Robert Tubbs

 

On his book What is a Number? Mathematical Concepts and Their Origins

Cover Interview of March 24, 2009

In a nutshell

I find that non-mathematicians often perceive mathematics as a self-contained, inaccessible, body of knowledge that was essentially completed sometime in the distant past.  Mathematics is seen as being isolated from most disciplines, especially from the humanistic endeavors of theology, philosophy, literature, and art.  The concerns of mathematicians are imagined to have little in common with those of humanists.  But this understanding of mathematics is mistaken on two accounts: mathematical objects and goals continue to evolve; and, mathematics is not now, and never has been, as separated from the more humanistic disciplines as it might appear to the contemporary eye.

At least since the sixth century B.C.E., theologians, philosophers, and artists have appealed to mathematical ideas and principles to inspire their work and further their arguments.  For example, the result that some numbers cannot be expressed as a fraction of whole numbers (such a number is called an irrational number) has been used to support theological and philosophical conclusions about the nature of both time and space.  At other times, appeals to provide intellectual underpinnings for a conception of reality or an aesthetic theory have been not to precise results but to general mathematical concepts such as the continuum or orthogonality.

What is a Number? offers an examination of the roles a few mathematical concepts—number, geometric truth, infinity, and proof—have played in our continuing attempts to understand the cosmos and our place in it.  Using examples from ancient through modern times, the book reveals the central role mathematical notions have played in the history of ideas.  Moreover, some of the examples used in the book illustrate how subtle mathematical relationships, such as the one between a line segment and the points it contains, have challenged both mathematicians and humanists.  Through these historical examples, we discover that mathematical ideas are not esoteric or divorced from other intellectual or artistic pursuits; they are dynamic ones intrinsic to almost every human endeavor.