“the researchers show that Pólya’s conjecture is true for the disk, a case considered particularly challenging.”
George Pólya stated the conjecture in 1954 and proved it himself in 1961 for shapes that tile the plane, like triangles and rectangles. A disk does not tile anything. Until last year, nobody had proved it for anything else. Polterovich, Filonov, Levitin and Sher took 70 years of mathematics to handle a circle.