On his book Mathematics in 10 Lessons: The Grand Tour

Cover Interview of June 03, 2009

In a nutshell

Mathematicians know two things that others do not. They know first that all mathematics flows from a few fundamental principles. Second, they know that aesthetic considerations provide both the motivation for mathematics and the standards for evaluating mathematics research once it is done.

In an earlier book, The Art of Mathematics, I presented to an intended audience of humanists the notion of mathematics as art. There, I emphasized the importance that mathematicians place on aesthetics as they create and then evaluate mathematics. The Art of Mathematics is a book about mathematics rather than a book of mathematics. The present book is unapologetically a mathematics book. Mathematics in Ten Lessons: The Grand Tour contains real mathematics, presented from the point-of-view of fundamental principles.

The topics in Ten Lessons range from basic logic to calculus. The topics are given in ten chapters, with each chapter being essentially a separate lesson. The basic notion is that there exists a large number of educated, intelligent, non-technical people who, for one reason or another, would like to understand some non-trivial mathematics. Moreover they can obtain this understanding provided the mathematics is presented slowly and carefully through the emphasis on fundamental principles. Mathematics in Ten Lessons does exactly that. Each topic begins at the beginning. Almost no prior mathematical knowledge is assumed.

Spontaneous generation is one of those wrong theories that clutter the basements of the biological sciences and that now look so very obviously wrong that it is hard to see how anyone could have taken them seriously in the first place. Why wouldn’t it occur to anyone that flies might be laying eggs that were too small for us to see? How simple would the crucial experiment be? What I have tried to do in much of my work is to turn this ‘obvious wrongness’ on its head—why, exactly, does it seem so obviously wrong?—and see what the new picture that emerges from that inquiry says about science and our belief in its results.

It’s commonplace to say that humor is subjective, since what’s funny to you might not be funny to me. But humor is also a loaded concept. If you – or your people – have no sense of humor, or the wrong one, that means you’re less rational, tolerant, understanding, or civilized. You don’t get it. Or, worse, you lack something human. Modern Chinese debates about humor were very much caught up with these fundamental questions of value.

## In a nutshell

Mathematicians know two things that others do not. They know first that all mathematics flows from a few fundamental principles. Second, they know that aesthetic considerations provide both the motivation for mathematics and the standards for evaluating mathematics research once it is done.

In an earlier book,

The Art of Mathematics, I presented to an intended audience of humanists the notion of mathematics as art. There, I emphasized the importance that mathematicians place on aesthetics as they create and then evaluate mathematics.The Art of Mathematicsis a bookaboutmathematics rather than a bookofmathematics. The present book is unapologetically a mathematics book.Mathematics in Ten Lessons: The Grand Tourcontains real mathematics, presented from the point-of-view of fundamental principles.The topics in

Ten Lessonsrange from basic logic to calculus. The topics are given in ten chapters, with each chapter being essentially a separate lesson. The basic notion is that there exists a large number of educated, intelligent, non-technical people who, for one reason or another, would like to understand some non-trivial mathematics. Moreover they can obtain this understanding provided the mathematics is presented slowly and carefully through the emphasis on fundamental principles.Mathematics in Ten Lessonsdoes exactly that. Each topic begins at the beginning. Almost no prior mathematical knowledge is assumed.