Comment by benreesman

15 hours ago

I’m far from being any kind of serious mathematician, but I’ve learned more in the last couple years of taking that seriously as an ambition than in decades of relegating myself to inferiority on it.

One of the highly generous mentors who dragged me kicking and screaming into the world of even making an attempt told me: “There are no bad math students. There are only bad math teachers who themselves had bad math teachers.”

Sadly, when I was a postdoc, an eminent mathematician I was working under once shared a story that he found amusing that one of his colleagues was once asked a question in the form: "This might be a stupid question, but..." and the response was "There are no stupid questions, only stupid people."

Run into too many people like that, who I daresay are common in the field, and it's easy to see how people become dispirited and give up.

Wouldn't it then follow that all students of the same teachers end up with the same skill level in math? Not sure that's the case.

  • Doesn't follow. Bell curve in, shifted bell curve out. Ideally this also tweaks the variance a bit.

    In other words: Some students flourish despite their teachers, some flourish because of them.

  • Cantor gave his life to the Continuum Hypothesis, Hilbert gave much of his life to similar goals.

    You’re making an argument somewhat along those lines, but given that I didn’t stipulate a convergence condition your conclusions can be dismissed by me.

    If it were a valid argument then we’d need Gödel.