The number e is a constant approximately equal to 2.71828 and is the base of the natural logarithm: the unique number whose natural logarithm is equal to one.

e is an irrational number as it cannot be represented as ratio of integers.

e is sometimes called Euler’s number after the Swiss mathematician Leonhard Euler or as Napier’s constant. However, Euler’s choice of the symbol e is said to have been retained in his honor. The constant was discovered by the Swiss mathematician Jacob Bernoulli while studying compound interest.

The first references to the constant were published in 1618 in the table of an appendix of a work on logarithms by John Napier. However, this did not contain the constant itself, but simply a list of logarithms calculated from the constant. It is assumed that the table was written by William Oughtred. The discovery of the constant itself is credited to Jacob Bernoulli in 1683, who attempted to find the value of the following expression (which is in fact e):

The first known use of the constant, represented by the letter b, was in correspondence from Gottfried Leibniz to Christiaan Huygens in 1690 and 1691. Leonhard Euler introduced the letter e as the base for natural logarithms, writing in a letter to Christian Goldbach on 25 November 1731. Euler started to use the letter e for the constant in 1727 or 1728, in an unpublished paper on explosive forces in cannons, and the first appearance of e in a publication was in Euler’s Mechanica (1736). While in the subsequent years some researchers used the letter c, the letter e was more common and eventually became standard.