{"id":10188,"date":"2026-11-08T10:55:29","date_gmt":"2026-11-08T10:55:29","guid":{"rendered":"https:\/\/silvybrand.com\/?p=10188"},"modified":"2026-11-08T10:55:29","modified_gmt":"2026-11-08T10:55:29","slug":"a-55-year-old-math-problem-was-solved-this-time-by-humans","status":"publish","type":"post","link":"https:\/\/silvybrand.com\/?p=10188","title":{"rendered":"A 55-Year-Old Math Problem Was Solved\u2014This Time by Humans"},"content":{"rendered":"


\n<\/p>\n

\n

The original version<\/span> of<\/em> this story<\/em><\/a> appeared in<\/em> Quanta Magazine<\/a>.<\/em><\/p>\n

The late Ronald<\/span> Graham wore two hats. He was a renowned mathematician<\/a> and, at one time, president of the American Mathematical Society. He was also a serious juggler and president of the International Jugglers\u2019 Association. \u201cHe loved tricks,\u201d said Fan Chung, a mathematician at UC San Diego who was married to Graham. \u201cYou know, spinning a ball, spinning a coat hanger, spinning several balls together, throwing pens against the wall.\u201d<\/p>\n

Sometimes Graham wore both hats at once. \u201cIt\u2019s interesting, in fact, that many mathematicians and computer scientists have an interest in juggling,\u201d he said in a 1980 television interview<\/a>. \u201cI think it\u2019s the search for patterns and structure that is responsible for this.\u201d<\/p>\n

He would go on to write numerous papers, some with Chung<\/a>, 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.<\/p>\n

Start 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, and so on, every \u201cpartial sum\u201d turns out different? In the language of juggling, this would mean that if each ball stays in the air for a different amount of time, you can always find an order to throw them in such that two balls won\u2019t come crashing down<\/a> on the same beat\u2014which would ruin the act.<\/p>\n

If the numbers are all positive, then the answer to Graham\u2019s question is obviously yes: The sums will always grow larger as you add more numbers. Similarly, if there are both positive and negative numbers in the mix, the answer is also known to be yes. But what if the numbers live in a finite world<\/a>\u2014like numbers wrapped around a clock, which repeat after a certain count?<\/p>\n

\n
\"A<\/picture><\/span><\/div>\n

The late mathematician Ronald Graham was also a skilled juggler.<\/span>Photograph: Peter Vidor<\/span><\/p>\n<\/figure>\n<\/div>\n


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Source link <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

The original version of this story appeared in Quanta Magazine. The 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\u2019 Association. \u201cHe loved tricks,\u201d said Fan Chung, a mathematician at UC […]<\/p>\n","protected":false},"author":1,"featured_media":10189,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[451,1294,1438,1624,1086,314],"class_list":["post-10188","post","type-post","status-publish","format-standard","has-post-thumbnail","category-gadgets","tag-math","tag-mathematics","tag-number-theory","tag-numbers","tag-quanta-magazine","tag-quantum"],"yoast_head":"\nA 55-Year-Old Math Problem Was Solved\u2014This Time by Humans - Silvybrand Lifestyle Blog<\/title>\n<meta name=\"description\" content=\"A group of young mathematicians found the solution to the long unanswered conjecture, first inspired by juggling, through randomness and friendship.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/silvybrand.com\/?p=10188\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A 55-Year-Old Math Problem Was Solved\u2014This Time by Humans - 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