New math theories reveal the nature of numbers: Ono and his research team have discovered that partition numbers behave like fractals. They have unlocked the divisibility properties of partitions, and developed a mathematical theory for "seeing" their infinitely repeating superstructure. And they have devised the first finite formula to calculate the partitions of any number.
"Our work brings completely new ideas to the problems," says Ono, who will explain the findings in a public lecture at 8 p.m. Friday on the Emory campus. "We prove that partition numbers are 'fractal' for every prime. These numbers, in a way we make precise, are self-similar in a shocking way. Our 'zooming' procedure resolves several open conjectures, and it will change how mathematicians study partitions."