In the prologue to his *Real and Complex Analysis,* Walter Rudin states matter-of-factly that $\exp$ is the most important function in mathematics (take note, not merely in analysis). This looked so incredible to me, and too much to claim (out of the infinite variety of conceivable mathematical functions extending beyond mapping subsets of $\mathbb{C}$ to other such subsets) that I began to wonder if this sentiment is a common one (I heard a math prof saying it's the second most important function -- he said this only as an afterthought; he had indeed claimed that it was the most important) and if so, what could so distinguish this function like this.

So, my question is twofold:

1. Do you think, or is it common knowledge to mathematicians, that the exponential function is indeed the most important in all of mathematics?
2. If so, why is this the case? What could make it more important than all the conceivable and inconceivable functions (linking arbitrary pairs of sets) out there?

Thank you.