The diagram involved 14 pieces, and the word "multitude" seemed to be associated with it. Heiberg and those who followed him thought this meant that you could get many figures by rearranging the pieces.
"This is part of the reason people didn't see what it was about," Netz said. But the old interpretation seemed trivial, hardly worth Archimedes' time.
As he examined the manuscript pages, piecing together their text, he realized that what Archimedes was really asking seemed to be, "How many ways can you put the pieces together to make a square?" That question, Netz said, "has mathematical meaning."
"People assumed there wasn't any combinatorics in antiquity," he went on. "So it didn't trigger the observation when Archimedes says there are many arrangements and he will calculate them. But that's what Archimedes did; his introductions are always to the point."
But did Archimedes solve the problem? "I am sure he solved it or he would not have stated it," Netz said. "I do not know if he solved it correctly."
As for the name, derived from the Greek word for stomach, mathematicians are uncertain. But Diaconis has a hunch.
"It comes from `stomach turner,'" he said. "If you get involved with it, that's what happens."
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