I went to a talk yesterday given by an eminent mathematician. He spoke on two related topics, one of which I listened to avidly, and the other I ended up completely tuning out.
From the perspective of the speaker the two topics were strongly related to each other. Yet from my perspective they couldn’t have been more different.
The difference was that for the topic I liked, I could form a geometric model in my head of the fundamental argument. Once I saw this geometry, everything became intuitive. I could play with it in my head, test the ideas for myself, and try out variations of his argument.
For the other topic, as far as I could tell, there was no geometric intuition — the arguments seemed purely symbolic. Intellectually, I could see how it might be interesting, but emotionally I felt no connection.
I guess it’s a good thing I’m in the field of computer graphics. 🙂