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Napier's e - Introduction

Amy Shell-Gellasch (Beloit College)

If you read John Conway and Richard Guy’s entertaining romp, The Book of Numbers [4], you will notice something odd on page 25. That is unless you are British, and then you probably will not notice anything at all. The curiosity is that they refer to e, the transcendental number 2.71828…, as “Napier’s constant.” Some might ask, Didn’t Euler discover e? In fact isn’t the “e” for Euler? Well, in truth, the answers to these questions are “not exactly” and “no.” That, like any other good mathematics problem, leads us to two new questions: “How much credit should Euler get for the discovery of e?” and “What role did Napier play in the discovery of Euler’s number?”

After π, e is probably the most well known mathematical constant. Everyone uses e to denote 2.718...; in fact, it is often referred to as Euler’s number. However, some people, notably the Brits, refer to it as Napier’s constant. How can something so universally known have two different names? Leonhard Euler is traditionally credited with naming this constant, and thus often assumed to be its discoverer. How and why mathematical objects get named after people, while others do not, is often a quirk of history. In our case, the story of e does not start with Euler; it actually ends with him. The trail back to the first appearance of what we call Euler’s number is filled with many interesting people and sidetracks along the way. Please join me on a light-hearted trip back through time to when e was young.

Amy Shell-Gellasch (Beloit College), "Napier's e - Introduction," Convergence (April 2010), DOI:10.4169/loci003209