Anyone who likes math probably knows Archimedes -- the one who yelled "Eureka!" when he discovered a method to calculate the volume of a body. Although the Greek mathematician is recognized for his theories and inventions, his full potential has yet to be revealed. In an essay published in the journal Science on November 1, Professor Reviel Netz, from Stanford University (USA), declares that he found unpublished texts by Archimedes in a manuscript with more than a thousand years, which show that he already dealt with the notion of infinite precisely.
It is believed that the Greeks did not use the notion of infinity, as they considered it confusing. The manuscript shows, however, that Archimedes may have used the concept of infinite sets -- such as the set of numbers or points on a line -- long before other mathematicians tackled the subject. The document also confirms the idea - already accepted in academia - that he intuited some principles of differential and integral calculus, whose invention is attributed to Newton and Leibniz in the 17th century.
The manuscript was found at the Walters Museum in Baltimore (USA). Despite the poor state of conservation, it is a priceless discovery. "In some ways it adds to what we already know and in others it's the only source," Netz tells CH online.
In the period when Archimedes lived (3rd century BC), works were recorded on parchments. In the 10th century AD, with the evolution of 'paper', a scribe from Constantinople (present-day Istanbul) - at the time, the center of studies of the theories of the ancient Greeks - copied texts by Archimedes into a book with leaves and bindings. Only 1% of these copies of ancient works have survived to the present time.
About two hundred years later, during the Fourth Crusade, Constantinople was invaded and sacked. The book, however, was unaffected. in part. With paper shortages, the religious used Archimedes' manuscript to record another work -- reuse that characterizes the book as a palimpsest.
The document was kept by the Church for many years, until it was donated to a library in Constantinople, where it was found in 1906 by the philologist Johan Ludvig Heiberg. With only a magnifying glass, he was able to identify, under the religious writing, the texts of Archimedes. As he could not remove the book, Heiberg photographed its pages and published its contents. Despite the precarious conditions, he was able to decipher almost 80% of the texts.
Already at that time Heiberg discovered that Archimedes accurately calculated numbers and volumes, an operation that even in the 17th century was still performed in an approximate way. Shortly after discovery, the manuscript disappeared again, and only reappeared in the 1930s, in a private collection in Paris. In 1998, it was sold for $2 million to a collector, who lent the book to the museum where it is being studied.
The re-analysis of the palimpsest used advanced technology, as the wear and tear of time rendered some sections virtually unreadable. The findings show that the history of science still has a lot to reveal. "We tend to believe that cultures are monolithic, and this is an example of the opposite," says Netz. Simplifying the form of the story can generate underdeveloped ideas.