"I have heard that many of the smarter Americans go into medicine or the law and that is why there are so few Americans in engineering. Is this true?"

No. It's not that the smart ones are, in particular, not going into science and engineering. It's that more _people in general_ are going into things like law, the financial sector, etc., which means that statistically more of the really good people will go in those directions as well (although we can, of course, point out that someone who is good at law or finance might not be good at engineering or science, and vice versa). Science and engineering no longer have the draw they used to, particularly after the tech bubble burst.

I don't really know why this is. Could be a lot of things. Could be that we're more materialistic, and that yes, you can ultimately make more money in those sectors (although most of the people I know who graduated from law school are fleeing the practice of law like rats from a sinking ship). Could be that people used to go into science because it was more prestigious and indeed patriotic to do so after Sputnik scared the living shit out of us. Nothing like a hostile nation launching something over your heads for the first time to convince you that falling behind technologically could leave you in the middle of mushroom cloud, momentarily wishing you'd studied more math before you vaporize.

Combine that with the fact that tech is the best way to get out of India and China and come to the US, and maybe that explains the disparity.

Regardless, it says very bad things about our future as a country.