Physics Research vs. Math Research

[Dishsoap]

Greetings all,

I've had the privilege over the past 3-4 years to do both physics and math research. I'm considering both for a career, and would like to know if my experience is the norm. My physics research is in QFT (mostly modelling the pair-creation process), and math research is in graph theory (finding triangle-free Euler tours in a metric crapton of special cases).

In my experience, physics research relies mainly on ability whereas math research requires more intelligence.

I've really excelled in physics research (at least at an undergrad level) because I'm dedicated to my work. Learning physics, math, and programming and being able to apply them is what it all boils down to. If you don't know something, look it up. It's hard, but your success is dependent on time and effort.

In math (maybe this is particular to graph theory), it requires intelligence. Problem-solving techniques are useful, but don't get you all that far. You need to be able to look at a problem, and deduce a method to solve it which you haven't used in any prior problems before.

Again, my question is this: is my experience typical of math and physics research? As your field increases in "purity" (i.e., chemistry -> physics -> math), does research rely more on intelligence than brute-force effort?

 

[homeomorphic]

I've only ever done math research, but I suspect your experience is specific to the particular things you were working on in each case.

 

[radium]

Physics research largely depends on creativity and interpreting results. You have to be able to understand what something physically means about a system. For example, in the '70s two physicists did a calculation that predicted the QHE, but the link between gauge invariance, quantization, and topology was not found until the '80s. This eventually led to people realizing that states of matter were not just classified by symmetry but also topology. This led to the discovery of topological insulators when two physicists realized that introducing a spin orbit term to a gapless system like graphene (quantum spin Hall effect) could be analogous to having two copies of the Haldane model, one for each spin. In this sense, spin orbit acts like a magnetic field affecting each spin and can cause band inversion which leads to a system having nontrivial topology. Time reversal is not broken by these effective magnetic fields, it is preserved overall since the spin orbit effective is in opposite directions for each spin. It also wasn't clear what topological invariant this corresponded to and how to calculate it. They spoke with mathematicians who could prove there was some topological invariant, but it was the physicists who learned how to calculate it.

In strongly correlated systems with no long lived quasiparticles, it is currently very unclear how you can get things like thermal partition functions since conventional methods break down. This lead to the use of the AdS-CFT correspondence in some cases which is not widely spread throughout the community.

So no, in that sense I don't think math and physics research are that different. It all comes down to understanding what has been done before at such a deep level that you build the intuition required to solve unknown problems. They both require creativity and unconventional ways of thinking. For example, you will have some people whose way of thinking is very suited to thinking about certain types of problems.