On his book Mathematics in 10 Lessons: The Grand Tour

Cover Interview of June 02, 2009

A close-up

Mathematics in Ten Lessons is intended for an audience of humanists, where humanist is interpreted in the wide sense to mean anyone in the humanities. But, because of the way mathematics has been presented to him or her in the past, mostly as a collection of rules that sometimes work and sometimes do not, a humanist “just browsing” the book will be naturally skeptical.

He or she might overcome some of the skepticism looking quickly at page 17. On this page I write that the typical reader of Ten Lessons might well be a poet. On page 18 I assert, flatly, that “the book is truly written for poets.” At the very end of the book, on pages 377-380, I describe a similarity between mathematics and poetry. In fact, I argue that the mathematician and the poet are essentially mirror images of one another. And who lives more deeply in the humanities than does a poet?

Our browser, like most of us, will have behind experience – perhaps painful – in many mathematics courses. Certainly, the browser had a dozen years of these courses in grades 1–12. He or she might have taken a college course or two in the subject. But it is unlikely that the browser will have thought about the nature of mathematics. Just what are mathematical objects? Where do you find them and who put them there? I address this question early on, on the pages 19-24. I assert that, like Macbeth’s dagger, mathematics lives in the mind.

Moreover I claim that mathematics is created and not discovered. Mathematics is used to explain the real world as mathematicians paint abstract pictures of pieces of the world. These pictures are made of mathematical objects like equations, or infinite series, or matrices. Mathematicians then manipulate the mathematics in these abstract models - they solve equations, sum series, invert matrices. By this process they discover new truths.

A humanist just browsing Mathematics in Ten Lessons will immediately notice the analog between this applied mathematics process and what an impressionistic painter does when the painter selects the salient properties of real-world objects to describe abstractly on canvas, in oil paint. Or what a poet does when the poet discovers eternal truths in ordinary things, as Keats did with the Grecian Urn.

[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 costs—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 self’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.

## A close-up

Mathematics in Ten Lessonsis intended for an audience of humanists, wherehumanistis interpreted in the wide sense to mean anyone in the humanities. But, because of the way mathematics has been presented to him or her in the past, mostly as a collection of rules that sometimes work and sometimes do not, a humanist “just browsing” the book will be naturally skeptical.He or she might overcome some of the skepticism looking quickly at page 17. On this page I write that the typical reader of

Ten Lessonsmight well be a poet. On page 18 I assert, flatly, that “the book is truly written for poets.” At the very end of the book, on pages 377-380, I describe a similarity between mathematics and poetry. In fact, I argue that the mathematician and the poet are essentially mirror images of one another. And who lives more deeply in the humanities than does a poet?Our browser, like most of us, will have behind experience – perhaps painful – in many mathematics courses. Certainly, the browser had a dozen years of these courses in grades 1–12. He or she might have taken a college course or two in the subject. But it is unlikely that the browser will have thought about the

nature of mathematics. Just what are mathematical objects? Where do you find them and who put them there? I address this question early on, on the pages 19-24. I assert that,like Macbeth’s dagger, mathematics lives in the mind.Moreover I claim that mathematics is

createdand not discovered. Mathematics is used to explain the real world as mathematicians paint abstract pictures of pieces of the world. These pictures are made of mathematical objects like equations, or infinite series, or matrices. Mathematicians then manipulate the mathematics in these abstract models - they solve equations, sum series, invert matrices. By this process they discover new truths.A humanist just browsing

Mathematics in Ten Lessonswill immediately notice the analog between thisapplied mathematics processand what an impressionistic painter does when the painter selects the salient properties of real-world objects to describe abstractly on canvas, in oil paint. Or what a poet does when the poet discovers eternal truths in ordinary things, as Keats did with theGrecian Urn.