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.

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.

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.

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

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.

... 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.