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Twenty-two centuries after Archimedes wrote his most revealing mathematical work, and eight centuries after a Christian monk erased what may have been the last surviving copy, the lost treatise has turned up and is being deciphered in a Baltimore museum. "Infinite Secrets" reports the story of the manuscript's amazing discovery and how modern technology is being used to read its startling contents.

Archimedes is famous for shouting "Eureka!" (Greek for "I have found it!") on stepping into his bath and realizing that its rising water level showed a way to measure the volume of his king's crown to determine if it was pure gold (it wasn't). The Einstein of his era, Archimedes had a sophisticated understanding of mathematics, including infinity, and designed marvelous war machines for his native Syracuse to use against invading Romans, one of whom killed him in 212 B.C. Relying on sophisticated image-processing techniques, scholars now believe that Archimedes was closer than anyone suspected to inventing calculus—the mathematical tool at the heart of advanced science and engineering.

Many of Archimedes' works disappeared during the Middle Ages, but some survived to help inspire the scientific revolution in the 16th and 17th centuries. One document that seemed irretrievably lost was his treatise The Method, which reputedly told how he achieved his brilliant results—secrets he revealed nowhere else.

But then in 1906 Danish scholar J. L. Heiberg discovered The Method, along with several other works by Archimedes, faintly visible beneath the bold lettering of a medieval prayer manual in an Istanbul library. A scribe in the 13th century had incompletely erased a 10th-century copy of Archimedes' work and had then written over it—a common practice that allowed reuse of valuable parchment and produced a palimpsest, or parchment or tablet used one or more times after a layer has been erased.

Fortunately, Heiberg photographed the palimpsest, because a few years later it disappeared in the turmoil surrounding World War I. But regrettably, many of Archimedes' words were illegible in the photos, and many others were lost in the folds of the binding. Heiberg also neglected to copy Archimedes' explanatory diagrams, which are crucial for understanding his thought processes.

All was set right in 1998, when the vanished palimpsest resurfaced at a Christie's auction in New York, having hidden for decades in an apartment in Paris. In the interim the book had acquired a shoddy new binding, a chronic case of mold, and a number of forged illustrations, apparently intended to increase the book's value. The forger didn't realize that the text covered by the inept fakes was itself priceless.

Even so, the palimpsest garnered $2 million from an anonymous high-tech billionaire, who promptly delivered it in a gym bag to the Walters Art Museum in Baltimore, renowned for its rare book conservation department. There, specialists have gone to work on the ragged little volume, which curator William Noel proudly calls "Archimedes' brain in a box."

What a scribe once copied in the 10th century, a monk erased in the 13th, and Heiberg perceived only faintly, if at all, in the early 20th is now coming sharply into view thanks to the marriage of chemistry, computers, and multispectral imaging. It's a process Archimedes himself would have delighted to watch—while no doubt offering his expert advice.