The Calculus Gallery: Masterpieces from Newton to Lebesgue

Some authors try to explain calculus to the literati with the hope of enlightening them a bit. They apologize at the inclusion of an equation, and wave hands like magicians. That's OK, for the innumerate. But the result is invariably like reading Julia Child's recipes and not cooking any of her meals. Not so William Dunham. The only way to appreciate the masterpiece that calculus really is, is to know your basic mathematics, and then plunge into such a book as his. This is a great book for students of mathematics. By following the counterexamples that mathematicians themselves create in order to test their own inventions (such as the Riemann integral), Dunham does better than most in showing us how tough the trek is to understanding. We feel the sense of humility that this handful of men develop in the face of the utterly unknown. And he gives us the sense of how unknown the frontier truly is in mathematics, because Cantor, for instance, cannot just build a better telescope and discover a new theorem. It's all done in the mind, many times in response to the needs of the sciences (e.g., Fourier), but ultimately, it's in the minds of these incredible men. Thus, well done, William Dunham! But if all you can read is Dickinson and Joyce, then you cannot appreciate this book.