And then the mathematics that happened around ~1940.. Kolmogorov, Fisher, Poincaré, Gödel, Von Neumann, Church, Turing...
Just crazy.
To drop a few names, we had Grothendieck, Serre, Deligne, Wiles, Illusie, (the elder) Artin ... and it's continued to this day. Wiles' proof of FLT built upon this beautiful synthesis of ideas, for example.
The first is the stuff you do in school. Always good to have context, which sadly there's little time for.
The second is fundamentals and computing stuff, and stats. There's a good chance you'll have to use a computer to calculate things over large datasets sometime in your life.
Crypto is interesting as well.
1.) What, if any, of mathematics has been invented concurrently in different regions (say within 10-20 years) without collaboration or knowledge of other derived work?
2.) To what extent is the rate of mathematical development associated with war or advances in knowledge sharing? Be it radio, printing press, persuing weapons development, crypto, or mass migration (eg post ww2).
I think 1.) comes about via natural scientific progress. Some mathematical ideas are dependent on the right set of tools being invented or environmental necessity. How many people independently came up with ballastics equations once soldiers starting flinging big rocks at each other?
The 2.) Question is very interesting to me. What is the network effect of mathematicians sharing ideas? What happens when the 10 smartest mathematicians in the world end up all working at the same elite university? Why isnt this just accelerating mathematical progress in the 21st century? Are breakthroughs harder now? Does the internet and peer review journals provide too much noise? Or is it simply that progress is so fast now we don't think of these things as extraordinary ?