Just in case you are not joking and for anyone not familiar with the terminology: Physics, and a lot of the hard sciences, are often broadly divided into "theoretical" and "experimental" halves. Experimental physicists design and run experiments, i.e. they "get their hands dirty", or at least the hands of their graduate students and post-doctorates. Their end goal is to find some actual fact about the actual universe, usually a quantified measurement. Theoretical physicists, on the other hand, create theories: mathematical and conceptual models that hopefully explain how or why the universe is the way it is. Ideally, the created theory not only explains the measurements that the experimental physicist has already observed, but also predicts the results of new measurements not yet observed.
I majored in both math and philosophy. I know many people who hold the exact opposite opinion from you, placing high value on math and considering philosophy a complete waste of time.
Certainly the quality and focus of instruction is a huge factor in determining how much a student enjoys the subject as well as how much long term benefit they receive from it. I've had both math and philosophy classes that I loved and many that I hated.
I think the largest benefit to the most people would come from focusing on where math and philosophy meet and overlap: logic, analysis, how to create and evaluate an argument/proof, the limits of human understanding, etc. Both math and philosophy have much to say on these matters. By focusing on both disciplines, maybe it will be easier to avoid reducing math to boring memorization of computational rules and philosophy to "pie in the sky" mental masturbation detached from all reality.