>>11290572Mathematics is that statement of truths that are derived logically from some axioms. Basically, philosophy with a notation system.
Physicists create a story about something physical based on an abstract idea, like a "force" or a "field", and then use the logically-derived theorems of math to represent the outcomes of those abstract ideas as they apply in the real world. Newton's kinematics equations are a good example of this: using the abstract idea of motion through space and time, he was able to model acceleration, velocity and change in position by putting those ideas in mathematical terms. The logical nature of algebra means that any calculations done within those equations, assuming that the conception of time and space that Newton used to invent them is correct, will produce a result that accurately reflects what happens in the real world.
Basically, Physicists use math to get hard numbers out of their ideas that they can use to predict things, however they don't always need math to come up with their ideas about the world or even to qualitatively test them. For example, the only proof I need of Newton's third law (taking as an axiom that Newton's idea of a force is correct) is to push my hand down on my table and realize that neither object in the table-hand system is moving.
I can then invent some units of measure to define the "forces" at play, and using my abstract conception of a force and of mass and of acceleration, create an equation which models the most basic form of the interaction of those variables: F=ma.
TL;DR: math and science are related in that physicists use math as a tool to logically deduce the outcomes of their ideas about the physical world, by taking those ideas as axioms and adhering to the logic of the math
