The number e, also called the natural number and Euler’s number, starts with the six numbers 2.71828 and extends into infinite more decimal places. Mathematicians indicate the various appearances of e in natural patterns, but its more practical usage appears in calculations of exponential growth, including the continuous compound interest formula A = Pert.
We may credit Scottish scientist John Napier (1550-1617) for introducing the idea of e in his efforts to create a model to simplify multiplication by transforming multiplication into addition. This idea would eventually promulgate in the logarithmic functions of today’s mathematics, and their addition property, whereby logb(xy) = logb(x) + logb(y).
Back to e, Napier himself did not define or explicitly acknowledge the number. This task passed to Gottfried Leibniz (1646-1716), one of the founders of calculus, who called it b. Its present designation as e comes from Leonhard Euler (1707-1783), who also played with the imaginary number i. 
Today computers can calculate e to millions if not billions of decimal places, saving mathematicians much time and agony. Nevertheless in the beginning the value of e was hand-computed.
A friend of Leibniz, Jacob Bernoulli (1655-1705) drew close to its discovery when he tried to solve during his investigation of compound interest, and determined that the answer lay between 2 and 3.  Euler, in his Introductio in Analysin infinitorum, found the real value of e using this limiting process. He also used summation to prove its value, in the equation .
Later calculations by Euler and French mathematician Charles Hermite (1822-1901) confirmed e as an irrational and transcendental number, meaning that one cannot state e as the quotient of non-zero integers p and q nor as the root of a single variable, non-zero polynomial equation with integer coefficients.
e ranks as one of the five most fundamental numbers of mathematics, falling in beside i, π, 1, and 0. In a previous post, I discussed the history and meaning of the number i. A future one will deal with π. In a final post, we will bring these five numbers together in the remarkable equation known as Euler’s identity.
 The number e