Is math really fundamental or would it not matter if physics did not depend on math?

Question

Can you disprove this please because it's been bugging me and I don't know much about physics at all as I'm only in 10th grade. It's one of those weird thoughts but I would like confirmation to keep it off my mind: at first there were the laws of math which are fundamental and simple not complex like arithmetic. Like 2+2=4. It is universal because always 2 apples and 2 apples will give you 4 apples exactly not 5 or 6. Same for atoms. This concept exists always and is absolute. So we have something absolute. This absolute knowledge of mathematics give rise to physical laws which are compatible with these mathematical laws. Like conservation and other laws since in conservation before and after everything is conserved just like both sides of the equation in math. So math gives rise to physical laws. And these specific physical laws compatible with math gives rise to our universe.

Answer 1

Math doesn't "give rise" to physical laws. Scientists make observations, plot things like motion over time, draw straight lines through the observed points. The straight lines have corresponding equations which suggest an underlying relationship, i.e. a Law. They postulate that relationship in the form of a math equation (e.g. gravity: $F=GMm/r^2$) and compare it to predictions, then use math to derive new equations from it and continue to compare with observations, making corrections or abandoning the law of it doesn't predict well. So math is a tool to model and predict reality, but doesn't "cause" reality (that we know of).

There has been much discussion among scientists and thinkers on the "Unreasonable Effectiveness of Mathematics," which may be a topic of further inquiry for you.

You might have said "And these specific physical laws compatible with math give rise to our model of the universe," and I think most people on this site would agree. Although "model of the universe" is a misleading idea, as is the term "Theory of Everything" often used, because we really do not have a mathematical or computer model of the who universe, or anything close to it. In truth we cannot even faithfully model the turbulent airflow over a single airplane wing. What we have is a collection of models that cover incredibly simple situations, which we can stitch together to predict most types of physical systems or events, as long as they are not too complex.

Quantum mechanical models tell us how a single electron in a single atom will interact with an incoming photon, or how a proton/anti-proton pair will interact in empty space, or even how a set of electrons will behave as a group in an ideal uniform conductor lattice.

General relativity can model a system of 1 or 2 astronomical bodies, or the entire "universe" idealized as a completely uniform soup of distributed matter. But there is no model that accounts for an entire galaxy of individual stars.

So physics is a patchwork of such simple models, which have been shown to be incredibly precise when the real system observed closely matches the simple model. But the complexity quickly grows to unmanageable levels in real systems, and we resort to predictions using broad approximations (which can be quite good, if done right).