Ask HN: Best resources to gain math intuition?

For a small buffet of abstract math topics (with lots of exposition putting ideas into historical context and an emphasis on building geometric intuition) try Courant & Robbins "What is Mathematics?". Covers number theory, number systems, geometry, topology, optimization, algebra, and knots, among others. You could also play around with branches of math like Knot and Braid Theory, which are interesting in their own right, give insight into lots of different branches of math, and many interesting problems are still accessible to lay people. Number theory is also like this

I think it can also be helpful to learn some things about the history of math and the historical context that different ideas came from. Here's a nice example covering complex numbers https://www.youtube.com/watch?v=T647CGsuOVU

Maybe tangential to your ends, but the Crest of the Peacock is a nice book on non-European mathematical traditions, which provides some insight into how the process of establishing and validating mathematical knowledge works in other cultures.

You might try books written by physicists or that are about mathematical physics (an author to look out for depending on your level is VI Arnold), since arguments will be of a more geometric or physical nature and appeal more to intuition. Stillwell is another author (not a physicist) that tends to write books that give context and geometric intuition

You might like playing around with Pinter & Humphreys for Algebra, or Jänich for Topology (fantastic book for building intuition around topology).

I'm interested in building up math intuition too. I'm engaging with math very slowly and just as a hobby, but part of what got me interested was encountering resources that are unreasonably effective at building intuition.

A common theme I have noticed is whatever it is, getting a geometric understanding of it aids intuition significantly. Others have mentioned the 3Blue1Brown videos. They are an excellent example of this.

These HN threads always bear out great resources and I've made note of (and acquired) a few of these, so I'll list them here.

Burn Maths Class - https://www.goodreads.com/book/show/26195956-burn-math-class

Book of Proof - https://www.people.vcu.edu/~rhammack/BookOfProof/

The Topology Of Numbers (number theory)- http://pi.math.cornell.edu/~hatcher/TN/TNpage.html

The Evolution of Trust (game theory) - https://ncase.me/trust/

Visual Information Theory - https://colah.github.io/posts/2015-09-Visual-Information/

Information Theory For Smarties - http://tuvalu.santafe.edu/~simon/it.pdf

Abstract Algebra - https://www.youtube.com/playlist?list=PLi01XoE8jYoi3SgnnGorR...

Algebra Cheatsheet - https://argumatronic.com/posts/2019-06-21-algebra-cheatsheet...

Control Theory Basics - https://www.youtube.com/user/ControlLectures/playlists

Thanks I’ve enjoyed your work especially the one on imaginary numbers

I second this, with emphasis. His videos cover the vast majority of topics at the intersection of math and hn. He has written custom software for the creation of the animations.

It’s on another level imo.

I've been trying to penetrate algebraic topology for a bit now (learning barcodes and such). Any suggestions on papers you think are particularly good?