
If mathematics is the queen of science, this book explains why category theory is the queen of mathematics.
https://www.youtube.com/watch?v=ho7oagHeqNc
and in a similar vein I am enjoying her book: "How to Bake Pi".
Getting more into the technical side of things, Bartosz Milewski has good lessons in this playlist:
https://www.youtube.com/watch?v=I8LbkfSSR58&list=PLbgaMIhjbm...
A History of Pi - Petr Beckmann
Journey through Genius: The Great Theorems of Mathematics - William Dunham
How to Bake Pi - Eugenia Chang
These are all sort of 'pop-math' books -- that is, they're more intended to spark a joy & love for math than teach rigorous mathematics. Great Theorems and A History of Pi include a lot of history (edit to add: in addition to covering the math involved!) -- did you know some mathematicians in history would duel over their theorems? That theorems were a carefully guarded secret instead of something you shared?
Introduction to Graph Theory is specifically intended as an introduction to mathematics for 'the mathematically traumatized'.
In my opinion, after reading these, if you've sparked a joy for the puzzles and fun of mathematics, then I would then suggest branching out into more formal presentations of them relevant to your interests... it's much easier to slog through a book on abstract mathematics when you receive from enjoyment from the puzzles presented.
On the other hand, I am very much enjoying How to Bake Pi by Eugenia Cheng, which is a few levels down in difficulty.
I did find a couple of things quite refreshing in the article, though: (1) Wigner's essay is delightful and I'm glad it's seeing a wider audience. We should be reminded of it every time this conversation comes up, if only for its last paragraph. (2) The reference to the fact that Galileo proved that falling objects accelerate at the same rate, not by some experimental demonstration, but wholly within his mind---and it's a proof that any middle-schooler has no difficulty completely understanding. As a reminder that mathematics isn't symbols and rules, but a way of looking at problems (Eugenia Cheng's book, How to Bake Pi, is an excellent look at this way of thinking and approaching the world.). (3) It managed not to get bogged down in the whole pointless and hypocritical "what is math good for" instrumentality debate, that these sorts of questions tend to devolve into.
