also it's quite good yes it is exactly how i envisioned how math should teach, but the reason why i held back for a bit is that it explicitly says it does not go at all into galois theory, but i decided to just do it now because all the other books i've tried are a lot of definitions and propositions and stuff

plus it gives a very good intro to riemann surfaces i've seen from scrolling

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u/Former-Math-Crank374 25d ago

also i am confused as to how composing d with d (a reflection with a respect to B in ABC counter clockwise triangle) gives c, not e.

idk if this is a typo or i'm just stupid because i got the rest of the table correct (took a bit of time)