In 1740, French mathematician Philippe Naudé wrote to Leonhard Euler asking in how many ways a positive integer can be written as a sum of distinct numbers. In his investigations of this, Euler established the theory of partitions, for which he used the term *partitio numerorum.*

Many of Euler’s results in number theory involved divergent series. He was courageous in manipulating these but had remarkable insight and, almost invariably, his findings, although not rigorously established, were valid.

** Partitions**

In number theory, a *partition* of a positive integer is a way of writing as a sum of positive integers. The order of the summands is ignored: two sums that differ only in their order are considered the same partition.

Continue reading ‘Number Partitions: Euler’s Astonishing Insight’

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