I will defer to others to write a general apology for mathematics. Here I will simply mention the reason Michael Spivak has given for writing books: namely, to learn the subject himself. Because of this, I would suggest that anything written by Spivak is worth reading.

So, why study physics? Answer: because Michael Spivak has written a book on the subject. Consequently, you now have available to you a map for understanding a subject with no less clarity than the mathematician who wrote it.