Physicist Freeman Dyson once observed that there are two types of mathematicians: birds -- those who fly high, enjoy the big picture, and look for unifying concepts -- and frogs -- those who dwell on the ground, find beauty in the scenery close by, and enjoy the details.
Of course, both vantage points are essential to mathematical progress, and
I often tend to think of myself as more of a bird.
(I'm, uh, bird-brained?)
Well one day I complained to my advisor, John Terilla -- you can see him doing cool math in that video above! -- about one of my classes which at the time felt a bit froggy:
Me: I'm having a hard time enjoying this class. I don't want to do a bunch of detailed computations on these objects. I'd rather spend my time learning category theory. I want to soar high and study the full landscape!
John: Well, yes, the sky is nice. But the ground -- and the ocean -- is nice, too. In fact, the best place to be is where the sky and the ocean meet, where the tips of the waves turn white.
That's the only place where you can go surfing.
That's where you want to be.
I think I've a new respect for the little details.
Let's go surfing!