Without the philosophy to back it up how can you justify your belief in the mathematics?
Sure, these articles could be fun to read, but one does not really expect to have more practical knowledge after reading them. How would you use Hume’s arguments to help you learn the theory of relativity better?
And it’s not just in physics. I can make the same claim in almost any field of science that values results over cheap talk. In game theory for example, does philosophy help you come up with something as magnificent as Nash Equilibrium? No, but Kakutani’s theorem does. Learn the math and practical knowledge, the rest is a waste of time.
See this link titled “The Purpose of Philosophy”: http://assets.press.princeton.edu/chapters/s10113.pdf