Customer Reviews

A Certain Ambiguity: A Mathematical Novel

5 star:		(7)
4 star:		(4)
3 star:		(1)
2 star:		(0)
1 star:		(2)

 

 

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.

As a person that chose a career of poor person's mathematics i.e., Computer Science,
instead of Number Theory that I was pursuing at that time - it was pure unadulterated fun reading this book. It is very well researched, and presented
without ever losing the sense of tempo. The topic is completely non-trivial, and
as some others have mentioned, is a bit of a fantasy to think of a judge in small town NJ to take up Euclid's Elements or the complete parallels saga. It made for great reading though, and I congratulate the authors heartily. It appears that they dug deep into their sense of appreciation for mathematical beauty and the nature of truth that lay there, and it shows. Good luck, you appear to be very good writers - even without the mathematics. I wish you a great career in writing as well.

This is a well researched, deeply thought out and crisply written book that must be enjoyed over several readings - each of which can reveal a certain beauty, a certain paradox and a certain truth! The authors mostly stay with basic number theory & geometry concepts making it accessible to most readers. They have also kept the characters and the storyline somewhat simple and ideal. But through this simplicity they have explored rich mathematical & philosophical ideas that most of us certainly would have debated ourselves at some point in our lives. As in life, they do leave some apparent loose ends and ambiguities that can only be rationalized through conjectures they lay forth in the beginning of the book.

A fantastic debut that I hope brings enough commercial success to the publishers to encourage more such writing; not only from Suri and Bal but also from other mathematicians who have a story to tell!

If you have studied mathematics or physics, then the topics that pin together this wonderful story will feel like old friends. In that sense, this book is a reunion. The unique thing about A Certain Ambiguity is that instead of meeting in an airless classroom, you get to hang out with your old friends at a cafe with pretty decent food and good coffee.

That's pretty cool.

I didn't know any mathematics before I read "A Certain Ambiguity." Yes, I'd taken Calculus in college, but I never quite saw its point, the way I saw the point of, say, literature. Novels made me think about life in a different way, and the better the novel the more profound the change it wrought.

So I was skeptical when I picked this book up. My son had it as a supplementary text in a college course and he had brought it home. I liked something about the cover and every time I walked by it I told myself to check it out. Finally I did. The first page grabbed me and then I read nothing else for the next two months! The book got "inside me" the way only the best novels have. It made me re-examine things and question assumptions I've always held.

In a quiet way the authors use mathematics to talk about our deepest beliefs and why they are beliefs in the first place. Strongly recommended.

I found this book to be a very enjoyable mix of plot, math, and philosophy. The overall arc of the story is not difficult to predict and the characters feel a little like they were written by mathemeticians (probably not a big surprise there!) but the story is enjoyable and the final quarter of the book develops solidly making it easy to forgive any earlier weakness. I would recommend this book to anyone who enjoys thinking while they read, and for some time after they finish.

The book is fantastic at introducing several of the most well known and intellectually stimulating theorems in mathematics. From the Pythagorean Theorem, to the infinitude of primes, to the Continuum Hypothesis, and even the logical equivalency of Euclidean and non-Euclidean geometry. While I do feel that a person without any mathematics instruction at the undergraduate level would struggle to fully follow the proofs and specificities of the mathematics, such a person would still greatly benefit by reading this book, as there is likely not a better place to find all of these concepts introduced in such elementary and casual terms. This is where the book succeeds, however it falls short in other aspects.

From a literary standpoint, the book is certainly not spectacular. Far too often sentences start with "So..." and go on to explain the implications of the previous passage. It is a minor caveat, but the frequency with which "So..." is used just makes it obvious the writers are mathematicians and not fiction authors. There are also several fortuitous happenstances that are all too unbelievable. However, if you are willing to forgive the author's literary shortcomings, then the book is still a nice read.

The philosophical component of the book is indeed stimulating. It makes one think quite a lot about what absolute "certainty" means. I do, however, find the conclusions at the end of the book to be all but unsatisfying. Essentially, the book concludes by saying that mathematical logic is still the best way to "know" something, but we can never be entirely sure which axioms are certainly true. It says that everyone must decide which axioms they think are true based on a feeling of overall "connectedness" and deduce their beliefs from those axioms; as long as people are "connected", then everything will be great. I guess I was expecting more out of the ending of this book. To simply end on a relativistic worldview in which cold hard logic built upon axioms derived from a sense of "connectedness" does no justice to the complexities of the religious faith, romantic encounters, and mathematical implications found in the bulk of the book. I am not saying that developing a philosophy that adequately incorporates all these things is an easy task, but I am simply saying that the authors did not succeed in doing so. I find that the philosophical outlook propounded by the authors comes up short in synthesizing absolute certainty with human experiences such as love, friendship, faith.

Overall, the book did earn all the three stars that I am giving it. I would recommend this book to those who are interested in two people's take on the philosophy of mathematics, certainty, and faith and are not shy of some stimulating mathematics. However, do not expect this novel to give you a fully satisfactory conclusion about the relationship between all these things.

I was very impressed with this book. This is the first book I have ever read, on mathematics or of fiction, that captures the beauty of mathematics. It reminds me of Rudin's splendid text on real and complex analysis, but that book is a painful, deep graduate-level text in math, and does not synthesize and bring together the disparate pieces of the puzzle of the exquisite beauty of modern mathematics. For myself, in carrying out often extremely demanding research in numerical analysis in far-from-ideal conditions, the beauty of the subject is far too easy to overlook in the day-to-day struggle to advance. A novel is a much superior milieu to display the wonder and beauty. Focusing on the "certain ambiguities" has a Kantian flavor that draws us into the intersubjective world of mathematics qua language. Also, despite the fact that the authors were mathematicians, I found the characters to be very appealing, although I must say that the judge in the book seems much more like a mathematician than someone dedicated to law. One of the nicest touches was the fabricated "letters". I really enjoyed reading these "letters" of mathematicians involved in the development of mathematics. This is a book that captures nicely what I see in mathematics, and seems to capture quite a bit of the spirit of mathematics.