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

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

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

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 division, you could only do it in one place, Heidelberg. This makes sense, since in my theory with Vladimir Retakh and Robert Wilson, addition and multiplications are cheap, but division is expensive.

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.

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