That spring day in his office, reflecting on his career so far, Tao told me that his view of mathematics has utterly changed since childhood.Gareth CookWhen I was growing up, I knew I wanted to be a mathematician, but I had no idea what that entailed, he said in a lilting Australian accent.I sort of imagined a committee would hand me problems to solve or something.But it turned out that the work of real mathematicians bears little resemblance to the manipulations and memorization of the math student. Even those who experience great success through their college years may turn out not to have what it takes. The ancient art of mathematics, Tao has discovered, does not reward speed so much as patience, cunning and, perhaps most surprising of all, the sort of gift for collaboration and improvisation that characterizes the best jazz musicians. Tao now believes that his younger self, the prodigy who wowed the math world, wasn’t truly doing math at all.It’s as if your only experience with music were practicing scales or learning music theory,he said, looking into light pouring from his window.I didn’t learn the deeper meaning of the subject until much later.
I would say this applies to many other fields beside mathematics as well, especially where creative thinking is involved: the theory learned as a student is just the tip of the iceberg; only after you start practicing you get a real sense of the work involved and it’s often very different than previous expectations.
Related: an animation of the relation between human right and left brain hemispheres and how their roles impact our understanding of the world.