As Ivan said, Mathematics is a tool which can be used to argue about the world, but to do so and to know the value of the conclusions you have to be careful about how it's done.

You can map the physical world to a mathematical model and make lots of provably true calculations about that model.
The problem is that unless the mapping is correct, the conclusions made by those calculations won't map back to the real world.

Ivan's example of mixing water and alcohol is an example of what can happen if the model is wrong.
Model assumption: mixing liquids can be modeled by adding their volumes.
Real world: Two beakers with water and alcohol.
Mapping: We look at the water and finds it reaches the 3ml mark, this we model as 3ml of water; we similarly measure the alcohol and model it as 4ml of alcohol
Mathematical operation using the model: We model mixing them, so 3ml+4ml=7ml
Mathematical result: 7ml of diluted alcohol.
Mapping back to real world: If we mix those we should get 7lm of diluted alcohol.
Now comes the science part: we try actually mixing them, then measure the result.
Oops, there is less than 7ml.

This does not mean the mathematics are wrong, it means our mapping from the physical world to mathematics was wrong.
In this case by inadequately modeling the result of mixing two liquids.

Mathematics can never show anything to be true, it can only show the expected consequences of our models, which can then be tested against the real world to see how well the model fits.

Though it's not often explained that way, the main part of learning basic physics is to learn the terms commonly used for this mapping and the basic models used.

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