Modern X-ray technology reveals Archimedes' math theory under forged painting

Archimedes Palimpsest Project Bergmann and Noel place fragments from the Archimedes Palimpsest

Bergmann, left, and Noel place fragments from the Archimedes Palimpsest in front of the X-ray beam.

Archimedes Palimpsest Project A scan of the palimpsest

A scan of the palimpsest reveals vertical text hidden beneath the paint. Multispectral imaging revealed that Archimedes was well on his way to developing calculus, nearly 1,000 years before Isaac Newton.

After more than 1,000 years in obscurity, the last unreadable pages of the works of ancient mathematician Archimedes are being deciphered, thanks to the X-ray vision at the Stanford Linear Accelerator Center (SLAC), which Stanford operates for the U.S. Department of Energy. This discovery gives us the most complete record of Archimedes' works since the Middle Ages, and Stanford scientists and scholars are helping unravel the final secrets hidden within an abused manuscript called the Archimedes Palimpsest.

"It is amazing how much the Archimedes Palimpsest project has gained from Stanford University," said Will Noel, curator of manuscripts and rare books at the Walters Art Museum in Baltimore, where the document is housed. "It is only with SLAC physicist Uwe Bergmann that we can read whole sections of text. And it is only with the Classics Department's Reviel Netz that we can understand it."

The manuscript uniquely records several of the works of the legendary 3rd century B.C.E. mathematician, who famously exclaimed "Eureka!" upon discovering how to measure the volume of a solid while sitting in his bathtub. Archimedes' work is considered to be the foundation of modern mathematics.

The current project is the culmination of 10 years of research to recover ancient Greek text erased more than 700 years ago when the parchment on which it was written was recycled, or "palimpsested."

In the 10th century, an anonymous scribe copied Archimedes' treatises in the original Greek onto the parchment. But three centuries later, a monk palimpsested the parchment by scraping away the Archimedes text, cutting the pages in half, turning them sideways and writing Greek Orthodox prayers onto the recycled pages. Adding further insult, forgers in the early 20th century painted religious imagery on four of the pages in an attempt to elevate the manuscript's value. The result was the near obliteration of Archimedes' work, except for the faintest traces of ink still embedded in the parchment.

The text of the Archimedes Palimpsest presented a monumental challenge for imagers to reveal and scholars to decode. As much as 80 percent of the text previously had been revealed by other researchers using standard imaging techniques. But the remaining 20 percent, obscured by grime and mold, had resisted all attempts at recovery.

To solve this problem, a team of scientists at SLAC used a special X-ray imaging technique, called X-ray fluorescence (XRF) imaging, to finally reveal the text, hidden from view since antiquity on the goatskin pages. X-ray fluorescence is typically used to detect small concentrations of metals and other elements. For the Archimedes Palimpsest, XRF was used to detect traces of iron pigment in the remnants of the ancient ink.

Uwe Bergmann, a SLAC physicist who had been studying photosynthesis in spinach leaves, said the idea to use XRF for the Archimedes Palimpsest came to him while at a conference in Germany.

"I read an article about the palimpsest and it said there were traces of iron in the ink," Bergmann said. "We were studying trace metals in spinach, so I thought we could do the same thing to image the palimpsest." Bergmann and Noel conducted tests to make sure the technique was safe for the manuscript, and not long after, images began to emerge.

Archimedes rediscoveredThe existence of the palimpsest was known in the 19th century, but it was not until 1906 that Johan Ludvig Heiberg—the world authority on Archimedes at that time—discovered that the ancient manuscript contained the work of the famous mathematician. Heiberg recovered what information he could from the palimpsest's pages and incorporated it into a new edition of the complete works of Archimedes, published around 1910. The palimpsest disappeared sometime after World War II, but Heiberg's work stood for a century as the most complete collection of Archimedes' work.

In 1998, the manuscript resurfaced in a French collection and was auctioned at Christie's in New York, where it was purchased by an anonymous collector. The new owner, who now privately funds the palimpsest project, entrusted the manuscript to the care of the Walters Art Museum in Baltimore for conservation and study.

Over the next several years, using a modern imaging technique called multispectral imaging, which relies on visible and ultraviolet light, the faint traces of remaining original ink began to yield up the hidden text and bring to light stunning discoveries about Archimedes. With these techniques, scholars determined Archimedes was well on his way to developing calculus, nearly 1,000 years before Isaac Newton. Archimedes also explored a branch of mathematics, now known as combinatorics, which deals with multiple ways of solving a problem. But perhaps most surprising of these discoveries, Archimedes used the concept of infinity—unheard of in ancient mathematics. Scholars consider this one of the most original and important findings in all of Archimedes' work.

But certain pages in the palimpsest resisted even the most intensive attempts at deciphering. Paint and stains completely obscured a few remaining parts of the original text, making it impossible to read using multispectral imaging. It was here that the intense X-ray beam produced at SLAC's Stanford Synchrotron Radiation Laboratory proved invaluable. The X-rays pass right through the grime and paint, like a child's magic pen that reveals invisible ink.

"We're getting a more complete understanding of one of the greatest minds of all times," Bergmann said. "We are also showing it is possible to read completely hidden texts in ancient documents without harming them."

The Archimedes Palimpsest, which comprises 174 pages, contains more than just the works of Archimedes. At least 10 pages contain transcripts of speeches given by 4th century B.C.E. orator Hyperides. Prior to this discovery, Hyperides was known to have existed only from papyrus fragments and quotations from his work by other authors. Six of the pages come from a yet unidentified philosophical text; four pages come from a liturgical book; and 12 other pages come from two different books, the text of which has not been deciphered.

In March 2006, experiments at SLAC revealed a previously indecipherable page of Archimedes' On Floating Bodies for the first time, an accomplishment Will Noel calls one of the team's greatest achievements at SLAC. The same experiments also brought to light the identity of the priest who erased the Archimedes texts. His name was Johannes Myronas, and he finished transcribing the prayers on April 14, 1229, in Jerusalem.

"We have already discovered an astonishing amount of new information using X-ray fluorescence and eagerly hope for more," said Noel.

From July 28 to August 7, 2006, Archimedes Project conservators and imaging scientists returned to SLAC from the Walters Art Museum and other institutions to scrutinize more of the ancient Greek characters revealed by the X-ray beam. This time the team paid special attention to seeing through the gold paintings that coat several pages, including previously unread sections of Archimedes' greatest treatise, The Method.

The 2006 Archimedes Palimpsest experiments also generated a tidal wave of press interest—television crews, including the History Channel, and newspapers and websites around the world carried news of the work happening at SLAC. And on Friday, a live webcast from both the Exploratorium in San Francisco and SLAC in Menlo Park revealed the manuscript text in real time. Noel says this kind of attention is exactly what is needed to ensure Archimedes' work does not again fall into obscurity. The team plans to make its findings available to the public once scholars have deciphered the text imaged at SLAC.

"The reason that Archimedes texts are now so rare is that very few people ever read him," said Noel. "Part of our task therefore, is to make sure that people know that Archimedes is now available in digital form, so that 'the digital Archimedes' does not get neglected."

Heather Rock Woods contributed to this report.