The unique model of this story appeared in Quanta Journal.
The late Ronald Graham wore two hats. He was a famend mathematician and, at one time, president of the American Mathematical Society. He was additionally a critical juggler and president of the Worldwide Jugglers’ Affiliation. “He cherished methods,” mentioned Fan Chung, a mathematician at UC San Diego who was married to Graham. “You already know, spinning a ball, spinning a coat hanger, spinning a number of balls collectively, throwing pens towards the wall.”
Generally Graham wore each hats directly. “It’s fascinating, in actual fact, that many mathematicians and pc scientists have an curiosity in juggling,” he mentioned in a 1980 tv interview. “I believe it’s the seek for patterns and construction that’s chargeable for this.”
He would go on to write down quite a few papers, some with Chung, on the arithmetic of juggling. However again in 1971, a long time earlier than he made that connection express, he posed a query that some mathematicians now say may need been impressed by juggling, too.
Begin with a random set of various integers, not together with zero. Are you able to all the time rearrange them in order that if you happen to add up the primary two numbers, then the primary three, then the primary 4, and so forth, each “partial sum” seems totally different? Within the language of juggling, this may imply that if every ball stays within the air for a special period of time, you may all the time discover an order to throw them in such that two balls gained’t come crashing down on the identical beat—which might spoil the act.
If the numbers are all optimistic, then the reply to Graham’s query is clearly sure: The sums will all the time develop bigger as you add extra numbers. Equally, if there are each optimistic and damaging numbers within the combine, the reply can be recognized to be sure. However what if the numbers stay in a finite world—like numbers wrapped round a clock, which repeat after a sure rely?
The late mathematician Ronald Graham was additionally a talented juggler.{Photograph}: Peter Vidor
