Ultimately, Lakoff and Nunez return to the nature of the existence of mathematical objects. Whether they are mental constructions, facets of an idealized reality, or just rule-governed manipulations (like the game of chess) is an issue that has resonated all through the history of philosophy and is certainly not settled in this book.
Whatever one's views on the nature of mathematical entities and truths, however, the book is provocative and beneficial in its emphasis on the metaphorical aspects of mathematical concepts. A deeper appreciation of the sometimes unconscious, usually mundane sources of mathematical ideas can only help us learn and teach mathematics.
To demonstrate this, the book ends with an extended case study of the authors' approach to mathematical idea analysis. In it they clearly explain all the layers and interconnections among the metaphors necessary to develop an intuitive grasp of Euler's famous equation, eπ*i+ 1 = 0, relating five of the most significant numbers in mathematics.
Bertrand Russell wrote of the "cold, austere beauty" of mathematics. In very different ways A Beautiful Mind and Where Mathematics Comes From remind us of the warm bodies from which this beauty arises.
Professor of mathematics at Temple University and adjunct professor of journalism at Columbia University, John Allen Paulos is the author of several best-selling books, including Innumeracy and A Mathematician Reads the Newspaper. His Who’s Counting? column on ABCNEWS.com appears every month.