A seminar course that I took as a part of my physics studies
has taught me probably more than any other course. The
professor who led the course was quite smart, and known for asking tough
questions. And I picked a pretty tough subject,
quantum gravity.
I wasn't very familiar with that subject, but I thought I had enough background
to be able to learn it sufficiently well in three months. And I
thought that I'd do a kind of overview about it.
Now, already when
preparing the speech I started thinking about all the kinds of questions
that the professor and other students could ask about this, and I
noticed that I just didn't understand this as well as I thought,
It was very good for me, I noticed that I studied the subject
much more effectively than I would have if I would have been just
browsing the book randomly. For three months, I spent
quite a lot of time every now and then on my presentation,
and I had a lot of fun preparing it. But when I finally gave the speech,
I ended up talking two hours on something I had thought I could cover
in half an hour, and the speech was still too sketchy and messy, although not
a complete disaster.
So I learned that..You should never be too quick to assume that you understand
something! When you can read an advanced physics / mathematics / whatever
book once, and then immediately give a good speech about the subject to a
smart audience, _then_ you can say you are a genius! The
really advanced math / physics books often don't have any exercises,
because the authors assume that you already know how to make exercises for yourself.
Well, my second seminar presentation, about quantum computers went better.. :)