While reading The Sand-Reckoner I couldn't get over the feeling that Bradshaw -- a Classics graduate of Cambridge University -- was just throwing as much historical information at me as possible without turning the book into a textbook. I can only presume that the book is relatively accurate from a historical point of view, and if so it is certainly informative as well as interesting. Also, the romantic tensions (between Archimedes and the king's half-sister and between Archimedes' slave and his sister) sometimes got a bit too thick for me. Apart from these minor flaws, I really enjoyed reading the book very much.

Of course, I was reading the book with special attention to the mathematical aspects. From that point of view, the most interesting thing is the tremendous power of Archimedes' mathematical knowledge, the way it allows him to easily do things that others find difficult or impossible, even though it is completely elementary mathematics from our modern viewpoint. For instance, it is his ability to solve the Delian problem (of being able to determine the amount by which one should scale the dimensions of a solid object in order to scale its volume by a certain amount) which allows him to build powerful catapults. In the following scene, Archimedes argues before the Regent that he should be allowed to build a huge catapult for the city while the present engineer tries to protect his job:

Though the famous scene of Archimedes' death (see also The Death of Archimedes) is recalled in the endnotes of the book, it is not part of the narrative which ends while the famous geometer is still in his 20's. Since the story takes place only during a very short period of time, it is not really a biography of Archimedes in any sense. Instead, it focuses on one particular aspect: the interplay of the various interests and goals that Archimedes has during this brief period in his life. From defending his city against a Roman invasion to helping his family slave (a former Roman himself), from his love of pure mathematics to his love of the king's sister Delia,between his desire to help his dying father and his mixed feelings about the fame that his inventions bring him, Archimedes has a lot to think about.

I strongly recommend this book for someone who wants to read some good mathematical fiction without needing to know any advanced mathematics and to anyone who wants to see some early mathematical developments placed in a historical context.

Yes, there are not many specific mathematical theorems or definitions that are relevant here. Rather, the whole idea of what makes math beautiful to some people and useful to others is a running theme throughout the book. But from my point of view, that is one of the most significant things a work of mathematical fiction can do. I consider addressing the "philosophy" of math (singular in the US, I'm afraid) to be something that can and should give a work a high "mathematical content" rating.