I'm not talking in generalities. I'm talking about the standard inner product space on R^n that most people use (either implicitly or explicitly) every day.

You are right that the normal distribution is not continuous because of the CLT. That was a typo. I meant "most important continuous" distribution.

Yes, other exponential distributions are convenient to work with, but the Gaussian maximum-likelihood estimate has a closed-form expression defined with just linear algebra. That's really damn nice in my opinion.

The point is that distance (in most real-world applications) is equivalent to the length of the hypotenuse of a right triangle in Euclidean space. So in my opinion, yes, high-school trigonometry governs a lot of advanced mathematics, including in statistics and machine learning.

Call it numerology if you want, I'm just trying to get people excited about math here.