I just finished reading the relatively new book by S. T. Yau (Field’s Medalist) and Steve Nadis “The Shape of Inner Space: String Theory and the Geometry of the Universe’s Hidden Dimensions” (see here).

I got my Ph. D in theoretical particle physics, back when string theory was just taking off, and have been trying to study it a bit since then, just for the sake of curiosity. Part of the basis of string theory is that there are tiny hidden dimensions that we can’t see, and that these have to be curled up in a particular way for the theory to work. The Calabi-Yau manifolds that the book explains are the best method of curling up these hidden dimensions.

Yau, the first author, did some work in the 70’s to confirm a conjecture of Eugenio Calabi, that manifolds with certain properties (that I won’t go into here) could actually be constructed, and it turned out that these were just the thing needed for string theory when its first revolution occurred in the mid 80’s. Since then there have been many developments in both math and physics centered around the geometry of Calabi-Yau’s. The book does an excellent job of telling this story, with enough human interest added to make for a very compelling story. In addition, the status of string theory as a barely, if at all, tested or testable theory is not overlooked. I particularly appreciated the even-handedness of the arguments.

The one thing I thought could be better was the end notes. As someone with a fair bit of physics and mathematics training, I would like to have seen more references to the original literature. (There are a few.) Anyway, with enough searching on the Internet I’ll probably be able to find the references I want.

This is one of the best books of the genre “make the complex math understandable to the rest of humanity.” Most of them are too dumbed-down; here, the authors went to a lot of trouble to give good pedagogical explanations.

On a side note, I knew a student of Yau’s when I was a grad student at Princeton. He will remain nameless, as all he ever did was play foosball!