Mathematicians have resolved Ronald Graham's 55-year-old conjecture about rearranging numbers so their partial sums are all different, even in modular arithmetic systems. The breakthrough came from young mathematicians across four papers using probabilistic methods and randomness to prove Graham's intuition was correct.
Mathematicians have resolved Ronald Graham's 55-year-old conjecture about rearranging integers so that partial sums remain distinct, even in modular arithmetic (clock arithmetic). The breakthrough came through a series of papers by young mathematicians, including Lisa Sauermann and Huy Tuan Pham, who used probabilistic methods and randomness to solve the problem.