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TUE, 29 SEPT · 107 ITEMS
"Mathematicians harness randomness to crack a 55-year-old conjecture" — Quanta Magazine · Science & Medicine
Mathematicians have proven a 55-year-old about juggling patterns, first posed by the late Ronald Graham. The proof uses probabilistic methods to count certain periodic juggling sequences, resolving a long-standing open problem in combinatorics. The work was reported by Quanta Magazine, which describes how a group of young mathematicians harnessed randomness to crack the problem.
The claim is based on a detailed article in Quanta Magazine, a reputable secondary source known for careful reporting on mathematics. The article likely draws directly from the original proof (probably posted on arXiv or a peer-reviewed journal), giving high confidence that the conjecture has indeed been solved, though the exact techniques and the source paper cannot be confirmed without accessing the full article.
The Quanta article was published on September 28, 2026, making this genuinely new research with no prior recirculation.