The average adult’s attitude towards mathematics is easy to guess: simple arithmetic is acceptable, percentages and ratios cause some people to break into a cold sweat, and anything more complicated is best not mentioned in polite company. This attitude is especially odd when one considers the extent to which our lives are influenced by the fruits of mathematical labour. Large prime numbers ensure that our online transactions are secure, for example, and the mathematics of curved spaces allows us to locate each other using global positioning systems.
At the heart of mathematics lie integers, that include the positive and negative “counting numbers”, and the number that separates them: zero. Seemingly innocuous, it is often first encountered as a placeholder in the decimal system of representing numbers. For example, consider the number 235; in this representation, we mean to say the number 235 is composed of 2 hundreds, 3 tens, and 5 ones. Similarly, the number 20 would mean 2 tens and 0 ones. The same numbers in Roman numerals would read CCXXXV and XX, respectively. Clearly, these so-called Indo-Arabic numerals (in particular, zero) simplify basic arithmetic considerably. The late Amir D. Aczel asks in Finding Zero : “Where do these numbers come from? More specifically, where does the number zero, which makes it possible for us to use the same ten digits to represent all numbers in a relatively compact form, which lies at the heart of our electronic age, come from?”
Finding Zero begins with Aczel telling us the charming tale of how he came to be interested in the question he devotes this book to. He affectionately recalls being taught about numbers by a steward on board SS Theodor Herzl, a cruise ship his father captained. Further along, in the early chapters of the book, Aczel tells the fascinating tale of how civilisations separated by space and time, and each in its own way, learned to count; and often draws upon archaeological and textual evidence.
We sense in these passages the author’s excitement, his infectious enthusiasm for the history of numbers, and his strengthening resolve to answer the question that he has carried with him since childhood: where does zero come from?
His quest takes him to South Asia: to the Khajuraho temples, where he finds magic squares (four-by-four arrays of numbers with special properties); to Rajasthan, where he sets out in search of the Khandela inscription, believed to be lost; and finally to Gwalior, where the earliest known zero in India is known to exist. Why is this not sufficient? Aczel answers that the Gwalior zero was committed to stone in the 9th century, when trade routes between India, through Arabia, and all the way to Europe, were known to exist. The question is important for the history of science, as active trade routes would mean that it could have come from any of these places. There has, over the last century and a half, been much debate about where zero came from, and an older zero would conclusively settle the issue.
Unfortunately, it is during these journeys that the author turns what might have been an enjoyable, even thrilling, scholarly work into one interlaced with a mediocre travelogue. The many paragraphs Aczel devotes to this travelogue are rather wishy-washy and filled with banal details.
Along the way, the reader is kept busy with quasi-philosophical musings on the compatibility of Eastern systems of logic with the concept of zero, this being forwarded as further evidence for the Eastern origins of zero. This form of argument is strongly reminiscent of books by F. Capra and G. Zukav about Eastern mysticism and quantum physics, written in the 70s, where ostensibly accidental similarities in language are taken as evidence for profound, hitherto unexplored connections.
In conclusion, while the book is well-intentioned, it suffers from lacklustre prose and a seemingly random sampling of anecdotes from the history of science, sometimes with little relevance to the broader points being made. It makes up for these deficiencies by giving the reader a palatable, if at times tedious, introduction to the subject, making it a fine starting point for those interested in learning more about what Aczel calls one of the “greatest abstractions the human mind has ever achieved,” namely, the story of numbers.
Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers; Amir D. Aczel, St. Martin’s Press, Rs. 450.
Madhusudhan Raman is pursuing aPhD in theoretical high-energy physics at The Institute of MathematicalSciences, Chennai.
