I've heard so many horror stories....

[clope023]

Well I think the biggest thing is that physics requires you to understand math at a higher level conceptually.

Still the purview of the mathematicians, plenty of physicists are the shut up and calculate type so not as much higher level conceptual understanding as you might think.

 

[radium]

Of course mathematicians will think most physicists don't do math rigorously. In the most abstract areas of math they never calculate anything. For things like the quantum Hall effect, mathematicians could tell you that the system in topologically nontrivial. However, if you asked them about calculating the hall conductance using this, many would not be interested at all. In fact, I highly suspect that my friend doing his math PhD may not even know how to use Mathematica.

Physicists use math by balancing of rigor and physical intuition in a way that allows us to both use math to understand physics and physics to understand math, which I think is a very useful advantage.

 

[George Jones]

I think the mathematics where you wade through the infinite sequence of definition, statement, proof, remark, definition, ...

I think that a physics student's exposure to this is dependent on the student's geographical location.

Why is location a determining factor?

Program details vary from country to country. For example, physics programs in continental Europe tend to place more emphasis on abstract/pure mathematics than do programs in Britain, which in turn tend to have more emphasis than do programs in North America. Again, these are generalizations, and there can differences at different schools in the same country.

Another difference in mathematics exposure for physics and engineering students in North America is that physics students do a double major or major/minor in mathematics than engineering students do. I took courses in real analysis, measure theory, functional analysis, topology, and abstract algebra, even though my physics program did not require me to do this.