The original version of this story appeared in Quanta Magazine.
\n\nThe late Ronald Graham wore two hats. He was a renowned mathematician and, at one time, president of the American Mathematical Society. He was also a serious juggler and president of the International Jugglers’ Association. “He loved tricks,” said Fan Chung, a mathematician at UC San Diego who was married to Graham. “You know, spinning a ball, spinning a coat hanger, spinning several balls together, throwing pens against the wall.”
\n\nSometimes Graham wore both hats at once. “It’s interesting, in fact, that many mathematicians and computer scientists have an interest in juggling,” he said in a 1980 television interview. “I think it’s the search for patterns and structure that is responsible for this.”
\n\nHe would go on to write numerous papers, some with Chung, on the mathematics of juggling. But back in 1971, decades before he made that connection explicit, he posed a question that some mathematicians now say might have been inspired by juggling, too.
\n\nStart with a random set of different integers, not including zero. Can you always rearrange them so that if you add up the first two numbers, then the first three, then the first four…
Original source: https://www.wired.com/