On a similar note, I have a friend who majored in math at Harvard. He once told me that he came into Harvard being arrogant because in high school he was always at the top of his class in math. He enrolls in his first college level math course thinking he's got this, but he soon realizes that "higher math", which is largely proof-based, is a completely different subject than what he learned in high school. A month in he bombs the first exam. He went to the professor, who is originally from Italy, and explained his situation and how he was a star in high school. He responds in a thick Italian accent "that was not math, that was computation. In this course I teach math".
The math you typically learn in high school is very important, but I wish that we did a better job of explaining to high school students that what they are learning is completely different from what "real mathematicians" study (although I do think that computation is quite important in engineering, for example).
For me it was the opposite, i was a pretty average math student in high school and fell in love with proof based math in college. Proof based math requires much more creativity and thus is much for fun for me at-least, i wish i was taught proof based math in HS.
One of the major problems is that most of the high school teachers are themselves not very familiar with math, and are more educated in the very different problem of corralling children.
To be fair to your friend, 90 years ago they probably could've had a productive career in applied math as an expert computer. There was a point when calc tricks could get you a PhD, but those days are gone.
On a similar note, I have a friend who majored in math at Harvard. He once told me that he came into Harvard being arrogant because in high school he was always at the top of his class in math. He enrolls in his first college level math course thinking he's got this, but he soon realizes that "higher math", which is largely proof-based, is a completely different subject than what he learned in high school. A month in he bombs the first exam. He went to the professor, who is originally from Italy, and explained his situation and how he was a star in high school. He responds in a thick Italian accent "that was not math, that was computation. In this course I teach math".
The math you typically learn in high school is very important, but I wish that we did a better job of explaining to high school students that what they are learning is completely different from what "real mathematicians" study (although I do think that computation is quite important in engineering, for example).