So you may be wondering what makes the number e so special. Well, e is the only number where the result of the function e to the power of x remains unchanged as you calculate its derivative, and the derivative of the derivative of that, the derivative of the derivative of the derivative of that, indefinitely.

Taking the function f(x) = power(e, x) that raises e to the power of x, d/dx of f(x) = f(x) for (d/dx)(d/dx) ... (d/dx). You can plot the value of x to measure the distance traveled, the tangent of the change of distance (velocity) and the tangent of the change of the velocity (acceleration), ad infinitum. Lo and behold, the value of the tangent will always be the same, that is it will remain equal to e to the power of x.

For me this rates high on my list as one of the most amazing insights of mathematics, as it applies to nature and the universe. The number e forms a fundamental concept in physics and appears endlessly in most of literature, especially quantum physics.

You might also be interested (but have probably guessed already) to know that the number e is an irrational number, meaning that there are no two integers p and q where p/q = e.

For those interested, please see: A proof that e is irrational.