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Can I choose all of the above? I'm finishing my second year of grad school, so I should be transitioning roughly from rigorous to post rigorous. Okay, that's probably true, but only in the areas of math I know best and use frequently. In other areas, I've never moved past the rigor stage; in yet others I'm not even that far along.

I'm pretty comfortable with probability and optimization, which is my day-to-day. I will probably never be better at topology than I was when finishing my undergrad degree. And in my one brush with differential geometry, I struggled to reach the rigor.

And even then it's more complicated, because human intuition is notoriously bad in probability.



I'd say pick the max over all subfields. I myself am about to get a PhD in mathematics yet I have an irrational fear of differential equations.




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