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The Power of Partitions

Writing a whole number as the sum of smaller numbers springs a mathematical surprise

By
3:52pm, December 13, 2002

Just a year before his death in 1920 at the age of 32, mathematician Srinivasa Ramanujan came upon a remarkable pattern in a special list of whole numbers.

The list represented counts of how many ways a given whole number can be expressed as a sum of positive integers. For example, 4 can be written as 3 + 1, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1. Including 4 itself but excluding different arrangements of the same integers (2 + 1 + 1 is considered the same as 1 + 2 + 1), there are five distinct possibilities, or so-called partitions, of the number 4. Similarly, the integer 5 has seven partitions.

The list that Ramanujan perused gave for each of the first 200 integers, the number of their partitions, which range from 1 to 3,972,999,029,388.

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