A few days ago, the BBC introduced a series of posts in which they asked mathematicians and physicists to share their favorite equations. It’s a fun list, and the original post can be found here.
One of the equations selected is known as Euler’s identity, and is written as:
.
In this equation, “i” is a so-called imaginary number, defined such that . This expression, which is a special case of a more general one known as Euler’s formula, is often considered to be mathematically beautiful because it includes five of the most important mathematical constants: 0, 1, i, π, and e.
An interesting discussion arose on Twitter when Evelyn Lamb posted the following in response:
I kinda agree with her, though maybe not for exactly the same reason! For me, as a researcher who sort of balances on the line between theoretical physics and applied mathematics, “beauty” in mathematics comes from an expression that really shows you something, and leads to insights and a sense of wonder. Euler’s identity doesn’t really do it for me anymore; it contains some insight, but its main attraction is the fact that it happens to include many mathematical constants.
This led to a gauntlet of sorts being thrown down by On This Day in Math!
https://twitter.com/OnThisDayinMath/status/690569843913940993
A fair question, and I thought I would share some of the equations that I find beautiful, taken from both math and physics.





