There are two particularly excellent bits - the opening section, which describes the young Amir's introduction to mathematics in his highly unusual upbringing often on a cruise ship (his father was the captain), where one of the stewards (who had a sideline in smuggling) looked after him, and as a mathematician, enticed the boy into the wonders and history of mathematics. Then, later on, the latter half of the book is an attempt to find the oldest known example of zero, which disappeared many years ago, a quest that has as many ups and down as any Hollywood tale.
Although I do love the personal storytelling part, I would have liked a bit more mathematical content, but when we do get it, there's some interesting stuff about the different early number systems and the origin on the characters we use to represent numerals, which seem to have come from India, but the route and the exact sources are still not clearly known.
I do have a couple of problems with the book. The big issue is that Aczel indulges in the same kind of woffly linking of Eastern philosophy and religion to scientific contents as the unfortunate Tao of Physics. The technique is to find something in ancient writing that bears a vague resemblance to modern science or maths and suggest that the ancients understood something that they clearly didn't. (This is nothing new - in medieval times it was common to think that ancient civilisations had much exotic knowledge that has since been lost.) This will put some readers off - but if you can get past it, there is much that is worth reading.
The other problem is that in trying to fight back against the early 20th century tendency to play down anything that came from the East, Aczel goes too far the other way, commenting, for instance, 'The three religions [Hinduism, Buddhism and Jainism] together give us concepts that did not arrive in the West until much later, in the late middle Ages. These concepts are zero, infinity and finite but extremely large numbers.' My issue with that is that infinity was discussed in the West since the Ancient Greeks (Aristotle, for instance, spent some considerable time on it) and you can't do better on finite but large numbers than Archimedes' magnificent Sand Reckoner, where he calculates how many grains of sand it would take to fill the universe. (To his credit, when I mentioned this to Aczel he broadly agrees with the criticism.)
What is impressive, though, is the central core of the book, the search for zero. It's not only a case of hunting for the oldest known written zero, Aczel makes a convincing argument that there is something about the Eastern religions, particularly Buddhism, that make it easier to conceive the concept of emptiness, or the void, as a worthwhile concept. It doesn't seem unreasonable that this viewpoint was behind the development of that incredibly useful mathematical widget, the zero.
So, a bit of a mixed bag, but well worth overcoming a negative reaction (should you have one) to waffly Eastern philosophy bits to get to the valuable insights into the early history of mathematics.
Review by Brian Clegg