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 - Algebra community (JoA, JoAG, JoPaAA, SIGSAM) - Math Logic community (The Journal of Symbolic Logic) - PL community (POPL/PLDI/OOPSLA) - 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)
Extra context and fun things - Process Metaphysics (Rescher) - Mathematics Without Foundations (Putnam) - History of Abstract Algebra (Grey) - History of Algebraic Geometry (Dieudonne)