It frustrates me when math explainers, and textbooks, seem to start from the "here's why our methods are insufficient to solve our problem" and fail to provide an example of the problem they are trying to solve.

What's the question this method is attempting to answer? What does an answer look like? How does this method lead to it?

> If you have ever tried to minimize a function with gradient descent

"and if otherwise, go kick sand," I guess.