Thought of the day

"Education is the process of realizing your own ignorance, then proceeding to do something about it."

I used to think I had a pretty good understanding of things like mathematics and physics, but as I have progressed in my studies, I have discovered that I did not understand things as well as I thought I did. Sometimes I have discovered that I have been doing things (solving partial differential equations, for example) without realizing it. Sometimes I have suddenly discovered that there were entire subfields that I didn't even know existed (abstract algebra, for example). Other times I have discovered that subfields were about completely different things than I thought (topology, for example). Yet other times I have realized that two distinct subfields obey the same mathematical equations (analytical mechanics and electrical circuits, for example). And there are yet other things that I should be able to do, but honestly am not comfortable with (solve a second-order ordinary differential equation, for example). I am working on all of these things, but I also realize that it is impossible to be an expert in everything.