Are math kids really smarter than everyone else?

I was wondering whether I inappropriately conflate mathematical reasoning ability with intelligence. While I don't actually think
intelligent <=> good at math,
I have been accused of having various biases, including

• Having (perhaps disproportionately) large amounts of respect for people who are good at math.
• Thinking someone who is very good at something else (writing, art) must also have the ability to be good at math if they tried (or perhaps they already are good at math).
• Thinking someone is smarter than me because they are better than math.

This heuristic I have developed makes a lot of sense given that the "math kids" at Harvard were really the best math kids in the world. Since being the best math kid in the world is highly correlated with being good at other things, I came away from undergrad with the impression that people who are good at math will school me in any subject. Taking chemistry? The math kids in the class will probably crush the premeds. English concentrator? You probably can't even tell who the math kid in your section is, s/he speaks and writes so well.

In summary, I don't think it's actually true that math kids are smarter. Different people are good at different things, and if someone is extremely good at one thing it is likely that they 1) have had a good education and/or 2) are "smart" in general, and as a result will be good at many other things. (It is not so unreasonable to think someone very good at music should also have the aptitude to be good at math!)

How much natural aptitude and education affect how "smart" someone seems is the subject of a future post.