It’s often said that if you want to understand the universe, you need to think in equations. While mathematics can easily set off a high school flashback, it’s often only the raw power of numbers that have the ability to express the inexpressible complexity and beauty of our universe.

So, surely with that in mind, BBC Earth asked a group of mathematicians and physicists what their favourite equation was. Their picks included: The Dirac equation, Riemann's formula, Pi (how it relates to the circumference of a circle), and Einstein's field equation.

This shortlist was then put up for the public to choose their favourite in an online poll. After nearly 60,000 votes, the winners were announced back in January, but as it's Pi Day we thought we'd take another look.

The most popular equation, with nearly 20,000 votes, was “the Dirac Equation.” The equation is loved both for its elegance and as a symbol of 20th century physics. The equation was proposed in 1928 by the British physicist Paul Dirac, in an attempt to weld together ideas of Einstein’s relativity with quantum mechanics. In essence, Dirac managed to explain how electrons behave when they travel close to the speed of light. This work went on to explain and predict the existence of antimatter; the idea that every particle has a mirror-image antiparticle. This, of course, turned out to be right on the money.

Coming in at number two was “Euler’s Identity”. The equation was first described in the 1748 book, “Introduction to Analysis of the Infinite” by Leonhard Euler. This cult favorite of equations has cropped up in “The Simpsons” on more than one occasion, and was also Richard Feynman's personal favourite, describing it as "the most remarkable formula in mathematics."

It combines five of math’s most fundamental constants: 0, 1, e, i, and π. On top of that is has three mathematical operations: addition, multiplication, and exponentiation. It also has a lot of applications outside the ivory tower, from communication, meteorology, medicine, navigation, energy, robotics, manufacturing, and finance. These characteristics have given the equation a reputation of being the key to something an infinitely connected universe and something deeply “transcendental”. 

The third most popular was Pi (π). It’s beauty stems from the idea it is simultaneously simple yet profoundly deep. Most simply put, the irrational number Pi explains the relationship between a circle’s diameter and its circumference. That number is 3.141... and so on, to infinity, in a non predictable pattern.

^{A visualization of how Pi works. John Reid/Wikimedia Commons}

Here’s the rest of the results, going from most popular to least: 4) Einstein's field equation 5) Riemann's formula 6) the wave equation 7) Euler-Lagrange equation 8) Bayes's theorem 9) a "simple" arithmetic progression 10) Hamilton's quaternion formula 11) the logistic map and 12) the Yang-Baxter equation. 

Make sure you check out BBC Earth for more information behind these little mathematical windows to the universe.