Editing Euler's identity (section)

==Mathematical beauty==
Euler's identity is often cited as an example of deep [[mathematical beauty]].<ref name=Gallagher2014>{{cite news |last=Gallagher |first=James |title=Mathematics: Why the brain sees maths as beauty |url=https://www.bbc.co.uk/news/science-environment-26151062 |access-date=26 December 2017 |work=[[BBC News Online]] |date=13 February 2014}}</ref> Three of the basic [[arithmetic]] operations occur exactly once each: [[addition]], [[multiplication]], and [[exponentiation]]. The identity also links five fundamental [[mathematical constant]]s:<ref>Paulos, 1992, p. 117.</ref>
* The [[0|number 0]], the [[additive identity]]
* The [[1|number 1]], the [[multiplicative identity]]
* The [[pi|number {{mvar|&pi;}}]] ({{mvar|&pi;}} = 3.14159...), the fundamental [[circle]] constant
* The [[e (mathematical constant)|number {{math|''e''}}]] ({{math|''e''}} = 2.71828...), also known as Euler's number, which occurs widely in [[mathematical analysis]]
* The [[Imaginary unit|number {{math|''i''}}]], the [[imaginary unit]] such that <math>i^2=-1</math>

The equation is often given in the form of an expression set equal to zero, which is common practice in several areas of mathematics.

[[Stanford University]] mathematics professor [[Keith Devlin]] has said, "like a Shakespearean [[sonnet]] that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence".<ref>Nahin, 2006, [https://books.google.com/books?id=GvSg5HQ7WPcC&pg=PA1 p. 1].</ref> [[Paul Nahin]], a professor emeritus at the [[University of New Hampshire]] who wrote a book dedicated to [[Euler's formula]] and its applications in [[Fourier analysis]], said Euler's identity is "of exquisite beauty".<ref>Nahin, 2006, p. xxxii.</ref>

Mathematics writer [[Constance Reid]] has said that Euler's identity is "the most famous formula in all mathematics".<ref>Reid, chapter ''e''.</ref> [[Benjamin Peirce]], a 19th-century American philosopher, mathematician, and professor at [[Harvard University]], after proving Euler's identity during a lecture, said that it "is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth".<ref>Maor, [https://books.google.com/books?id=eIsyLD_bDKkC&pg=PA160 p. 160], and Kasner & Newman, [https://books.google.com/books?id=Ad8hAx-6m9oC&pg=PA103 p. 103–104].</ref>

A 1990 poll of readers by ''[[The Mathematical Intelligencer]]'' named Euler's identity the "most beautiful theorem in mathematics".<ref>Wells, 1990.</ref> In a 2004 poll of readers by ''[[Physics World]]'', Euler's identity tied with [[Maxwell's equations]] (of [[electromagnetism]]) as the "greatest equation ever".<ref>Crease, 2004.</ref>

At least three books in [[popular mathematics]] have been published about Euler's identity:
*''Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills'', by [[Paul Nahin]] (2011)<ref>{{cite book |last=Nahin |first=Paul |title=Dr. Euler's fabulous formula : cures many mathematical ills |date=2011 |publisher=Princeton University Press |isbn=978-0-691-11822-2 }}</ref>
*''A Most Elegant Equation: Euler's formula and the beauty of mathematics'', by David Stipp (2017)<ref>{{cite book |last=Stipp |first=David |title=A Most Elegant Equation : Euler's Formula and the Beauty of Mathematics |date=2017 |publisher=Basic Books |isbn=978-0-465-09377-9 |edition=First }}</ref>
*''Euler's Pioneering Equation: The most beautiful theorem in mathematics'', by [[Robin Wilson (mathematician)|Robin Wilson]] (2018).<ref>{{cite book |last=Wilson |first=Robin |title=Euler's pioneering equation : the most beautiful theorem in mathematics |date=2018 |publisher=Oxford University Press |location=Oxford |isbn=978-0-19-879493-6 }}</ref>