Are Mathematics the language of the universe? I am a high school student and next year i am going to be a physics major, so this year i put all my effort on physics and mathematics, since it a great tool for physicists. 
But now i wonder, in creating a new physics theorem , can we rely solely on mathematics? I mean have there ever been published theorems that are mathematically valid but do not apply in the real world? / Is a mathematically valid model necessarily a real model, or a theorem is only proven by experimental data?
 A: Good question. When we build a theory we start from a couple of assumptions that we BELIEVE that are valid, i.e. in the everyday life, and/or in previous experiments, they were confirmed. From this point we use mathematics and obtain other results. As long as we need our new results for proving even more theorems, things may be fine. But a physical theory is worth NOTHING if not experimentally confirmed.
And if the experiment says otherwise than our theory, we begin to look which assumption may be incorrect.
We have all the time such problems in building theories (models) for describing the world. In the microscopic world (atoms, electrons, protons, etc.) we have bad surprises. And it is not simple to clarify them, because these tiny particles are so delicate that our measurements disturb them.
In trying models of the universe we also have problems. And it is difficult to elucidate because information that we get from galaxies, tells us what happened with them an enormous time ago.
So, prepare yourself, the life of a physicist is not roses (but it is a great challenge).
Good luck !
A: Newton described his theories with maths, and they worked great, until Einstein came along and found that as objects approached the speed of light, Newwton's maths broke down.
Empirical evidences trumps theory.
