[zoogeny]

People here are giving you mathematical answers which is what you are asking for, but I want to challenge your intuition here.

In construction, grading a site for building is a whole process involving surveying. If you dropped a person on a random patch of earth that hasn't previously been levelled and gave them no tools, it would be a significant challenge for that person to level the ground correctly.

What I'm saying is, your intuition that "I can look around me and find the minimum of anything" is almost certainly wrong, unless you have a superpower that no other person has.

[whatever1]

That is true we are only good at doing it for specific directions of the objective function. The one that we perceive as the minimizing direction. If you tell me find the minimum with a direction of 53 degrees likely I will fail, because I can’t easily visualize where this direction points towards