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.

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

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.

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

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.

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