What exactly is a physicist anyway? And what’s an applied mathematician?
I’m teaching a course on the History of Physics this semester. One of the students gave a presentation today on Galileo’s contemporaries, focusing on Descartes, and came to the conclusion that this time period – very beginning of the 17th century – marked the true beginning of what we view as modern physics. We discussed this for awhile and, in the end, agreed with his reasoning and rationale. I wish to note from the beginning that this student of mine intends to become an experimentalist and not a theorist.
One of my colleagues in the Philosophy Department has given the definition of philosophy, rather broadly, as “thinking long, hard, and carefully about something” (I may be paraphrasing since it is second-hand). My students agreed that physics seemed to be the merging of that particular definition of philosophy with rigorous mathematics, as free as possible of aesthetic or metaphysical motivations. Thus their definition would be that physics is the combination of mathematical rigor with, essentially, critical thinking and logic. Note that this is a broad definition of physicist that goes beyond simply the physical sciences. But this helps to explain why so many physicists have found their way into such diverse fields throughout history including biology, economics (there is even a burgeoning and respected field known as econophysics that uses physical models to make economic predictions), political science, etc.
I then asked what an applied mathematician was. I was curious about this because I’m one of those anomalies to whom many labels apply. I have a PhD in math, a master’s in physics, and a bachelor’s in engineering. We finally agreed to settle on the idea that a physicist is someone who works from the physical problem to the mathematical model, usually in search of a mathematical model that best describes a given physical problem, while an applied mathematician works in the other direction, beginning with a mathematical model or theory and finding physical problems and systems to which it may be applied. These are, of course, broad generalizations, but it gives the basic idea. See the figure below.
Oddly enough, it still doesn’t provide a label for yours truly since I’ve taken both approaches. But the student who led the discussion today pointed out that, while he was at Jefferson Lab this summer, he worked with a guy who was a physicist who regularly partnered with applied mathematicians. This guy seemed to confirm this idea since, given both approaches and abilities in a single situation, you’re more likely to find a match between the math and the physical phenomenon (or more rapidly find a match, perhaps). In other words, he’d often present the mathematicians with a physical problem and they’d say, “oh, yeah, sure, we can model that with this…” A little simplistic, perhaps, but interesting to contemplate nonetheless. Any thoughts?