However... being a math major is really different from a career in academia. People really should be encouraged to major in math.
Somewhere in this thread there is a link to Francis's lectures and they are wonderful. The method/enthusiasm be has for teaching is wonderful and makes all the difference to students.
Rather than going through online courses and paying for them (many university classes are mostly online math problems, and proctored during a specific time.)
EDIT: The way math is currently taught really forces people to dislike math and think they suck at it. (in general)
Starting in primary school with basic arithmetik. (I help a young boy with his homework) They don't really teach them Math, how to solve thing, they tech them to memorize different algorithms, which they can handle after a while, but don't know what they are doing at all ...
So the best mathematicians there are not the ones who can think best, but who can memorize and follow orders the best.
I met a woman from South Korea who was taught all drill and no concepts. She was solving differential equations in high school but had no intuitive concept of derivative and integral or what they were used for. In fact, she had no interest in math. She was just a diligent student focused on getting into the top university. She was obviously trained the way you describe.
I have also personally, in the United States, been in math classes where many students suffered because they couldn't string together correct calculations consistently enough to validate and reward their high-level understanding. They learned a lot of the words and pictures, could explain what an integral was for, and could listen to a lecture and feel like they got it, but if you asked them to apply what they knew to a real problem, they responded with a kind of rueful helplessness. To them, mathematics was like magic in the Harry Potter universe: anybody could explain it, but it worked for some people and not for others, for reasons that seemed to them to be innate.
Each system stressed one aspect at the expense of the other, and in each system, there were many students who picked up both, but also many students who only learned the part that was stressed by their teachers. It was certainly the case in my classes that a student who only learned the concepts, without the mechanics, was unlikely to progress much farther in the math curriculum.
A balanced method treats the two aspects as complementary, each enabling the other. Treating one as the hero and the other as the villain might make sense locally as a response to a warped system, but it can easily become a warped approach in itself.
Of course, most students do just memorize equations and follow orders. But in my experience the most successful students are always the ones who understand the material on a fundamental level and memorize very little (on some level, memorization is all but required by even the best).
Later on, things get better, yes, but not much.
Common Core in the US is supposed to solve this. I've seen some common core math homework for myself and despite the odd outrage most people have towards it, I think both the idea and execution are at least decent, and an improvement.
^ THIS.^
If math education could only be more like: https://betterexplained.com