Hehe.. I am tempted.
As said at Harvard: "In theory, a future research mathematician should be able to go through all three stages with the help of only a good library."
https://www.math.harvard.edu/graduate/guide-to-graduate-study/
Good mathematics art is so underrated.
Credit to the K-theory YouTube channel.
https://www.youtube.com/channel/UCRXC6M65qiFlHaXGDNC--VA
I wonder how analysis made it into mathematics. Now there is just a schism in the doctrine in a lot of places.
I think it is a "does it 'solve' problems I care about?” kind of thing. I think it is the foundation for validating inferences in math. The choice axiom went from, being considered problematic, to being mostly accepted because new problems from it did not hurt old problems.
I am pretty curious about how to use automated reasoning systems to help discover new things, use and verify old ideas, and generally make my life easier.
Current events I try to keep up on
- Math Logic community (The Journal of Symbolic Logic)
- Statistics community (JASML, AoS)
- Algebra community (JoA, JoAG, JoPaAA, SIGSAM)
- Formal Methods community (CAV/TACAS)
Passing the learning curve up to current events
- Abstract Algebra (Dummit, Foote)
- Commutative Algebra (Eisenbud)
- Algebraic Geometry (Hartshorne)
- Mathematical Logic (Mendelson)
- Model Theory (Marker)