A Tour of the Calculus, David Berlinski (ISBN 978-0-679-74788-8, Vintage Books)

A Tour of the Calculus is a strange and unique book. According to text on the back it is likely to become a classic as Gödel, Escher, Bach. But I doubt that very much. The book was written in 1995 and so far I haven’t come across it in any list of classics. I also read Gödel, Escher, Bach and I can say that that book made a lasting impression on me and is a classic also in my book. A Tour of the Calculus is not of the same order. It is a strange mix of popular mathematics, history of mathematics, diary and novel by an author who is a philosopher turned mathematician, turned evangelist of the calculus. It is not a traditional history of the calculus, the people that created the calculus are only briefly mentioned in connection to contributions they made to fundamental concepts and theorems of the calculus. You could read the book as a sort of genesis of the calculus describing the various concepts as they were defined in history. This mixed with elements of the author’s life and even fictional or imagined dialogues and situations. The style is florid, something the author recognises when he comments that in the anonymous feedback from his students they mention that Berlinski really likes to hear himself talk. The book is a bit like that, a long narrative of a series of lectures given by the by the author trying to explain the calculus and impress upon his audience the brilliance, importance and beauty of the calculus. This mix of elements defintely make it a unique book, I never read a book on mathematics that is like it. But I find it low on content density to my taste and I doubt a reader that has no prior knowledge of the calculus will take away a lot from this book. I you want to read only one layman’s book about the calculus then I wouldn’t recommend reading this one. But I did find it an interesting experiment and certainly not dry, sometimes even funny even though a bit long winded. Every now and then I stumbled across an insight and the connection between real numbers and continuity and reality was interesting. Interesting book, not sure who the right audience is.