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The Sand-Reckoner (2000)
Gillian Bradshaw
Highly Rated!

In this historical novel whose title is copied from one Archimedes' own works, the famous Greek mathematician is your typical math nerd, always so wrapped up in his computations that he is barely aware of what is going on around him. Since she is the wife of mathematical physicist Robin Ball it is not too surprising that the author is able to make these characteristics of Archimedes come off believably, although perhaps a bit too cliched. According to this story, if not for the help of his faithful slave and the affections of an aristocratic woman, Archimedes would probably never be have been able to achieve his tremendous success as the engineer of the water-snail (a spiral which allows one to raise water with almost no effort) and the powerful catapults he designed to save his city of Syracuse.

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:

(quoted from The Sand-Reckoner)

"The Alexandrians have come up with a formula," said Archimedes with satisfaction. "You probably wouldn't know it because it's still new, but they did a lot of trials on it and it works. You take the weight to be thrown,multiply it by a hundred, take the cube root, add a tenth and you ge the diameter of the bore in finger-breadths."

Eudaimon sneered. "And what in the name of all the gods is a cube root?" he asked.

Archimedes blinked, too astonished to speak. The solution to the Delian problem, he theought, the keystone of architecture, the secret of dimension, the plaything of the gods, how could someone who was supposed to build catapults not know what a cube root was?


"You think that you can make catapults because you know mathematics?" the chief catapult engineer demanded.

Archimedes kneeling at his feet...glared up at him. "Yes, by Zeus!" he exclaimed hotly. "In fact, I'd say it is perfectly evident that a man who doesn't know mathematics can't make catapults. You don't, and can't, or I wouldn't be here!"

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.

Contributed by sarah

"I had to read this book for my History and Philosphy of Mathematics Class as an outside reading book and was dreading it! However, I really enjoyed the book, and having already covered Archimedes in the text book, this novel only reinforced the factual information and even made him seem interesting to someone who is not interested in mathematicians! :)"

Contributed by Anonymous

The "philosophy" of maths is almost more important than the maths.

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.

Contributed by Irene

I was looking for some math history for my daughter, and didn't appreciate the gratuitous sensuality (references to nudity and prostitution); some will say that these references were historically realistic, but the descriptions didn't contribute anything on that count, in my opinion. I won't pass the book on to my daughter, but I really did come to love Archimedes. Picturing him as a young man slightly absent-minded and struggling with regular old growing-up issues really brought him to life for me. That was a gift.

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Works Similar to The Sand-Reckoner
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The Goddess of Small Victories [La déesse des petites victoire] by Yannick Grannec
  2. The Death of Archimedes by Karel Capek
  3. Pythagoras the Mathemagician by Karim El Koussa
  4. Ahmes, the Moonchild by Tefcros Michaelides
  5. A Szirakuzai Óriás [A Giant of Syracuse] by Száva István
  6. Archimedes, a planetarium opera by James Dashow
  7. Dead Ancients Trilogy by Peter Hobbs
  8. The Divine Proportions of Luca Pacioli by W.A.W. Parker
  9. Long Division by Michael Redhill
  10. A Beautiful Mind by Sylvia Nasar / Akiva Goldsman
Ratings for The Sand-Reckoner:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
Mathematical Content:
3.31/5 (10 votes)
Literary Quality:
4.2/5 (10 votes)

GenreHistorical Fiction,
MotifGenius, Anti-social Mathematicians, Real Mathematicians, War, Romance,

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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.

(Maintained by Alex Kasman, College of Charleston)