*Read December 2004*

The differential and integral calculi are amongst mankind's great inventions; more's the pity that so few understand it. The notation is partially responsible: in his Huygens and Barrow, Newton and Hooke, Arnol'd says that the Leibnizian notation for calculus ``permits people who don't understand analysis to teach it to people who will never understand analysis''. (I was one of these; it wasn't until I began to study temporal logic that the genius of ``the'' calculus finally dawned on me.)

Into this world, then, a popular book on the calculus would surely be welcome. I flipped through this volume to find, goodness me, equations! So I bought this book, in the hope that it would prove to be just the volume I could give less numerate friends and family—a not-so-subtle new year's gift, say.

Berlinksi's book begins on a promising note. He is direct, he appears to read the reader's mind, and he demonstrates a remarkable power of language. But he doesn't know how to limit a good thing; I was soon reaching for my notebook to pen words that I needed to look up, his use of italics began to grate, and the superfluity of his prose got to breaking point. For instance, calling the Cartesian coordinates of a point ``the mark of its domesticity'' (p. 27) is unenlightening, potentially misleading and ultimately irrelevant. His irreverence, while initially enticing, becomes pathetic, such as his use of Kronecker (p. 58-60) for a pointless comic interlude (``You've got to be kidding, Leo''). His oblique references to T.S. Eliot are too little, too late, a small uptick in a dismally flawed work. There's no point even going into the details of the mathematics (digressive and therefore barely decipherable). If even someone who has grown to love the calculus can barely get through this book, can anyone else?

What I don't understand is how this book made it to print from a
respectable house (Random House/Vintage). Did Berlinski bribe or
threaten the editor? Do they think *this* is what it takes to
write a popular book on mathematics? Were they overwrought by the
concept of noble failure? On the one hand, you have applaud their
courage to publish a book with actual math in it (especially since it
will take at least a generation to get over that horrendous equation
of symbols to the halving of sales, for which we have Stephen Hawking
to thank). On the other hand...this?

This book has such a noble goal, and fails so badly. It's a Greek tragedy. If a publisher is reading this, please—find a mathematician who can write, such as Jordan Ellenberg, and put a contract in his hand instead.

Berlinski's opening biographical sketch tells us of his ``tendency to lose academic positions with [...] embarassing urgency''. We rapidly understand why. There are limits to what even academia should tolerate.