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.

[M]odern art still commonly refers to a rather narrow range of meaning and scope. It basically focuses on developments in Paris (Impressionism etc.) in the nineteenth century, and to selected Euro-American movements in the twentieth century (Cubism, Abstract Expressionism etc). But if we understand modernity as a socially transformative condition that was in force across much of the world from the nineteenth century on, how are we to understand artistic practices that were associated with these momentous changes?

The two world wars of the twentieth century were a product of the dislocations brought about of modernization in an environment where great power competition and the drive for hegemony were conducted primarily by violent means. Now that this era has passed in Europe and is receding in much of the Pacific rim, and hegemony achieved by force is no longer considered a legitimate ambition, the security requirements and fears of great powers should decline.

## 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.