Laws of Universe - are they laws of physics or rules of mathematics?

Physics is an experimental science in which we make objective observations (measurements) and discover certain rules and laws that the Universe obeys.  But after a close look at these rules (or after new experimental discoveries are made) we find that these laws are the direct mathematical consequences of more simple/broad laws. We then call new laws “more fundamental laws” and downgrade former laws to “follow from” status. Some other laws actually are just definitions of certain physical quantities, or direct mathematical consequences of such definitions (!)

It seems that if the mathematical origin of some physical phenomenon is known - then we call it a rule of mathematics, but if it is still unknown - then we call it a law of physics. To only discover later that it too has a mathematical origin.  So, is there any physics in “physical” reality, or is the whole Universe (including us) just a big mathematical illusion?

Examples of various laws of physics with the analysis of their mathematical origin, and with the insight into what mathematics is (and why it is so powerful in describing, explaining and predicting behavior of objects in our Universe) are discussed in the presentation.