Philosophy of Mathematics and Natural Science

Hermann Weyl was certainly an excellent mathematician, and the work he did on gauge theories (although they proved useless for uniting gravitational and electromagnetic forces) paid off much later.

However, I didn't get much insight from this book (I read the original version, from a library). He doesn't give a lot of detail about the mathematical or physical ideas, the book is really about the philosophy of these topics. It's just not as inspiring as I would have expected.

Herman Weyl (1885-1955) has been described by Roger Penrose as the most influential mathematician who worked entirely in the 20th century. Many of his books are in print but not this one; Atheneum did a very small font reprint in the 1960's and even that is not available. Yet this book, which I have to read in a library copy, is a treasure. Weyl wrote it for a German-language encyclopedia in the 1920's and revised it in the late '40's for an English translation. It gives brief and clear accounts of Weyl's unique approaches to general relativity and quantum mechanics. He was way ahead of his time in recognizing the importance of symmetries and in taking a sophisticated geometric approach. He was particularly astute in noting important features that unified the different branches of physics (notably in the case of gauge invariance which he doesn't mention much here). His analysis of the problem of the ether is particularly lucid and stimulating as his discussion of the relationship between kinematics and dynamics. He also gives an account of the foundations of mathematics up to the discoveries of Godel. Weyl regarded physics and mathematics as essentially one, both being parts of the study of nature and thought that the same philosophical principles underlay both. He was an unusually openminded scholar who was quick to abandon an innovative but less successful approach for a better one. I don't think he would have fit in with a popular late 20th century style of doing physics that scorned philosophy, and insisted that the current generation was saying the last word on basic physical theory. Maybe that's why this beautiful, intelligent and very readable book was allowed to fall out of print. Its time to bring it back!