...and this is why no one needs to care about philosophy. If philosophers insist that philosophy needs neither empirical evidence nor formal proving, then all that is left is made-up bullshit.

There are plenty of people doing actual, real, non-made-up research that might be called philosophy, but since they have evidence and formal logic to prove their ideas, they generally don't have to call it philosophy.

This attitude defeats the scientific method! There’s a motivating state of inspiration prior to evidence collection. It’s the hunch. Every scientific development begins at a hunch.

More or less, what I’m referring to above, is the generalization of this “hunch”.

This is called a "hypothesis", a concept which science doesn't need philosophy to define.

As I said before, sure, you could call this philosophy, but a philosopher without any practical science experience isn't going to have anything interesting to say about it, so I'd just as soon call it "science" and cut the unqualified opinions out of the conversation.

If motion of matter can be formalized with mathematics, this rules out supernatural processes. How would you derive this conclusion without mathematics? Philosophic conclusions are often broad, so naturally they use all available tools to draw insight from.

I suppose certain types of stupidity and/or ignorance could also derive that conclusion, tools which I consider important for philosophy as well.