Archimedes, the name rings a bell. Wasn't he one of those Greek guys? Something to do with math, right?

Yup, something to do with math.

Imagine if you will, a box full of sand, a pointed stick and a compass or two to etch calculations in the sand, and a board to smooth the sand when room is needed to make more calculations. With those tools, an abacus and the brain between his ears for analysis and storage -- and without a zero -- Archimedes, in the third century BCE, invented a kind of pure mathematics, a calculus that no one else, it seems, would be able to understand or work with for another 2000 years.

The available historical record gives us no one until Galileo and Leibnitz in the 17th century who works with this calculus again. In U.S. history, I can think of only two examples of people using their brains in any comparable fashion -- Stephen Hawking and Sequoia, the 18th-century Cherokee, an illiterate man who went into the woods with some pages torn from a book and came out with a written language for his people.

The Sand-Reckoner is a timely book because now, using the kind of technology that is reading the stuck-together layers of the Dead Sea Scrolls, scientists are reading a palimpsest of a copy of Archimedes' work that was first deciphered in 1906 by the Dutch mathematician J.L. Heiberg using only a magnifying glass and strong light. The top layer of the palimpsest is a Greek prayer book found in 1899 in Constantinople by Athanassios Papadopoulos-Kerameus.

I tell you what, if I find out in my next incarnation that we are not now coming into an age of enlightenment, I'm going to be real disappointed in all of us. We have at hand all kinds of tools to help us access so much of our inherited genius.

Think of it, some 10th century monk, in his Christian fervor to complete his prayer book, takes from his stack of old parchments a copy of several texts of Archimedes, including "The Method" and "On Floating Bodies." This monk scratches off the old ink and writes his prayers crosswise on the sheet. Then, the prayer book experiences whatever history it does for another millennium until Papadopolous-Kerameus, in the last year of the 19th century, finds it and recognizes the ancient Greek underlay as possibly Archimedes' work. Then, Heiberg gets wind of it and and travels to Constantinople to see it and ends up deciphering it. Heiberg's work is validated in the scientific community and eventually the palimpsest is sold at auction for $2 million.

Now, using ultraviolet technology, the ancient Greek is being read and Archimedes, the mathematician, is being brought to light for us. Finally, any one of us will be able to read his works.

The Sand-Reckoner, Archimedes' name for himself, is convincingly fleshed out for us and brought to life in this well researched book by the classicist Gillian Bradshaw. Necessarily, the book is fiction; so little is known about Archimedes himself. We know that he lived in Syracuse on Sicily in the time of the First and Second Punic Wars but it took diligent research on the part of this writer trained in Classic Era scholarship to build a foundation on which to fashion her story from educated guesses. Besides the characters, Bradshaw gives us a good look at the society, the events of the First Punic War on Sicily, the machinery of that war and the technology of the civilization.

In the book, Archimedes returns home from a stay in Alexandria where he lived the life of a Museum regular. His father is terminally ill, Rome has invaded Sicily and Syracuse is at war. The family is impoverished by Phidias' illness and Archimedes must find a way to support them all, including four adult slaves. His ability to turn pure math into practical mechanics gains him the confidence of the tyrant and the jealousy of others in the defense works. His absentmindedness gets him into and out of otherwise complicated situations and charms the tyrant's sister.

As a character, I like Bradshaw's Archimedes. Many years ago, I spent a good bit of time in close proximity to a math graduate student. Michael, like Archimedes, was so focused on the magic inherent in his numbers and equations that all else was secondary. If he couldn't relate to something numerically, it was too confusing. He loved the 19th and early 20th century European classical composers and he had a great time discovering and trying out recipes for the most intricate desserts. He was happiest though, when he was working out some math problem. He'd disappear into his office after a class and turn on the music. Pretty soon, he'd come bursting out, waving a chewed-up pencil, and read me some probability proof like it was poetry. Bradshaw got that right on the money.

I'm afraid that I, having been educated in the social sciences, could only smile and think how cute he was when he was like that. A reaction not much better than those Bradshaw grants her other characters.

Working out those other characters must have been fun for Bradshaw. She could say for certain only that Archimedes' father was an astronomer named Phidias and that they lived during the reign of the tyrant Heiron, who was held up by Polybius as a prime example of a good ruler.

In that era, one didn't mention a respectable Greek woman by name, so the author got to create the women out of whole cloth. She does a good job of this, creating believable women of almost every social caste and using their daily lives to describe the intricate relationships between classes in that time and in that place.

There are two references Bradshaw uses to construct the person of Archimedes' wife. We know that he was married because his "household" is mentioned in a report of the seige of Syracuse during the Second Punic War and Plutarch says that Archimedes was related to Heiron.

The author chose to have Archimedes' wife be Heiron's sister. That works as far as establishing a relationship and Delia (Bradshaw's name for her) is a useful vehicle for describing some of the social dynamics of the time. I am skeptical, however, of some of the freedom of movement Bradshaw allows this character. It seems to me that a wealthy young woman who is daughter of one king and sister of another would have been more closely guarded, especially during time of war. Had she been watched as I think she would have been, Archimedes' proposal for her would not have come as a surprise in the tyrant's household.

Another relationship described in the book doesn't work well for me. The unrequited longing of Archimedes' slave, Marcus, for his master's sister seems out of place. Of course, that sort of feeling was inevitable in many slave owning households in every age but I wondered why it was there in this story. It seemed gratuitous.

Nevertheless, this is first and foremost a novel written to give us an accessible Archimedes and set him firmly in context. It does that. I recommend the book to anyone interested in the ancient Greeks or in history in general. I recommend it further as a crafted work in terms of use of language. It's such a joy when I come across, from time to time, a book that actually seems to have been composed and/or edited by someone who understands what they're about.

There is an Archimedes website full of fascinating information and it even has his epigram on the Cattle of the Sun. I love those kinds of problems.