Hardy and Ramanujan’s most famous joint paper was in the theory of partitions, the ways of representing a given whole number n as the sum of positive whole numbers. The number 5, for example, can be “partitioned” seven ways: 5 = 5 5 = 4 + 1 5 = 3 + 2 5 = 3 + 1 + 1 5 = 2 + 2 + 1 5 = 2 + 1 + 1 + 1 5 = 1 + 1 + 1 + 1 + 1 As n grows, the number of partitions balloons. For n = 10, there are 42. For n = 50, there are 204,226. For n = 100, there are 190,569,292. And for n = 200 there are 3,972,999,029,588. In 1918, in a forty-page paper on partition theory, Hardy and Ramanujan offered a surprisingly accurate asymptotic formula for the number of partitions of an integer n. In 1942, Erdős was able to show that Hardy and Ramanujan didn’t need to use heavy machinery to deduce the first term of their formula, that the term could be found by “elementary” methods. Elementary techniques are not necessarily simpler. In this context, elementary means that the proof of the formula relies on a restricted set of numbers, the so-called real.