But the Walters researchers wanted to be certain.

So the museum recruited teams of scientists from the Johns Hopkins University and New York's Rochester Institute of Technology, who used imaging technologies first developed for medical and space research.

"New technologies have the potential to fundamentally change how we know things," Noel says. "When we started out, we were delivering images through FedEx."

The scientists bombarded the parchment with light from various spectrums. Some rays were longer than a football field. Others were shorter than an atom. Then the different images were superimposed on top of one another.

"There are things that can be seen in one kind of light that can't be seen in another," Noel says.

They also attacked the problem another way, by placing each sheet in a magnetic field. The ink contained traces of iron that caused detectable changes in the field. The result from all the imaging tests created a kind of topography of the hidden writings. All the major features of the landscape were visible, but they couldn't be viewed up close.

Finally, more detailed results were achieved after the scientists flooded the text with a type of X-ray that created maps of the chemical elements present on individual pages.

At a resolution of 800 dots per inch "the images are just barely good enough for scholars to read," Noel says. "They're rather miraculous."

And what the scholars found amazed them, starting with the geometrical drawings on several pages.

"Heiberg paid no attention to diagrams," Noel says. "He was a lover of language. But ancient mathematicians thought in diagrams. They are part of Archimedes' logic."

In addition, a careful perusal of "The Method" reveals that the ancient Greeks had a far more sophisticated understanding of infinity — perhaps the most crucial concept in all of mathematics — than had been previously suspected.

Another breakthrough was made by Revel Netz, a philosophy professor at Stanford University. He hypothesized a link between "The Stomachion" (in which Archimedes was working on what appeared to be a children's game) to the modern field of cominatorics, which seeks how to determine how many different ways a single problem can be solved. It took modern scholars six weeks to determine that the answer that Archimedes gave for his puzzle — 17,152 — is in fact, correct.

For the researchers, spending 12 years in Archimedes' mind was like inhabiting a dwelling that was spacious, calm and radiated light.

"He's like Bach," Noel says. "His cleverness is beautiful. Understanding Archimedes is like understanding the most elegant joke in the world."

Lost speeches

Finally, the palimpsest also contains works by other authors — most notably, two lost speeches by the famed orator Hyperides.

In 334 B.C., Hyperides was in trouble. Four years earlier, he had advised the generals leading an alliance of Greek city-states to resist an attack by the Macedonians. It turned out to be poor advice. The Athenians were massacred, and Hyperides was prosecuted for treason.

The palimpsest contains the eloquent defense he gave during the trial.

The court, however, was unpersuaded. In 322 B.C., Hyperides' golden tongue was cut out and he was put to death.

Twenty-three centuries later, his voice is being heard again.