On his book Mathematics in 10 Lessons: The Grand Tour

Cover Interview of June 02, 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.

[T]he Holocaust transformed our whole way of thinking about war and heroism. War is no longer a proving ground for heroism in the same way it used to be. Instead, war now is something that we must avoid at all costsâ€”because genocides often take place under the cover of war. We are no longer all potential soldiers (though we are that too), but we are all potential victims of the traumas war creates. This, at least, is one important development in the way Western populations envision war, even if it does not always predominate in the thinking of our political leaders.

The dominant premise in evolution and economics is that a person is being loyal to natural law if he or she attends to selfâ€™s interest and welfare before being concerned with the needs and demands of family or community. The public does not realize that this statement is not an established scientific principle but an ethical preference. Nonetheless, this belief has created a moral confusion among North Americans and Europeans because the evolution of our species was accompanied by the disposition to worry about kin and the collectives to which one belongs.

## 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.