Step 34 of 37
You narrow to one area. Sample widely before you commit.
Main fields
- Algebraic geometry
- Number theory
- Analysis and partial differential equations
- Geometry and topology
- Probability and stochastic processes
- Combinatorics
- Logic and set theory
- Applied and computational mathematics
- Mathematical physics
Learn from
- The Princeton Companion to Mathematics, for a survey
- Then a gateway text such as Hartshorne (algebraic geometry), Evans (partial differential equations), or Durrett (probability)
Move on when
You can name open problems that interest you and who works on them.