The Archimedes Palimpsest in 1999 bound and open to fols. 103v-105r. (John Dean Photography )

Call it the iceberg problem, the dilemma facing cultural organizations as diverse as museums, archives, art galleries and opera companies. Innumerable hours and extraordinary amounts of the budget go to work that is essential to the mission but mostly invisible to the public: scholarship, conservation, rehearsal, publication. It creates a hidden economy that makes cultural institutions look inefficient, if they’re judged on how much they cost and how much the public feels it benefits from their existence.

“Lost and Found: The Secrets of Archimedes,” which opens Sunday at the Walters Art Museum, is an exhibition about a book, a 10th-century manuscript that was overwritten in the 13th century with Greek Orthodox prayers. But it is also an exhibition about the iceberg, the laborious work it has taken to make the book legible, understand its origins and importance, decipher its text and translate its contents. It is an exhibition about ancient science and the drama of how thoughts from the 3rd century B.C. were transmitted from the mind of the great mathematician Archimedes to papyrus to sheepskin to digital files now available to anyone with access to the internet. It is a smart and engaging effort that forgoes the usual sacralization of the object itself — a musty old book — in favor of the tools and techniques and especially the passion that has motivated work on this ancient codex.

Even the Walters curator of manuscripts and rare books, William Noel, admits that the restored Archimedes Palimpsest isn’t much to look at. There is no brilliant before and after drama, as with a painting that has been cleaned or a building that has been meticulously restored to former glory.

But as the show opens, there is enormous expectation in the scholarly community about the arrival of the first copies of a new book from Cambridge University Press, which contains full color images of the palimpsest, a technical account of how the images were made and complete transcriptions of the texts. It’s too early to say whether this will revolutionize our understanding of Greek mathematics, but it will contain new texts thought to have been lost forever by the Greek orator Hyperides and the most complete versions of several works by Archimedes, including two books which exist only in this manuscript. This is the iceberg in full view, a massive tome that took more than a decade to produce, recovering — perhaps as fully as can ever be hoped — texts that miraculously escaped the oblivion of decay and destruction.

The story has now been told in newspapers, on television, an episode of NOVA and in a breathlessly popularizing but nonetheless smart book, “The Archimedes Codex,” authored by Noel and Reviel Netz, a scholar of ancient Greek science who played a large role in deciphering the Archimedes texts.

Anonymous (Spanish), Processional Cross, 1510, silver and translucent enamels. (The Walters Art Museum, Baltimore)

A palimpsest is created by partially erasing and writing over an earlier work, a process that is relatively easy to do with documents written on parchment, or animal hide. The Archimedes Palimpsest was created in the 13th century, in Jerusalem, reusing valuable parchment that had originally been inscribed with copies of texts by Archimedes in the 10th century, among other sources. The 13th century work was a prayer book, with incantations for the dead and prayers for purification of polluted containers, the storage of grain and other minutiae of the divinely regulated life. These were written over essential texts by Archimedes, the mathematician famous for (supposedly) shouting “Eureka!” in his bathtub but certainly one of the greatest mathematicians of his or any age, and arguably the progenitor of modern calculus and thus much of the modern world we live in.

If you have a sentimental attachment to rationality, enlightenment and science, it is infuriating to think of Archimedes defaced with a prayer book. Noel argues otherwise — that the recycling of Archimedes helped preserve what otherwise might simply have been lost or discarded.

And even when it was new — when the Archimedes text was scraped off and overwritten — the palimpsest still held a legible echo of that text, according to Abigail Quandt, senior conservator at the Walters.

“It was basically a utilitarian book,” says Quandt, meaning that the ghost of the old text never bothered anyone so long as the new prayers were legible. So when the book resurfaced in Constantinople in the 19th century, much of the original text was recovered. In 1906, a Danish scholar transcribed what he could decipher and photographed the pages he thought relevant.

The palimpsest went underground, into a private collection, through most of the 20th century, during which it suffered damage far more grievous than anything that had befallen it during its first 700 years of life. Forgers painted over several pages with faux-Byzantine imagery to increase its marketability among rare-book collectors. Mold attacked it and undermined many pages. Misguided restoration efforts introduced alien glue into the binding, making it difficult to separate the pages and read them.

As much of that damage as can be safely be undone has been undone during the restoration. Using multi-spectral imaging techniques and computer algorithms, digital images have been produced that help the original Archimedes and ancient texts stand out from the visual clutter around them.

Scholars associated with the Walters project have poured through the images and come up with their best attempt at a transcript. Noel says that there are thousands of small and some very large changes to the version created by the Danish scholar in 1906. In 2007, when he co-wrote “The Archimedes Codex,” Netz was already excited by what he considers two major changes in how we will think about Archimedes. He argues that in a passage impossible to transcribe in 1906, Archimedes advances the understanding of infinity far beyond what scholars assumed was the case among the ancient Greeks. And in another text called the “Stomachion,” Archimedes conceptualizes problems that now fall under the branch of mathematics known as combinatorics, or how to calculate the finite — but often very large — number of solutions to a particular problem.

“I don’t think there is a complete consensus about either of these points,” says professor Alexander Jones of the Institute for the Study of the Ancient World at New York University. But Jones, who studies ancient science and mathematics, is excited by the imminent arrival of the Cambridge University Press volumes and the chance to see the material for himself.

From what he’s seen, the new version of the “Stomachion” is the most promising material.

“What we have here is a very early example of a kind of mathematical thinking that until a few years ago we didn’t think the Greeks did at all,” he says.

As the story of the Archimedes palimpsest has been told and retold, it is the computer-age imaging that often dominates the narrative, which is ironic given that one of the most exciting discoveries in the codex has nothing to do with science. Among the parchment pages gathered into the prayer book were Greek texts by the Athenian orator Hyperides that had never been seen before. They are a window into the litigious world of Athens during its decline. In one text already released in translation, Hyperides answers the charges of his accuser Diondas, revealing a man with a lawyerly mind methodically and elegantly defending his actions and his patriotism.

Whereas the Archimedes material was known to exist and had been partially transcribed and photographed, the Hyperides speeches were assumed entirely lost.

The museum’s curators have wisely chosen to include examples of Quandt’s conservation tools and techniques, her careful tracings of every page onto Mylar sheets, preserving for posterity every hole, crease, tear and discoloration, and a card file filled with small plastic bags in which she saved every fiber, flake and extraneous matter removed from the book.

The show ends with a room that has nothing to do with palimpsests but rather demonstrates for visitors ongoing research and preservation projects at the museum. It is, in the end, a bit of self-advertising for the iceberg, but it’s not out of place. The enormous costs of saving and transcribing the Archimedes texts were paid for by the book’s private owner. Other objects, in museums across the country, don’t have this kind of patronage. By telling the story of the Archimedes Palimpsest in depth the Walters is making an argument about the humanist tradition that goes well beyond its own holdings.

Lost and Found:
The Secrets of Archimedes

Through Jan. 1 at the Walters Art Museum in Baltimore. 410-547-9000.