innerproduct

Yitang Zhang's story is truly an inspiration. It shows us that there are other ways of being a mathematician than being on the faculty of a research university. Of course, most of us who choose to do math in this way (or in the conventional way), will not have the level of success that Prof. Zhang has achieved.

All I need now is a job where I can have a few quality hours every day to devote to doing mathematics. (And open/free access to research papers.)

Prof. Frenkel, I have a couple of questions:

1. Have you read Cédric Villani's book "Birth of a Theorem: A Mathematical Adventure"? If so, what do you think of it?

2. How many languages do you speak? What is the last (natural) language that you have learned and at what age did you learn it?

Thanks for doing this AMA. By the way, I really enjoyed your contributions to the 1+2+3+... = -1/12 debate/controversy.

Disclaimer: I know a fair bit of graduate level mathematics but I am a physics novice. And this question is vague and poorly worded because I am deeply confused about it myself:

What kind of a mathematical object is the universe ("spacetime"?) of General Relativity?

Presumably it's a 4 dimensional manifold (perhaps with some singularities) but it's also seen as an object, or a 3-manifold, that's evolving in time according to some flow equations. What I want is an intrinsic description of the universe. In particular, this description would not treat time any differently than the three spatial dimensions.

I started thinking about this question because I could not find a satisfactory (intrinsic) definition of Schwarzschild radius.

I'll go ahead and ask a silly question: what's your favorite function?

Mine is sin(pi/x) * e^-1/x2 -- can you guess why? But I also like e^x.