A Certain Ambiguity: A Mathematical Novel [Hardcover]

Gaurav Suri (Author), Hartosh Singh Bal (Author)

Book Description

ISBN-10: 0691127093 | ISBN-13: 978-0691127095 | Publication Date: July 2, 2007 | Edition: First Edition

While taking a class on infinity at Stanford in the late 1980s, Ravi Kapoor discovers that he is confronting the same mathematical and philosophical dilemmas that his mathematician grandfather had faced many decades earlier--and that had landed him in jail. Charged under an obscure blasphemy law in a small New Jersey town in 1919, Vijay Sahni is challenged by a skeptical judge to defend his belief that the certainty of mathematics can be extended to all human knowledge--including religion. Together, the two men discover the power--and the fallibility--of what has long been considered the pinnacle of human certainty, Euclidean geometry.

As grandfather and grandson struggle with the question of whether there can ever be absolute certainty in mathematics or life, they are forced to reconsider their fundamental beliefs and choices. Their stories hinge on their explorations of parallel developments in the study of geometry and infinity--and the mathematics throughout is as rigorous and fascinating as the narrative and characters are compelling and complex. Moving and enlightening, A Certain Ambiguity is a story about what it means to face the extent--and the limits--of human knowledge.

Editorial Reviews

Review

Good stories need rich characters that we care about, not mathematical theorems, however fascinating. So a work of fiction subtitled A mathematical novel makes you fear that it may only expose the tremendous difficulty of blending science and logic with the emotion and dramatic tension required of good literature. Fortunately, in this case that fear is misplaced, because A Certain Ambiguity succeeds both as a compelling novel and as an intellectual tour through some startling mathematical ideas.... A Certain Ambiguity is a brilliant and unusual novel. -- New Scientist



I loved this novel. I hope we see more 'mathematical novels' being published in the future. -- Donald L. Vestal, MAA Review



The writers have created a book that could fascinate those who have just a rudimentary knowledge of math... -- India Abroad



In the delightful, yet deep tradition of Lewis Carroll, Martin Gardner, A.K. Dewdney, and Marco Abate comes A Certain Ambiguity by Gaurav Suri and Hartosh Singh Bal...There is no doubt that Suri and Bal have set a difficult goal for themselves and have succeeded in making difficult mathematical ideas accessible...[W]hat makes the work of Suri and Bal a fine example of this tradition is what makes any successful and more traditional novel work--rich and warm characterization, an interesting plot, and a conclusion that illustrates the equal proportions of ingredients of certainty, ambiguity, frustration, and joy in the proof of our human-ness. -- Gurunandan R. Bhat, The Financial Express



Suri and Bal's unconventional book praises the beauty of mathematics and the logical inevitability of its proofs. The book is also a discourse on the struggles between truth, faith, and reason. All this is woven into two weeks in the life of Ravi, an Indian student at Stanford University, and his accidental discovery that his grandfather was once convicted of blasphemy in a New Jersey town...Among the many books that aim to make mathematics more accessible to the nonmathematician, this is a remarkably pleasant and successful achievement. -- J. Mayer, Choice



The book sweeps up those who are sensitive to the intellectual adventure of mathematics. It accurately portrays the attraction and enjoyment that are to be found in the play of ideas. I recommend it highly to all those who have an interest in mathematics. -- William Byars, SIAM Review

From the Inside Flap

"A Certain Ambiguity is an amazing narrative that glows with a vivid sense of the beauty and wonder of mathematics. The narrator is deeply troubled by the ancient question of whether the objects and theorems of mathematics have a reality independent of human minds. Mixing fiction with nonfiction, A Certain Ambiguity is a veritable history of mathematics disguised as a novel. Starting with the Pythagorean theorem, it moves through number theory and geometry to Cantor's alephs, non-Euclidean geometry, Gödel, and even relativity."--Martin Gardner

"This is a truly captivating thriller that will take you on a whirlwind tour to infinity--and beyond. But be warned: once you start reading, you won't be able to put it aside until finished! A masterly-told story that weaves together criminal law, ancient and modern history, a young man's quest to know his deceased grandfather-and some highly intriguing mathematics."--Eli Maor, author of e: the Story of a Number and The Pythagorean Theorem: A 4,000-Year History

"This rich and engaging novel follows the path that leads one young person to become a professional mathematician. By deftly blending the young man's story with mathematical ideas and historical developments in the subject, the authors succeed brilliantly in taking the reader on a tour of some of the major highlights in the philosophy of mathematics. If that were not enough, the book also examines, through the minds of its characters, the natures of faith (religious and other) and truth. I am strongly thinking of building a university non-majors math course around this novel."--Keith Devlin, Stanford University, author of The Math Gene

"A Certain Ambiguity is a remarkably good effort to work through some fundamental issues in the philosophy of mathematics in the context of a novel. Crucial to the success of such a venture is creating characters and a plot that are strong enough to hold a reader's interest. Suri and Bal succeed particularly well in the story of Vijay Sahni and Judge Taylor. This well-written book will, I believe, find readers not only among mathematicians, but in a wider audience that is intrigued by mathematical meaning."--Joan Richards, Brown University

"Suri and Bal convey the beauty and elegance--as well as the fascination--of basic mathematical concepts."--Alexander Paseau, University of Oxford

See all Editorial Reviews

Product Details

• Hardcover: 292 pages
• Publisher: Princeton University Press; First Edition edition (July 2, 2007)
• Language: English
• ISBN-10: 0691127093
• ISBN-13: 978-0691127095
• Product Dimensions: 9.3 x 6.1 x 1 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (14 customer reviews)
• Amazon Best Sellers Rank: #663,342 in Books (See Top 100 in Books)

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Customer Reviews

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37 of 38 people found the following review helpful:

5.0 out of 5 stars Amazing novel about mathematical truth., August 22, 2007

By 

David R. (Cary, NC USA) - See all my reviews

This review is from: A Certain Ambiguity: A Mathematical Novel (Hardcover)

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.

14 of 14 people found the following review helpful:

4.0 out of 5 stars A physicist's view, November 25, 2007

By 

Jorge Medrano "Retired physicist" (Houston, TX USA) - See all my reviews
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This review is from: A Certain Ambiguity: A Mathematical Novel (Hardcover)

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.

14 of 15 people found the following review helpful:

5.0 out of 5 stars A novel of ideas, September 16, 2007

By 

Punya Mishra "Punya" (Michigan) - See all my reviews
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This review is from: A Certain Ambiguity: A Mathematical Novel (Hardcover)

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.