What is the most “beautiful” mathematical equation? For millenia, many mathematical formulas and concepts have been described as beautiful (and some defining beauty, as the golden ratio does). In the mathematical world, the adjective “beautiful” is used in the sense that certain mathematical concepts, despite the fact they are rational and objective, are so pure, simple and elegant that they can only be described as art.
One such formula is Euler’s identity:
Renowned physicist Richard Feynman described it as “the most remarkable formula in mathematics”. What makes this array of symbols and numbers so beautiful? Firstly, it contains the three basic arithmetic operations exactly once each: addition, multiplication and exponentiation. It also connects five fundamental mathematical constants with nothing other than themselves and the arithmetic operations.
0 is the additive identity, as adding it to another number results in the original number. 1 is the multiplicative identity for the same reason as 0. Pi(π) is one of the most important mathematical constants in the history of mathematics that is ubiquitous in Euclidean geometry and trigonometry. Euler’s number(e) is the base of natural logarithms and is used widely in mathematical and scientific analysis. i(√-1) is the imaginary unit of complex numbers, a field of imaginary numbers that are not “real”, allowing for the calculation of all roots of polynomials. Euler’s identity neatly sums up the relation between these five numbers that are so crucial in the field of mathematics. It is also interesting to note that these five numbers were discovered at different points in history spanning over 3000 years.
Some people describe mathematics as a distinct language in itself. Not only that, but mathematics is considered the universal language as it is both universal and ubiquitous. If that is the case, than Euler’s identity can be considered an extremely pithy literary masterpiece.