You Can't Understand Physics Without Understanding Its Math and I'm Certainly Too Dumb to Understand the Math
I'm not even qualified to make this point!
In 2013 or maybe 2014, during summer break from my PhD program, I went to a party in Chicago. It was one of those grad student parties that was simultaneously insufferable and invigorating, where everybody was giving you their best material like a nervous potential SNL cast member putting together an audition tape but also where what was being said was often genuinely brilliant. It’s just one of those many aspects of grad school where the annoying meets the sublime.
There I met a guy who was getting his PhD in math at another university. His research involved using extra-dimensional geometry to try and resolve some sort of fundamental incompatibility in physics, which of course was not just beyond my ability to understand but which defied my attempts to define what exactly I wasn’t understanding. (How could the existence of certain kinds of geometry resolve a physical question? I didn’t and don’t know!) Which was fine. I had absorbed Purdue into my bones, and Purdue is a big constantly-churning engine of math and science and engineering, most of which I also could never understand. Purdue’s campus has a beauty to it that you can discover, if you try, but it’s not beautiful like Indiana U’s campus because Purdue is made of brick both physically and emotionally and, like, ideologically. Anyway - I was used to barking out a self-deprecating laugh and admitting all that I didn’t understand. But this guy pressed a little deeper. He was a real character, a Black Frenchman who proved to have idiosyncratic politics and a deep Euro-chauvinism that was both obnoxious and charming.
After doing the requisite amount of admitting that I knew nothing, I told him that I read physics books and watched YouTubes and got the standard popular science accounts of where the field was. I expected him to dutifully say “yes yes, quite right,” or whatever, to be condescending but vaguely in favor of learning about physics even as we both understood that I knew nothing. But this was not his reaction. On the contrary, he was utterly adamant: all of those popularizations, in his view, were so inherently distorted compared to the actual physics - compared to the math - that they were not just insufficient, but actively wrong. He was very, very convinced that all of the ways that physics is typically distilled down for a popular audience result only in greater ignorance. It wasn’t that the way the math was conveyed in math-free terms was wrong; it was that the very project of trying to explain any physics beyond the most basic Newtonian mechanics, without math, was inherently wrongheaded.