8th
Help!
I want to start figuring out what area of math to study. I’m not sure if any mathematicians read me here, but if they do I’d love to hear about how you chose what to write your PhD thesis in and about what it’s like to study what you study.
In the absense of any grown-up mathematicians, maybe I can just use this blog to collect my thoughts. Here are some vague ideas around what I’d like to study:
1. I want it all! Specifically I don’t want to choose between being “pure” and “applied”. I want to prove theorems of exceptional beauty and have those theorems turn into astronaut dinosaur robot-cheetahs that run revolutionary preschools.
2. As far as I can tell, I’m not so much into differential equations. I might not be into analysis at all, really, but it’s too early to make that call. Certainly since applied math involving diff Eqs seems to grow on trees, I need more help finding applications from other fields.
3. Topology seems pretty cool jus’ sayin’.
4. I always like number theory too. And group theory.
5. But really that’s just a list of the things I’ve studied the most; I could probably like anything. So it’d be best to decide to like something that’s being studied by a really smart, dynamic professor at the U of M who would be a good mentor for me.
6. I think I like topology because I like using my geometric and algebraic intuitions in concert. I like seeing the same thing multiple ways, or seeing how different things are really the same. Making connections between two apparently different structures and using those connections to tell you more about each. Category theory just freakin’ delights me.
Okay that’s enough. Everyone tell me about applied topology. Or applied anything other than Diff Eqs. Also the application has to be something I’d actually care about helping to create; not weapons or stock portfolios.
