Researchers have found a fractal pattern underlying everyday math. In the process, they've discovered a way to calculate partition numbers, a challenge that's stymied mathematicians for centuries.
Partition numbers track the different ways an integer can be divvied up. The number 3, for example, has three unique partitions: 3, 2 + 1, and 1 + 1 + 1. Partition numbers grow so fast that mathematicians have a hard time predicting them.
"The number 10 has 42 partitions, but with 100 you have 190,569,292 partitions. They get impossibly huge to add up," said mathematician Ken Ono of Emory University.
Since the 18th century, generations of mathematicians have tried to find a way of predicting large partition numbers. Srinivasa Ramanujan, a self-taught prodigy from a remote Indian village, found a way to approximate partition numbers in 1919. Yet before he could expand on the work, and convert it to a clean equation, he died in 1920 at the age of 32. Mathematicians ever since have puzzled over Ramanujan's manuscripts, which tie the primes 5, 7 and 11 to partition numbers.
