How much Physics should a Mathematician know?

[deluks917]

One often hears the reverse question but in your opinion how much physics should a mathematician know. Some more specific questions:

a) how much physics should you know when you start grad school (in pure math)

b) how much physics by the time you graduate math grad school

 

[Simon Bridge]

As much as he wants to.
Depends where in math he wants to go. Most of the mathematicians I've worked with have insisted that I don't tell them the physics as it just distracts them from the math. I can appreciate that because I don't want an answer in terms of lamas and corraleries ... or... whatever those things are called...

If you are going to do a lot of mathematical modelling, then some physics experience is an advantage. So ... you questions:

a) by grad school, I'd hope that the course that got you there included all the physics you need for the field you will enter already.

b) as much as you needed to graduate

These courses are usually well worked out by that level.

 

[chiro]

One often hears the reverse question but in your opinion how much physics should a mathematician know. Some more specific questions:

a) how much physics should you know when you start grad school (in pure math)

b) how much physics by the time you graduate math grad school

For pure math, I don't think anyone should know any physics. As a motivation for those seeking some application, then maybe applications of differential geometry to relativity and functional analysis to QM, but by no means should that be required in any pure graduate program.

Physics and pure math are completely different things: they both have different ways of thinking, they both focus on completely different things, and they have are put in completely different contexts.

 

[homeomorphic]

For pure math, I don't think anyone should know any physics. As a motivation for those seeking some application, then maybe applications of differential geometry to relativity and functional analysis to QM, but by no means should that be required in any pure graduate program.

Physics and pure math are completely different things: they both have different ways of thinking, they both focus on completely different things, and they have are put in completely different contexts.

I strongly disagree, although I would not go as far as V. I. Arnold to say physics is the branch of mathematics where the experiments are cheap. However, there's a whole continuum between physics and math. There isn't even a sharp division between the two fields. There are a few people in physics departments who do things essentially indistinguishable from people in math departments. So, you have mathematical physicists, more on the physics side, mathematical physicists who treat it as pure math, and everything in between.

Physics is very helpful to know. I don't know if it's essential. Depends on what you want to do. Some very educated people say you really can't understand physics without math and vice versa. I don't know how true that is.

As someone who knows a fair amount of physics, I think it does help a little with the math. So much math has its roots in physics. I think functional analysis is more meaningful to me because I know some physics. It gives me a reason to CARE about because physics is closer to reality than pure math.

In my opinion, PDE is an extremely ugly subject if it is not approached with some physical reasoning. The key examples are the wave equation, the heat equation, and the Laplace or Poisson equation.

Depends where in math he wants to go. Most of the mathematicians I've worked with have insisted that I don't tell them the physics as it just distracts them from the math.

Not at all true for me. Physics makes me care about things more and brings in more intuition and motivation. But people don't focus enough on the aesthetics of things and intuition, and that could be why they can't see the value of it.

But it goes further than motivation. Ideas from physics have had a strong influence on topology and certain other branches of pure math. Donalson and Seiberg-Witten invariants of 4-manifolds, topological quantum field theory, Chern-simons, mirror symmetry...

The fact that I know some quantum mechanics and classical mechanics is quite relevant to my future research plans, although up until now, the role of physics has been mostly to provide motivation for many concepts. Of course, maybe learning physics has slowed me down, but personally, that's not an issue for me because physics is an end in itself, which I pursue for its own sake. I just learn what I am interested into an extent, although I am trying to formulate an appropriate research direction which will make the most advantage out of my knowledge of both fields.