Time for some mathematical poetry

Reading my newsfeed this morning, I saw the Google Labs Aptitude Test. Question 12 is "What is the most beautiful equation ever derived?".

To me the most beautiful equation (derived or not, I don't care) is without any contest

e^{i * π} + 1 = 0

This equation is not a mathematical expression, it's pure poetry:

• You've got e and π which are two numbers we are not able to know (i.e. to compute exactly) but still can be found everywhere in our universe.
• You also got i which exists only in our imagination but still can describe accurately phenomenons happening in the nature.
• 1 which is the beginning of many and finally O who exists only to describe what does not exist.

When I explain to some friends what I like some much in mathematics (and to a lesser extent in computing), I show them this equation and rewrite it as:

1 = -e^{i * π}

Then it shows that something as simple to apprehend as 1 can also be viewed as something as complex and cryptic as -ei * π. They are exactly the same thing, yet they are two different entities seemingly unrelated except by the power of our imagination and intelligence.

Simplicity and complexity sometimes are differents facets of the same entity and they may differ only in how you look at the entity.