e

e, in mathematics, irrational number occurring widely in mathematics and science, approximately equal to the value 2.71828; it is the base of natural, or Naperian, logarithms. The number e is defined as the limit of the expression (1+1/n)ⁿ as n becomes infinitely large, orIn 1873 the French mathematician C. Hermite proved that e was transcendental, i.e., not a root of any algebraic equation; this proof constituted a great contribution to the growth of mathematics. The number e is also known as Euler's number, for Leonhard Euler, who discovered the famous formula e^iπ=−1, where i=√−1, thus expressing the relationship between the numbers e, i, and π. The exponential function e^x, often written exp(x), occurs in various applications ranging from statistics to nuclear physics.

Bibliography

See study by E. Maor (1994).