... The approach of von Neumann and Connes to the use of non-commutative algebra in physics is naive, the situation is much more complicated.

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

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.

... The approach of von Neumann and Connes to the use of non-commutative algebra in physics is naive, the situation is much more complicated.

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.

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