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

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

In the Middle Age, in Germany, if you wanted to learn addition and multiplication, you could go to any university. But if you wanted to learn divisio….

They have the idea that non-commutative algebra should remind one of commutative algebra, but the former is more sophisticated. I believe that non-co….

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 ….

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

Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only o….

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

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

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

People think they don’t understand math, but it’s all about how you explain it to them. If you ask a drunkard what number is larger, 2/3 or 3/5, he w….

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