When I was a young naive undergraduate student, I took some smarter and older grad student’s “advice” that the “best” place to learn field theory and string theory was Polyakov’s “gauge fields and strings” book. At the time I didn’t know any better, and was very much clueless about the field theory and string literature. I know now this smarter and older grad student was just joking around, and was trying to scare me away from theoretical physics in a “tongue and cheek” manner at the time. The last time I saw him, he joked about it and couldn’t believe I took his “advice” as if it was a “gopel truth”. Turns out that trying to learn introductory field and string theory from Polyakov’s book, would be like trying to learn introductory quantum mechanics from Dirac’s book. Both Polyakov and Dirac’s books are really nice books to read once you know the subject well, but are difficult to learn from if you don’t have any previous knowledge of the subjects.

I ended up wasting a whole summer trying to figure out the calculations in Polyakov’s book, where I spent most of my time in the library trying to figure out his papers that were referenced in his book. After that I still had a hard time figuring out Green, Schwarz, and Witten’s books on superstring theory. Somehow I was able to reproduce most of the calculations in Polyakov and the Green, Schwarz, and Witten books, but I was still relatively clueless as to what the physical picture underneath all the mathematics was about. At the time I think took the Feynman idea of “shut up and calculate” mentality to the extreme. (I don’t know if the quote was originally Feynman’s, but over the years it seems to be attributed to him like an “urban legand”.)

The talk was intended for an audience of mathematicians and had the presumptious title “Physicist’s view of mathematics”. P started out with the thesis that math history has had three phases, characterized by the slogans

“Things are numbers” (5th century BC)
“Things are topological invariants” (20th century AD)
“Things are words” (21st century AD)

By topological invariants he means things which do not change at all under small deformations (I might have preferred the word “universal”), and gave three examples from physics:

1. The quantum Hall effect, where conductivity is given by sigma_xy = n e^2/hbar, n integer.

2. Instantons and their connection to the Atiyah-Singer index theorem and Donaldson’s invariants.

3. Critical exponents in the 2D Ising model and minimal models. With Schramm, Smirnov and Werner in the audience, I was somewhat surprised that he didn’t make the very timely connection between CFT and SLE at this point.

The “things are words” part turned out to be about his recent work on the connection between some 4D Yang-Mills theory in loop variables and some theory of random surfaces in 5D. This seems eminently plausible; if you take the intersection between a generic surface in 5D and a 4D hyperplane you’ll end up with a loop in 4D, which may perhaps be a Wilson loop of some Y-M theory.

Alas, the model stood by itself, without any reference to 10D or 26D or Calabi-Yau, even as a motivation. It seems like the smart string theorists are starting to pretend that those things never happened and go back to study 4D field theory again. It is difficult to be critical about using an extra dimension as a technical trick to study Y-M theory in 4D, although I got the impression that P’s model isn’t the physical Y-M theory of the standard model. Anyway, I missed the details because P didn’t give any due to time limitations.

At this point one may wonder where the “things are words” slogan enters. The point, if there is any, is that correlation functions can be regarded as words, with elementary fields and their derivatives being letters. Natural enough, but surely people knew about OPEs before the 21st century…

In the question section it became clear that P didn’t think very highly of Wolfram’s New Kind of Science. But then again, who does?

http://www.xs4all.nl/~rpronk/conference.htm

With the conference proceedings detailed here:

http://www.j-walk.com/other/conf/summary.htm

For those with a rightious sense of political correctness who don’t appreciate the humour of these links, that will quickly disappear if (like me) you have to delete 20-30 of these damn things virtually every day! At any rate, physicists could perhaps adopt the conference advice given on “uppercase letters” in order to make their preprints stand out in the hep archives:)