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This is the story of a book that could have changed the history of the World. To the untrained eye, it is nothing more than a small and unassuming Byzantine prayer book, yet it sold at Christies for over $2m. For faintly visible beneath the prayers on its pages are other, unique, writings - words that have been lost for nearly two thousand years. The text is the only record of work by one of the world's greatest minds - the ancient Greek, Archimedes - a mathematical genius centuries ahead of his time. Hidden for a millennium in a middle eastern library, it has been written over, broken up, painted on, cut up and re-glued. But in the nick of time scientists have saved the precious, fragile document, and for the first time it is revealing just how revolutionary Archimedes' ideas were. If it had been available to scholars during the Renaissance, we might have reached the Moon over a hundred years ago. The trail begins in the tenth century, when a scribe made a unique copy of the most important mathematics that Archimedes ever developed. For 200 years the document survived, but the mathematics in it was so complex that no one paid it any attention. So when one day a monk was looking for some new parchment - an expensive commodity at the time - to write a new prayer book, the answer seemed obvious. He used the Archimedes manuscript. He washed the Greek text off the pages, cut them in half, rebound them, and turned the Archimedes manuscript into an everyday prayer book. As he piously wrote out his prayers, he had no idea of the genius he was obliterating. Several hundred years later, the Renaissance was under way. Scientists were beginning to grapple with new concepts, working out how mathematics could be used to explain the World around them. Little did they know that many of the problems they were just encountering Archimedes had already solved more than a thousand years before. So, tragically, they had to do that research all over again, setting back the development of science and technology immeasurably. Then in 1906, in Constantinople, the document mysteriously turned up in a monastic library. An opportunistic scholar called Johan Ludwig Heiberg identified the text as Archimedes' writings. Although the Greek text was very faint, Heiberg was able to decipher some of it. What he found astonished him, and made the front page of the New York Times. He revealed that Archimedes' manuscript contained something called 'The Method', which showed not only Archimedes' final proofs, but for the first time revealed the process of how he went about making his discoveries. But then disaster struck again. World War One broke out and in its aftermath the Archimedes manuscript disappeared. Scholars had given up any hope of seeing the manuscript again, but in the 1960s odd rumours began to surface that it was to be found in Paris. It took 30 more years, but in 1991 an expert from Christies found it in the hands of a French family. When it reached auction, it was sold to an anonymous millionaire, who has now loaned it to the Walters Art Museum in Baltimore for conservation. Although the text is incredibly difficult to read, with state-of-the-art imaging equipment, they are gradually piecing together all of the writing for the very first time. And as the team in Baltimore peel back the glue, leather and centuries of dirt, dissolve the blue-tack and unfold the lines of Greek that are buried in the spine of the book, they are building up a picture of a man who was thousands of years ahead of his time. Not only was Archimedes coming to terms with the profound subject of infinity, he had taken the first crucial steps towards calculus, a branch of mathematics that had to be reinvented after the Renaissance, and which is today used to describe every physical phenomenon from the movement of the planets to the construction of a skyscraper. Who knows what human minds could have achieved if they had only known what Archimedes already knew?

• Genres: Documentary
• Language:  English