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

... 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 life may be encapsulated by one of Graham Greene's "entertainments" titles: 'Loser Takes All'. Since I was thrown out of highschool for political reasons, I was free to study on my own and develop my own ways of thinking.

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.

If you understand something, you understand that it is obvious.

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

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