Free Is God a Mathematician? by Mario Livio Page B

and sizes of the Earth and Sun and the Moon and the whole universe the proof will carry conviction. And it was for this reason that I thought the subject would not be inappropriate for your consideration.
    The beauty of The Sand Reckoner lies in the ease with which Archimedes hops from everyday objects (poppy seeds, sand, fingers) to abstract numbers and mathematical notation, and then back from those to the sizes of the solar system and the universe as a whole. Clearly, Archimedes possessed such intellectual flexibility that he could comfortably use his mathematics to discover unknown properties of the universe, and use the cosmic characteristics to advance arithmetical concepts.
    Archimedes’ second claim to the title of “magician” comes from the method that he used to arrive at many of his outstanding geometrical theorems. Very little was known about this method and about Archimedes’ thought process in general until the twentieth century. His concise style gave away very few clues. Then, in 1906, a dramatic discovery opened a window into the mind of this genius. The story of this discovery reads so much like one of the historical mystery novels by the Italian author and philosopher Umberto Eco that I feel compelled to take a brief detour to tell it.
    The Archimedes Palimpsest
    Sometime in the tenth century, an anonymous scribe in Constantinople (today’s Istanbul) copied three important works of Archimedes: The Method, Stomachion, and On Floating Bodies. This was probably part of a general interest in Greek mathematics that was largely sparked by the ninth century mathematician Leo the Geometer. In 1204, however, soldiers of the Fourth Crusade were lured by promises of financial support to sack Constantinople. In the years that followed, the passion for mathematics faded, while the schism between the Catholic Church of the west and the Orthodox Church of the east became a fait accompli. Sometime before 1229, the manuscript containing Archimedes’ works underwent a catastrophic act of recycling—it was unbound and washed so the parchment leaves could be reused for a Christian prayer book. The scribe Ioannes Myronas finished copying the prayer book on April 14, 1229. Fortunately, the washing of the original text did not obliterate the writing completely. Figure 12 shows a page from the manuscript, with the horizontal lines representing the prayer texts and the faint vertical lines the mathematical contents. By the sixteenth century, the palimpsest—the recycled document—somehow made its way to the Holy Land, to the monastery in St. Sabas, east of Bethlehem. In the early nineteenth century, this monastery’s library contained no fewer than a thousand manuscripts. Still, for reasons that are not entirely clear, the Archimedes palimpsest was moved yet again to Constantinople. Then, in the 1840s, the famous German biblical scholar Constantine Tischendorf (1815–74), the discoverer of one of the earliest Bible manuscripts, visited the Metochion of the Holy Sepulcher in Constantinople (a daughter house of the Greek Patriarchate in Jerusalem) and saw the palimpsest there. Tischendorf must have found the partially visible underlying mathematical text quite intriguing, since he apparently tore off and stole one page from the manuscript. Tischendorf’s estate sold that page in 1879 to the Cambridge University Library.
    In 1899, the Greek scholar A. Papadopoulos-Kerameus cataloged all the manuscripts that were housed in the Metochion, and the Archimedes manuscript appeared as Ms. 355 on his list. Papadopoulos-Kerameus was able to read a few lines of the mathematical text, and perhaps realizing their potential importance, he printed those lines in his catalog. This was a turning point in the saga of this manuscript. The mathematical text in the catalog was brought to the attention of the Danish philologist Johan Ludvig Heiberg (1854–1928). Recognizing the text as belonging to Archimedes, Heiberg traveled to Istanbul in