I actually put off reading this for a while just because the title implied some Templeton-like hand waving in which I really have no interest. It turns out, though, that religion doesn't make an appearance in the very interesting answers that Livio develops for the two perennial questions in the philosphy of mathematics: Is math created or invented? and Why does math seem to describe our universe so well? ( )

Eugene Wigner, a Nobel laureate in physics, wondered about the “unreasonable effectiveness of mathematics” in explaining the nature of the universe. Mario Livio, in Is God a Mathematician?, demonstrates how unreasonably effective math (or as the British say, “maths”) is [or is it, “are”?]. Livio shows that Newton’s inverse square law of gravitation has proved to be correct to better than one part in a million, while the measurements available to him were correct only to 4%. Even more extraordinary is the prediction of the magnetic moment of the electron, which the equations of quantum electrodynamics predict with the accuracy of 11 decimal places!!

Livio points out an even more extraordinary power of pure math when he shows how concepts explored by mathematicians with absolutely no application in mind have turned out decades (and sometimes centuries) later to be unexpected solutions to problems grounded in physical reality! For Example, “group theory,” developed by Evariste Galois 1832 to determine the solvability of algebraic equations has become the language used by physicists, linguists, and even anthropologists to describe all the symmetries of the world. And a non-Euclidian geometry outlined by Riemann in 1854 turned out to be the tool Einstein needed 60 years later in his general theory of relativity.

Physicist Roger Penrose identified three different kinds of “worlds”: (1) the world of our conscious perception; (2) the physical world; and (3) the Platonic world of mathematical forms. These in turn produce three enigmas: (1) why does the world of physical reality seem to obey the rules of the Platonic forms; (2) how do perceiving minds arise from the physical world; and (3) how did those minds gain access to the Platonic world by discovering or creating and articulating abstract mathematical forms and concepts.

Livio devotes the book to the question that has bedeviled philosophers from Plato to the present: whether the mathematical world we perceive is a preexisting entity that is “discovered” by humans or whether, instead, it is “created” from scratch by mathematicians. Before attempting to answer the question, he takes the reader on a quick (200 or so pages) tour of the history of the great mathematicians. He explores the relationship between math and pure logic, illustrating Russell’s paradox and Godel’s incompleteness theorem.
He treats us to lively descriptions of the biographies and work of many mathematicians from Pythagoras to Godel, ranking Archimedes, Newton, and Gauss as the three greatest. [He also seems to hold rather fond opinions of Galileo, Russell, and Godel.] One suspects that the real purpose of the book is to acquaint the general public with the history of math rather than to answer the deeply profound question of its very nature.

In finally proposing a solution to Wigner’s enigma of whether math is created or discovered, Livio concludes that math is partly discovered and partly created. Since our brains evolved to deal with the physical world, it should not be surprising that they developed a language (math) well suited for that purpose. Mathematical tools were not chosen arbitrarily, but on the basis of their ability to predict correctly the results of the experiments at hand. Livio argues that some math is “created”: “…through a burning curiosity, stubborn persistence, creative imagination, and fierce determination, humans were able to find the relevant mathematical formalisms for modeling a large number of physical phenomena.” On the other hand, for math to be “passively” effective (i.e., solve physical problems that had not been anticipated when the math was first articulated), it was essential that it have eternal validity, and those aspects of math have been “discovered.”

In all, this is a clearly written, fascinating book that is accessible to non-mathematicians. ( )

One of my great intellectual regrets is that I never quite "got" math in school. As I get older, that gap in my knowledge makes depresses me. It's not that I'd have chosen another profession -- I'm in the perfect job. But I do feel as if an entire field of knowledge is effectively sealed off to me.

Mario Livio's Is God A Mathematician helped shed some light on what has largely been terra incognita for me. The book takes a look at the history of math by asking the question of whether or not math is a human invention or a discovery of a preexisting system. The book tackles attempts to understand the world through mathematics and looks at the people behind these efforts. The chapters on probability and statistics were especially interesting to me. I hadn't really thought about those topics as having a history, but they most certainly do.

Livio never adequately addresses the origins of math (for me at least), but the book raises so many fascinating questions, that I'm willing to overlook that particular gap. What jumped out for me is the realization both of how important math is and how completely overlooked it is in our study of history. How is this possible? It's the language of science and we don't look at it. But then again, science gets overlooked as well.

Maybe I'm just becoming too much of a materialist in my dotage, but look at what advances in medicine and technology have done to change our lives. Yet they get barely a mention in most history books. I'm as guilty as anyone in this, so I'm not casting stones here. It just stuns me. For those of you who would like to start addressing this oversight, Mario Livio's book is a great place to start. ( )