Mathematician: I’ll add a few more comments about the Gaussian distribution (also known as the normal distribution or bell curve) that the physicist didn’t explicitly touch on. the exponential distribution, Laplace distribution, Cauchy distribution, gamma distribution, and so on.) That is a fancy way of saying that the gaussian distribution represents its own frequency components. We generally end up solving these problems by trying to maximize something related to the log of the probability distribution under consideration. If we use a normal distribution, this takes the unusually simple formwhich is often nice enough to allow for solutions that can be calculated exactly by hand.

When you want to outsmart the world, you turn to the facts. And the facts are in the science.