A 55-Year-Old Math Problem Was Solved—This Time by Humans
A group of young mathematicians found the solution to the long unanswered conjecture, first inspired by juggling, through randomness and friendship.
In 1971, mathematician Paul Graham posed a seemingly simple question that has stumped experts for decades: given a set of different integers, can they be rearranged so that the partial sums of the first two, three, four, and so on numbers are all unique? This problem, which Graham believed might be inspired by juggling, remained unsolved until recently.
Mathematicians Lisa Sauermann of the University of Bonn and Huy Tuan Pham of the University of Chicago finally cracked Graham's conjecture in a proof spanning four papers. The key to their solution lay in the power of randomness. By treating the problem through a probabilistic lens, the mathematicians demonstrated that it's possible to find an ordering of numbers that meets the criteria, even when dealing with finite sets of numbers.
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