Concepts

e (Euler's Number)

the letter E, said as its own name

Also Known As Napier's Constant

Citation Formats

General Reference

Mathematics Atlas. "e (Euler's Number)." Accessed August 30, 2026. https://mathematics.interactiveatlas.org/concepts/e-eulers-number.

APA Style

Mathematics Atlas. (n.d.). e (Euler's Number). Retrieved August 30, 2026, from https://mathematics.interactiveatlas.org/concepts/e-eulers-number

BibTeX

@misc{mathematicsatlas-e-euler-s-number,
  author = {Mathematics Atlas},
  title = {e (Euler's Number)},
  year = {2026},
  url = {https://mathematics.interactiveatlas.org/concepts/e-eulers-number},
  note = {Accessed August 30, 2026}
}

The base of the natural logarithm, approximately 2.71828, and the unique number whose exponential function is its own derivative, which is why it appears throughout calculus, compound growth and decay, and probability. Jacob Bernoulli encountered the underlying limit implicitly in 1683 while studying compound interest taken to its continuous extreme, but it was Leonhard Euler who studied the constant systematically, proved it irrational, and gave it the letter e, first in unpublished work from 1727 to 1728 and then in his widely read 1748 Introductio in analysin infinitorum, which made the notation standard.

Facts

Origin Year

1727 1

Dates Euler's earliest known use of the letter e for the constant, in unpublished work; Jacob Bernoulli had encountered the underlying limit implicitly in 1683 without naming or systematically studying it.

Cross-Tradition Connections