admittedly… (1) is a reminder to myself too, as I’m giving a talk on Monday about the family of graphs that made me question my soundness-of-mind 🫠

3. “Novelty” does not imply mathematical significance, but if you’re enjoying the exploration, and remain open to critique, the time-spent is worthwhile.

I’m somewhat biased, but Richard Stanley’s undergraduate textbook on Algebraic Combinatorics is awesome! And of course, graph theory, in all “forms,” is beautiful as well!

Dropping a cool polytope for inspiration:

Of course! And sorry for getting dramatic at the end haha.

Discrete is an awesome area to start… still one of my favorite classes. Also, you might enjoy diving into some more combinatorics later on, given your background! :D

Also, from a fellow “dumb student,” self-confidence is somewhat necessary.

Remain humble, but know that success in math is not all measured by speed or “natural talent.” You have dedication, and the insight to ask mentors for advice — that makes you intelligent.

3. Don’t forget to engage with “recreational math.” Watch youtube videos on theorems and general ideas you’re curious about, and maintain curiosity!

1. Spend a long time on each chapter, even if you “feel like you already understand enough.” You should be able to reproduce the (shorter) example-proofs before moving on.

2. Work on math with others! Ask questions on forums, chat with peers. Remember, it’s never shameful to be lost/wrong.

Math student here — if you don’t have formal training in proof-writing, start there… and slowly. I recommend “The Book of Proof” by Richard Hammack for early exercises.

If you also/instead pick up a textbook on a topic you’re curious about, here’s how I’d go about reading it: