Leonhard Euler was a famous 18th century mathametician and physicist is possibly the greatest mathematician of all time. One formula he is known for is the Euler identity (shown on the left) which is a specific instance of Euler's general formula.

e is the base of the natural logarithm and is used to describe natural effects like a normal distribution and radioactive half-life. It is an irrational and transcendetal number.

pi is the ratio of the circumference of a circle to it's diameter. The circle or sphere is a perfectly symetical shape and this ratio of the circumference to the diameter is constant. pi is also a irrational and transcendental number.

i is the square root of -1 which is a number which cannot even be visualized. Indeed this number by itself is a paradox and is call an imaginary number.

And now the amazing part, these irrational, transcendental, imaginary and fundamental constants are related in a very simple way by Euler's identity. Starting with a irrational number and raise it to the power of another irrational number multiplied by an imaginary number and you get -1! No one can explain this mystery.

I remember it was amazing to me when I first encountered it in a class on complex variables. This relationship between these variable is astounding and profound. A reader poll conducted by Mathematical Intelligencer named the identity as the most beautiful theorem in mathematics. Another reader poll conducted by Physics World in 2004 named Euler's identity the "greatest equation ever", together with Maxwell's equations. The book Dr. Euler's Fabulous Formula [2006], by Paul Nahin (Professor Emeritus at the University of New Hampshire), is devoted to Euler's identity; it is 400 pages long. The book states that the identity sets "the gold standard for mathematical beauty." Constance Reid claimed that Euler's identity was "the most famous formula in all mathematics." After proving the identity in a lecture, Benjamin Peirce, a noted nineteenth century mathematician and Harvard professor, said, "It is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth." Stanford mathematics professor Keith Devlin says, "Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence."

If this formula is not astounding then you do not understand mathmatics deeply enough. We cannot call this formula a coincidence. We cannot call this a fluke. We cannot even say that this is just interesting. We must use adjectives such as "mystery", "paradox" and "beauty". It is not too much to call this identity "supernatural". For those who will not believe in God unless they see a miracle with their own eyes, here is that miracle. You may observe this miracle whenever you like and be amazed. If you cannot see this miracle, it is not the fault of God, it is your knowledge that must expand. Study, see, then believe.