Further to my post a couple of weeks ago about BIG idea physics, I think I should add a further one. To do so I’ll use the words of one of my favourite physicists*, Paul Dirac.
It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power…
and then, later on in the same paragraph
One could perhaps describe the situation by saying that God is a mathematician of a very high order+
In other words, there’s something that intrinsically links physics and mathematics. To fully grasp physics, one has to grasp mathematics as well. Now, this is a bit controversial given the desire of many educationalists to divorce the two subjects and neatly package-up each in complete isolation of the other. Indeed, I’ve exercised some double-think on this: On the one hand I’ve previously published work looking at the relationship between the two, but on the other I actually go to some lengths to reduce the maths content of my physics classes, mostly to make them accessible to more students. But while I maintain that physics is not the same as applied mathematics, and that physics is not explained by maths, and that one can indeed grasp a lot of physical concepts without delving into the mathematics of them all, there is indeed an underlying descriptive mathematical structure to how physical things behave. And, as Paul Dirac said, it can be really beautiful. If you miss the maths, you miss that dimension. Perhaps learning physics without maths is like viewing the world in black-and-white. You see enough to function, but you miss out on something BIG and beautiful.
*He’s a favourite physicist because I worked with his relativistic formulation of quantum mechanics during my PhD.
+Written by Paul Dirac in 1963. An interesting quote since Paul Dirac was an enthusiastic atheist.