Euler’s Number

2.71828182846…

Episode #2 of the course “Most important numbers in the world”

While computing questions of compound interest in the 17th century, John Napier and later Jacob Bernoulli discovered a natural limit to the rate of the interest. It was less than 50 years later when both unpublished and published works began to feature and theorize on this logarithmic constant, but it was Swiss mathematician Leonhard Euler who gave the term its signifying “e.” Therefore, it is commonly known as Euler’s number, but it does not have the same value or applications as Euler’s constant, signified by the Greek letter Gamma (γ) or the calculation known as Euler’s identity.

“E” is one of the most important mathematical constants along with Pi, 0, 1, and i. It is the basis of the natural logarithm, expressed as ln. As an irrational number, “e” does not specifically describe the relationship of any two integers. It is also a “transcendental” number, meaning it is not a root number of any non-zero, rational number. Although infinite, “e” is often approximated as 2.71828 for simple calculations.

In addition to compound interest, “e” is used in probabilities, such as when calculating the rate of return in a randomized statistical system like a slot machine, or in the probability of standard and normal distributions. E is also present in calculus to calculate differential equations with exponential limits and in trigonometry to calculate functions of overlapping shapes. Because it is such a foundational, difficult number, it has become something that contemporary mathematicians and computer engineers often reference and pay tribute to in pop culture.

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