Note: Despite being on arXiv, this article doesn't presuppose any significant knowledge (other than a high school reading level).
I found this a few months ago while browsing arXiv. I very much enjoy philosophy, and did so before reading this article, but I was always discouraged to hear fellow STEM students being so apathetic towards it, especially in my physics classes. It's been tiring defending philosophy from the assault of my peers, and I think de Haro establishes why the two fields are better friends than enemies.
If this article sparks an interest in the philosophy of science, then this article is a good (albiet very basic) overview. For philosophy of mathematics, this is best, but presupposes familiarity with certain concepts and symbols from basic logic. If you're really interested, then Thinking about Mathematics by Stewart Shapiro is widely considered the best introductory Philosophy of Mathematics textbook; while Theory and Reality by Peter Godfrey-Smith is widely considered the best text for introductory Philosophy of Science. You may purchase those books or "find" them quite easily for free.