Every piece of knowledge that a human knows is based on a few parameters. Those parameters include sense impressions, inference, and basic beliefs. For example, if I see lightening strike a tree I and see the tree fall, I infer that the tree fell because it was hit by lightening. The reason that I infer this is because I have a basic belief that when something happens (e.g., a tree falling) it happens for a reason that can be properly inferred using human reason.
Now, something as direct and observable as lightening hitting a tree and causing the tree to fall is still a belief. It is a cogent belief that we might say is a 'fact', but it is still a belief. Let's take the counter argument and say it wasn't a belief. If so, then what in the rare case that I am wrong. Let's suppose that unbeknownst to me that the glare of the lightening misled me in believing that the tree was struck. Let's say that what really happened is that lightening struck a lighting rod a few feet from the tree. Later, after investigating further, I found that the tree really fell because someone earlier had cut the tree in the intention of bringing the tree down, but because it was lightening decided to go inside just in case lightening struck. In that case, I might have paid no attention to the wind of the storm and missed entirely the wind blowing the tree at the time of the lightening bolt.
Mathematics, contrary to what you allude, is not in the business of determining the laws of nature. This is the job of science. Mathematics provides tools for science, but they are just tools. The job of a physicist is to apply mathematics and theoretical reasoning in an effort to test to see if nature really performs according to theory. However, THIS is not an absolute pursuit of truth. For that reason, it is impossible to decipher if scientific models capture the absolute truth of the situation. Hence, scientific theories are always to remain part of the set of human beliefs. We may consider them among our best and most reliable beliefs, but they are still beliefs.
Warm regards, Harv