> The top-rated answer is either defeatist, or just rationalization for the sentiment "I had to go through this and figure out everything myself, so you should too".
Yes, I agree this MO answer (and several others) seem to be rationalizing the situation rather than acknowledging how suboptimal it is.
I think I'm a good example of the system's failure. Coming in to college, I was something of an ideal candidate for becoming a mathematician. I had some success in Olympiads and already had decided I wanted to study math. My goal in life was to be a math professor.
I enrolled in a top college and took many graduate-level classes. However, by my senior year, when it was time for me to decide the next step in life, grad school or industry, I had become somewhat disenchanted with theoretical math. Math was so abstract I started losing interest: all this commutative algrebra (for example) I learned wasn't making me feel like I had any new insights into solving math problems, outside commutative algebra problem sets.
And so I went into industry.
However, I can't help but think that if I had more knowledge of the motivation behind all the abstract math, I wouldn't have lost interest. All that machinery of commutative algebra was invented for specific reasons, such as solving polynomial equations in the rationals through algebraic geometry. Years later, through casually reading math on the internet, I've been getting hints as to what power these highly abstract frameworks give you for solving concrete problems. But without seeing the end goal, and having some idea why I should be learning this in the first place, I felt like I was just getting lost in abstract nonsense.
>Most of that foundational information is lost when it's not written down somewhere accessible; contrary to the answerer, only a small fraction is reconstructed by students as they learn the subject.
This is exactly right. I personally failed to reconstruct enough to keep myself interested in the subject.
Yes, I agree this MO answer (and several others) seem to be rationalizing the situation rather than acknowledging how suboptimal it is.
I think I'm a good example of the system's failure. Coming in to college, I was something of an ideal candidate for becoming a mathematician. I had some success in Olympiads and already had decided I wanted to study math. My goal in life was to be a math professor. I enrolled in a top college and took many graduate-level classes. However, by my senior year, when it was time for me to decide the next step in life, grad school or industry, I had become somewhat disenchanted with theoretical math. Math was so abstract I started losing interest: all this commutative algrebra (for example) I learned wasn't making me feel like I had any new insights into solving math problems, outside commutative algebra problem sets.
And so I went into industry.
However, I can't help but think that if I had more knowledge of the motivation behind all the abstract math, I wouldn't have lost interest. All that machinery of commutative algebra was invented for specific reasons, such as solving polynomial equations in the rationals through algebraic geometry. Years later, through casually reading math on the internet, I've been getting hints as to what power these highly abstract frameworks give you for solving concrete problems. But without seeing the end goal, and having some idea why I should be learning this in the first place, I felt like I was just getting lost in abstract nonsense.
>Most of that foundational information is lost when it's not written down somewhere accessible; contrary to the answerer, only a small fraction is reconstructed by students as they learn the subject.
This is exactly right. I personally failed to reconstruct enough to keep myself interested in the subject.