Anyone earning a degree in math, physics, or other branch of science will very likely be required to take at least one arts elective. Some dread this while others see it as an opportunity to pick up some easy credits, frequently by taking an introductory course in a language they are already fluent in. When asked, I try to steer my students toward either technical writing or philosophy.
Technical writing is an obvious choice because writing proposals and publishing one’s work are fundamental activities in most scientific careers.
The philosophy suggestion usually surprises people. Until I started teaching computer programming years ago I had no use for the subject. To me it was just some obscure topic in Greek history. I couldn’t even keep straight the difference between Socrates, Plato, and Aristotle. I knew that one was a student of one of the others and that someone was pressured into drinking hemlock for his influence on the youth of Athens. Beyond that, I was clueless.
Then a new student came along. He had a degree in philosophy but almost no computer skills. Within a few weeks he was doing very well because he had an outstanding grasp of logic. From him I learned that all philosophy students are required to learn some formal logic and that some specialize in it.
Computer science students must study logic but their required exposure to the subject is very narrow. Those in philosophy are the ones who get to see the full richness of logic as an academic discipline.
What has this got to do with math and physics? For mathematics, the obvious answer is that mathematics students spend a lot of time learning how to construct proofs. This work requires careful use of formal logic. For physics and other branches of science the value of logic shows up in not being fooled by others and, even more importantly, the most vital scientific talent of all–not fooling yourself.
Thou Shalt Not Commit Logical Fallacies offers a wonderful explanation of how we can be fooled by others and by ourselves. Imagine a world in which we had to prove an understanding of each of the identified fallacies before graduating from high school. I suspect we would all be much more demanding of those aspiring to leadership positions.