Euler's identity is considered by many to be
remarkable for its mathematical beauty.
These three basic arithmetic operations
occur exactly once each: addition, multiplication, and exponentiation.
The identity also links five fundamental
mathematical constants:
- The number 0, the additive identity.
- The number 1, the multiplicative identity.
- The number π, which is ubiquitous in
trigonometry, the geometry of Euclidean space, and analytical mathematics (π =
3.14159265...)
- The number e, the base of natural
logarithms, which occurs widely in mathematical and scientific analysis (e =
2.718281828...). Both π and e are transcendental numbers.
- The number i, the imaginary unit of the
complex numbers, a field of numbers that contains the roots of all polynomials
(that are not constants), and whose study leads to deeper insights into many areas of
algebra and calculus, such as integration in calculus.
A poll of readers conducted by The
Mathematical Intelligence magazine named Euler's Identity as the "most
beautiful theorem in mathematics". Another poll of readers that was conducted by Physics World
magazine, chose Euler's Identity tied with Maxwell's equations (of
electromagnetism) as the "greatest equation ever".
