does doing math really make you smarter?

Is there any empirical evidence that doing math actually strengthens
your logical skills? It's the kind of claim you hear tossed around a
lot but I'm wondering if there are studies showing that it's true.

Of course I'm not talking about the fact that doing a particular kind
of math problem over and over will make you better at solving that
particular type of problem. I know that if you do a lot of calculus,
you'll get better at calculus. But will it make you better at solving
the type of logical/mathematical problem that you've never seen before?


A completely rigorous study would be one in which:
1) You have one group of test subjects practice on the kinds of math
problems that you think will make them smarter. The control group
doesn't engage in any kind of extra practice.
2) At the end of the practice period (which could be an hour, or
several weeks, whatever), you give both groups a set of math problems
that are completely different from the kind that you gave the test
subjects during the practice period, and are also completely different
from any type of math problem that you would normally encounter in
school.

Then you see if the test subjects who did the math practice, score
better than the control group.

.

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