A Certain Ambiguity: A Mathematical Novel [Anglais] [Relié]

Good books that attempt to explore mathematical ideas are somewhat rare. Well written novels on deep subjects of any sort are perhaps less rare, but are still hard to find. But a well written novel that explorers the philosophical foundations of math and statements of truth is the rarest of all. Yet Suri and Bal have managed to create a wonderful story of a family and the events that occurred over three generations that also delves deeply into the basis of mathematical and philosophical truths, all while keeping the reader riveted.

The tale of the grandfather's arrest on blasphemy charges in New Jersey in 1919 provides a fascinating background for a dialog between a Judge and the mathematician/grandfather on the subject of certainty and truth. The grandfather teaches the Judge about the foundations of mathematical philosophy, focusing on Euclid's Elements and exploring many areas of math in a simple and clear manner such that anyone could grasp the concepts with only the most basic mathematical background (i.e. middle school level math).

Perhaps the only flaw I can find with the novel is that the Judge is almost too good to be true. He shows an interest in the field of math that I would not expect to find in someone of his position in that time period, but that is a pretty small nit to pick with this wonderful novel.

The novel jumps between the past and the present where the grandson discovers the records of the grandfather's trial and begins to uncover the details as he attends a math class for non-math majors in his last year of college. The grandfather, the grandson, the teacher of the math-for-non-math-majors class, the grandson's friends, and even the judge are all well written, believable characters, people who you care about and want to learn more about.

Reading this book makes me want to learn not just more about the characters, but about math in general. It motivates me to get my hands on a good geometry text that explores Euclid's postulates, a book that explains more about Cantor's infinities of infinities, one that cover's Gödel's theorem, and one that teaches me more about how proofs are constructed. This novel opens up the world of mathematical ideas to anyone who wants to learn, to anyone who wants to understand the basic ideas of philosophy and science and how we know what we know.

Generally speaking the book is excellent. It of course requires some previous familiarity with Math to fully follow the reasoning in the examples and/or demonstrations. Needless to say, the judge Taylor is way too good to be true. I very much doubt any judge in the '20s or at any other time would have gone to the trouble to understand rigorous reasoning, such as Euclides' "Elements." As a (retired) physicist however, I don't understand the emotional turmoil that Vijay and the judge himself went through when the Eddington's empirical proof that Einstein's view of space-time-gravitation in General Relativity, was right. They agonize over whether Euclides' fifth axiom is true or false. In my view, an axiom cannot be "false." It is a statement that you accept, to be able to build a logically consistent theoretical edifice, following rigorous mathematical reasoning. If you then find contradictions, it means the set of axioms is useless for that purpose, or that they are not logically independent. The question that bothers them is in reality whether that particular theoretical construct, Euclidean geometry, describes physical space in the Universe. And the answer, from a practical point of view, is a resounding "yes" - almost everywhere in the Universe. Only in the vicinity of very large concentrations of mass, such as stars, the curvature of space as described in the equations of General Relativity, has to be taken into account. Of course, I am not trying to trivialize General Relativity in any way; I am perfectly aware of the enormous importance of its new ideas, in particular its new explanation of Gravity, as curvature of space. But curvature is a local property; the Universe is not homogeneous and isotropic on small scales. So, what's all the fuss about the fifth postulate?
I am more or less aware of at least part of Godel's work, but I don't see anything in it that will change my "physicist's view."
Another part where I think things have been forced a little is toward the end, where it seems that both Vijay and the judge finally agree that both in Math and religion some things have to be taken on faith. I don't know of any version of the Philosophy of Mathematics that makes that claim. Please authors, correct me if I am wrong.
All in all however, I give the book four stars, with the caveat I said before; you will enjoy it the most, if you are familiar with Math.

A Certain Ambiguity is a novel of ideas. A novel about mathematics and its pleasures wrapped up in a mystery (actually two, one about people and the other about mathematics). The manner in which these two mysteries tie into each other lies at the heart of the story. It is a smooth, easy read, despite the serious mathematics that threads through the book. There are people who will focus on the characters and the story and others who will focus on the mathematics, and others who will shift their attention back and forth between the two. (I am guilty of being of the third type, which is great because this is a book that rewards multiple readings.) People who like Douglas Hofstadter and Martin Gardner will love this book, but the author who most comes to mind is Richard Powers. Though the authors don't engage in the same verbal fireworks that makes Powers famous, they, similar to Powers, develop a story that is honest both to the characters and the ideas. No small feat.

Just a side note: This is a book that could not have existed without the Internet - as the two authors live on separate continents. This book was conceived and written as a genuine collaboration using email and regular bouts of instant messaging.

Full disclosure: The authors are old school-friends of mine and this review is based on a pre-publication draft of the book.