What is the most beautiful equation you have ever seen?


This is supposed to be one of the Google interview questions in the book Are You Smart Enough to Work at Google. I immediate thought of the equation e^(i*Pi) = -1. The Euler’s equation is a simple and neat equation that is also quite important for engineering students. But it is “beautiful’ to me because of a beautiful memory I have related to this equation.

It was on a Saturday afternoon at home when out of nowhere someone asked me the question “what is e to the power of i pi”. I did some mental calculations (because I couldn’t remember the equation off-hand) and answered -1. He smiled and said “you are smart”. I’m not sure if being able to answer a simple question like this is considered as smart, but it is perhaps one most enjoyable experience to have geek talks with someone who shares the same interests and is also a geek like me. It always a sometimes a very scientific or “geeky” thing can be made beautiful because of a wonderful memory shared with an important person in life.

Beauty is really a subjective matter. For me beauty is something that relates to our memory, it is unique and personal because no two people have the same memory, even if it’s of the same event.

I was surprised to see that the exact same equation is actually the canonical Google answer to this question. An interesting and amusing answer given by Richard Feynman is U = 0. His argument is that everything in the universe can be reduced to this equation. Euler’s equation, Einsteins’ equation, Schrodinger’s equation all add up to 0. Of course he was half-joking, but that is as simple as an equation can get.