A number puzzle first proposed by the brilliant mathematician Srinivasa Ramanujan (1887-1920) has finally been solved. Karl Mahlburg, A graduate student at the University of Wisconsin at Madison has submitted a 10-page paper of his results to the Proceedings of the National Academy of Sciences.

Srinivasa Ramanujan (1887-1920)All natural numbers (1,2,3,4,...) can be broken down into sums. For example, the number 4 can be broken down in 5 ways (called partitions): 4, 3+1, 2+2, 2+1+1 and 1+1+1+1. Ramanujan realized that curious patterns - called congruences, existed for some numbers: for example, the number of partitions for any number ending in 4 or 9 is divisible by 5 (The number 4 can be broken down into 5 partitions, as shown above). He also discovered that for some other numbers, the number of such partitions is divisible by 7 or 11. No one knew why!
In the 1940s, physicist Freeman Dyson discovered a rule, called a 'rank', explaining the congruences for 5 and 7. Mathematician George Andrews was able to explain (in the 1980s) the case (called a 'crank' ;-)) involving the number 11. Then in the late 1990s, Mahlburg's advisor, Ken Ono, stumbled across an equation in one of Ramanujan's notebooks that led him to discover that any prime number - not just 5, 7, and 11 - had congruences! This was totally unexpected. But again it was unclear why. It was Mahlburg who was able to prove why it was so.
Such a study into the nature of numbers might seem esoteric. But the solution may one day lead to advances in particle physics and computer security. As Mahlburg noted, such partitions have been used previously in understanding the various ways particles can arrange themselves, as well as in encrypting credit card information sent over the internet.