Who is better at Math, a physicist or a mathematician?

[timpani]

Who is better in Math?

I was told that a physicist may be a good autodidact mathematician, but a mathematician may be a mediocre autodidact physicist.

 

[Cruz Martinez]

I was told that a physicist may be a good autodidact mathematician, but a mathematician may be a mediocre autodidact physicist.

Most physicists who teach themselves pure mathematics are mathematicians at heart, i.e. they have the mindset and the taste for mathematical rigour that is required for high level pure math. I suppose it goes the other way around too: a mathematician can have a taste and mindset for physics, and therefore be able to teach it to himself. I think it all comes down to that really, both fields have extremely intelligent and capable people, but their personal preferences are not the same.
It might be less common for a mathematician to like physics, but I can't say if that's true for sure.

 

[Borek]

I was told that a physicist may be a good autodidact mathematician, but a mathematician may be a mediocre autodidact physicist.

And both may be mediocre cooks. Or mediocre crooks. Or whatever.

People are different, so yes, you will probably find examples for every such a statement.

 

[S.G. Janssens]

Do not exclude the other disciplines. Some engineers (Kálmán, Luenberger,...) are better at mathematics that some mathematicians will likely ever be.

Come to think of it, on this forum I go by name of an engineer, although in my mind he is more of an early numerical analyst.

 

[mathwonk]

Ed Witten, ostensibly a physicist, (but a history major in undergrad), won the highest award in mathematics, the Fields medal. Has any mathematician ever won (or deserved) a physics award? (Gauss, Riemann, Archimedes, Arnol'd?)