One of the reasons we don't do as well as we should is that we are all over-taught.

People (or students) do not have shortcomings, only uniquenesses. The goal of a good teacher is to turn these uniquenesses into advantages.

My seminar is for highschool students, decent undergraduates, bright graduates, and outstanding professors.

Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.

I used to say: "Everything is Representation Theory". Now I say: "Nothing is Representation Theory".

The older I get, the more I believe that at the bottom of most deep mathematical problems there is a combinatorial problem.

They have the idea that non-commutative algebra should remind one of commutative algebra, but the former is more sophisticated. I believe that non-commutative algebra is just as simple, but it is different.