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Let's assume that I were looking for someone academic and intelligent -- and along came a mathematician and a physicist, and I'd have to choose between the two. Which is valued more, and why?

I ask this because we get problems in mathematics that are very textbook-related, and we are asked to solve problems using mathematical models every once in a while. Whereas problems in physics seem to require much more thought, to be honest. I have also always been in awe of how much a physics teacher knows compared to a mathematics teacher -- why is this? I ask this because pretty much every one of my peers agrees.

So which is better -- a mathematician, or a physicist?

Thanks.