Turns out that the famous puzzle of partition numbers may be a case of mathematicians not seeing the forest for the trees.

On the surface, partition numbers seem simple. 4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1, so there are 5 partitions of the number 4. However, this sequence of integers quickly becomes unmanageable; for the number 100, there are already more than 190 million partitions. In fact, until the mid-20^{th} century, mathematicians couldn’t compute past the first 200 partition numbers. Emory mathematician Ken Ono put this limitation in perspective: “In the mathematical universe, that’s like not being able to see further than Mars.” Ono and his team of mathematicians decided to take on the problem and wrestled with partition numbers for months. Finally, as Ono and a colleague were hiking, they noticed patterns in clumps of trees and started wondering what it would be like to “walk” through partition numbers. That’s when it hit them. Click here to read about the new theory that reveals the very nature of numbers.