I don't know much about the history of math or the history of physics. I don't know many famous physicists. But I do know that much of the cool math that mathematicians study comes from great physicists. Isaac Newton is famous for the invention of calculus. He was a great physicist and calculus is being studied by almost all mathematicians. Analysis is one of the major fields of study in math.

Now, I suppose it isn't fair to call Gauss a strict physicist (since he did just about everything), but he was nonetheless a very good physicist and he came up with great math as well. He is often said to be the father of modern mathematics and, from what I know of the subject, that would be an accurate assessment. I don't know precisely how famous he is in the physics world, but I would assume that he is not much less well-renowned there.

I'm really going to show my lack of knowledge on this next bit, but I'm going to go out on a limb here. I don't know how much math Einstein developed on his own, but I do get the impression that the physics he developed required a great deal of mathematics to explain it and that that kind of math is interesting both in the physics world and in the math world. Topologists almost all study Riemannian Geometry--differentiable manifolds and things like that all relating to relativity. Embarrassingly, I just had my first course in that subject this past school year even though I'm more than halfway through with my PhD.

Since this is my first post, I think I'll keep it short and not make too big of a fool of myself right off the bat.

Keith, yes, physicists and mathematicians have historically contributed to each other's fields for sure.

ReplyDeletePhysicists pay a huge tribute to mathematicians and visa versa. For example, to add to the names mentioned, how many of us could solve simple modern physics problems without the work of Legendre, Euler, Lagrange, Bessel, Hilbert, Poincaré and Fourier just to name a few?

Historically, the interplay between mathematicians and physicists have been paramount.

Witten winning a Fields medal is an excellent recent example of this interplay.

ReplyDeleteMy adviser's degree is actually in applied math (although pretty much all theoretical physics in Brittan is called applied math), so there is definitely some strong crossover.

ReplyDeleteOn another note, I recently saw a presentation by an education grad student here at CU who was contributing to a high school curriculum that combines math and science, using physics, chemistry, biology, and engineering to teach algebra, geometry, statistics, etc. Their argument was that almost all math was developed in some scientific context and trying to teach it divorced from that context is one reason why many people have such a hard time with math.

You're describing how "cool physics → cool math". The other direction is interesting as well, namely, "cool math → cool physics". For example, it's just stunning how the study of abstract group theory by Galois and Abel (for studying roots of polynomials), and later Sophus Lie, was much later discovered to lie at the foundation of both quantum theory and general relativity. It's almost too good to be true; Wigner even called it, the reasonable effectiveness of mathematics in the natural sciences.

ReplyDeletep.s. A comment on the history: I suspect Einstein discovered very little in the way of new mathematics en route to GR. Einstein apparently didn't even like diff-geom. (which was already well-developed), but was driven to ask Marcel Grossmann to tutor him on it, because of how much it simplified the physics. For some very nice history of Einstein's development of GR online, try John Norton's webpage.

ReplyDeleteBryan's right (and group theory is a great example).

ReplyDeleteRiemann, who was already named, is another example as Riemannian Geometry is the foundation of General Relativity. And if sting theory turns out to be real physics topologists will really deserve a lot of credit.

(And even if string theory is not fully correct, topology will have inspired many useful ideas in the heads of physicists.)

And Grad Student brings up a great point with Witten.

ReplyDeleteI enjoy mathematics, I was very good at it, I can remember that sometimes I was even not going to the lectures but was able to have one of the best marks if not the best one. So I will enjoy reading you Keith (even if I am not a lot in mathematics actually :) ).

ReplyDeleteP.-S. : Currently I am not doing a lot of mathematics but it can happen that I have to do some.

ReplyDeleteIt's certainly interesting. I think of "engineer" as a code word for "applied mathematicians." The big names for us are Lyapunov, Kalman, Weiner, Fourier, Gauss, Lagrange, Euler, etc. For control engineers, Lyapunov is probably the most widely recognized scientist/mathematician. If you can find a Lyapunov function...you WIN!

ReplyDeleteTo jmb275 : I use fractals for my work and Lyapunov's fractals are interesting, but I need some motivations in order to try to find a fractal which can correspond to my model (currently I wait for more acknowledgment).

ReplyDeleteIt is fair to say that physicists invented modern calculus, just as biologists invented modern statistics. Mathematical methods are seldom developed in an intellectual vacuum, but motivated by a particular need.

ReplyDeleteSturla,

ReplyDeleteThat's an interesting idea that biology had such a tremendous impact on modern statistics. If that is true, that's really interesting indeed!