Greek mathematician Archimedes was far ahead of his time using calculus

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February 24, 2009

Scholars are reconsidering what ancient Greek mathematician and inventor Archimedes knew of the concept of infinity, thanks to new ways of looking beneath the surface of ancient objects.
Using modern X-ray and spectral imaging, researchers are uncovering two ancient manuscripts by Archimedes, who lived in Sicily in the third century B.C., Uwe Bergmann of the Stanford Synchrotron Radiation Laboratory told a meeting of the American Association for the Advancement of Science on Sunday.
In the 1300s the texts were scraped off the parchment and written over to create a prayer book, Bergmann said. But now scholars have been able to discern the original writing of Archimedes' "The Method" and "The Stomachion," volumes that exist nowhere else.
It emerges that Archimedes was far ahead of his time, using a form of calculus and devising ways to add an infinite number of sums, Bergmann said.
What is known of Archimedes' concept of infinity is likely to have to change from this, he said at a symposium on using modern methods to uncover the secrets of the past.
The document, called the Archimedes Palimpsest, came to light in 1997 when an anonymous collector purchased it at auction and sent it to the Walters Art Museum in Baltimore for study. The document was originally written in the 10th century, Bergmann said, and no earlier copies remain.
Archimedes was a famed mathematician in his own time and is still studied today. Roman soldiers killed him when they conquered Syracuse in 212 B.C.

By RANDOLPH E. SCHMID  AP Science Writer