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It is based on both, that is what you do not realize. Theoretical physics is not mathematics and it is not philosophy, it is instead a mixture of both. Newton described all of this in detail when he invented this field that we today call (theoretical) physics.vanhees71 said:Well, the methods of theoretical physics is based on mathematics, not philosophy.
Physics is natural philosophy based on first principles that have been mathematicized. Physics is, so far at least, the only field which has been capable of being mathematicized in such a way.