Mathematics vs Physics degrees & Theoretical vs Computational Physics

I was on the Physics stand for Saturday’s university open day for prospective students and their parents. I got a lot of questions from prospective students who were still deciding whether to do a maths degree,  a physics degree, or maths & physics. They were doing maths and physics A levels, but unless they go for a maths & physics joint honours, they will have choose one or the other at university.

On the stand I said the standard stuff. Stuff like physics uses maths but that we physicists have a different attitude to maths, we view it more as means to an end – understanding the natural world – and don’t worry about mathematical rigour. Whereas for mathematicians, the maths is much more than a tool, it is the thing they care about, and many mathematicians are big fans of rigorous maths proofs of the sort that physicists just use.

A couple of the prospective students were thinking of going into theoretical physics and were wondering which degree, maths, physics or maths & physics, would be best. That’s a fair question, and I am not sure I answered it well. Since then I have, in the now traditional way, sought inspiration by asking Google. And I was a bit more surprised by the results than I should be, given that I am supposed to be a physicist.

For example, one of the links was to Peter Woit’s How Much Mathematics Does A Theoretical Physicist Need To Know?, which suggests knowing five advanced math topics, starting with Riemannian geometry. I know none of them. I have never even heard of deRham cohomology.

In my defence, I am basically a computational physicist not a theoretical physicist, and we computational people seem to be able to do without knowing much about cohomology. I then turned to Wikipedia which has articles on both theoretical physics and computational physics. I was interested to read that both Wikipedia and Woit when they discuss theoretical physics mostly think about particle physics, with some cosmology. Roughly speaking, their idea of theoretical physics is to discover fundamental theories for the universe, i.e., the sort of thing Einstein, Dirac and others did early last century, which nowadays often means to develop string theories and their competitors.

That is a very mathematical stuff, so a maths & physics degree or a straight maths degree, would be probably be best for careers here. But I would say that there are relatively few careers here. Even in academic physics, this is a minority activity. Many physics and maths departments have theoretical physics groups, but that is about it for employment of theoretical physicists.

Computational physics is a bit more widespread, in many areas of physics, such as condensed matter (= biggest area of modern physics, it stretches from semiconductors to water), nuclear, fluid dynamics, etc, we already know the fundamental theory but need a fair bit of number crunching to actually get this theory to make predictions for things experimental physicists can measure. And with the rise of data science as a career, computational physicists can and go apply their skills to crunching a huge range of numbers from web clicks to stock prices. And for computational physics, a physics degree may be best, although maths & physics would also work.

I guess this leads to the, kind-of obvious, conclusion that what degree you should do depends, in part, on what you want to do with it. If you are deciding between these three types of degree for a different reason than an interest in theoretical physics, please just comment below and I’ll have a think.

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