Alan Baker: Transcendental Number Theory (1975)

Edition: Cambridge University Press, 1998
Review number: 75

This book has been the standard survey of the theory of transcendental numbers for some time now - the first edition was published in the mid-seventies. The author is a prominent researcher in the field, and several chapters draw heavily on his own work.

My own mathematics training is in areas other than number theory, and I found large parts of the book difficult to follow. I have a copy of the basic number theory textbook written by Baker, A Concise Introduction to Number Theory, and I would have expected some discussion of concepts used in Transcendental Number Theory but absent from the more basic book.

The other problem is with Baker's writing style, and it is shared with An Introduction to Number Theory. His mathematics is extremely condensed in style, and it is often difficult to work out what is going on. In a survey this is less of a problem than in a textbook, but I still felt I would have found it easier to follow if I were attending a course of lectures based around the book at the same time as reading it.