It’s funny how things that you’ve puzzled over for ages sometimes come to you in the strangest of places. Kent & Ono realised the connection between partitions and fractals whilst out hiking – Deskarati
For centuries, some of the greatest names in math have tried to make sense of partition numbers, the basis for adding and counting. Many mathematicians added major pieces to the puzzle, but all of them fell short of a full theory to explain partitions. Instead, their work raised more questions about this fundamental area of math.
On January 21, Emory mathematician Ken Ono will unveil new theories that answer these famous old questions.
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 explained the findings in a public lecture 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.”
Read the whole article here New math theories reveal the nature of numbers.