HISTORY LECTURE by George E. Andrews Pennsylvania State University on Euler's contributions to "Partitio Numerorum"
Abstract: Chapter 16 of Euler's Introductio in Analysin Infinitorum is titled "De Partitione Numerorum". The care with which Euler inaugurates the study of partitions has influenced all subsequent work in this area. We shall examine how exactly Euler began the theory of partitions, note some surprising connections with subsequent developments and reveal how Euler's bizarre presentation of an ancient chestnut (every nonzero integer is uniquely the sum or difference of distinct powers of 3, e.g. 55 = 3^{4} - 3^{3} + 3^{0}) leads to new insights in the theory of partitions.
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