9 ms·

Is this guy trolling? First two paragraphs sound to me similar to what some of my math untalented friends said about it in highschool. "Power to understand and

by rednum 15y ago

Is this guy trolling? First two paragraphs sound to me similar to what some of my math untalented friends said about it in highschool. "Power to understand and predict" is not limited only to those who can manipulate abstract symbols - for some reasons it seems that such abstract manipulation is the best way to do it now. The second paragraph is even worse. This guy have simply no idea what he is writing about. 'Assigning meaning to set of symbols' is just abstracting unnecessary details and focusing on important information in problem, 'blindly shuffling symbols according to arcane rules' - um, calling math 'arcane' is a clear indicator of person's lack of understanding. Rules are not arcane, everything has explanation (proof) and is derived from other things in logical way (and as far as we know, world acts logcailly) - some of the are axioms, which seem to be abstractios of most basic properties. Also, 'shuffling blindly' is in fact spotting patterns in things on different levels. Sure, explainig things on more intuitive level, using e.g. graphical representations is sometimes really helpful. However sometimes intuition doesn't work, and how do you graph 3-dimensional manifold embedded in R^4? Or finite field? Also, I can't imagine of other way of doing math that would be consistent and useful other than the one we are using now.

hassy 15y ago
This "guy" studied electrical engineering and computer science at Caltech and UC Berkeley, I am sure his grasp of mathematics is ok. Perhaps you should try to stop feeling offended at his proposal and try to see where he might be coming from. Also as he admits in the article, it is by no means a comprehensive set of thoughts, but rather a few hunches hinting at a bigger idea.
- bermanoid 15y ago
  This "guy" studied electrical engineering and computer science at Caltech and UC Berkeley I'm actually quite surprised by that. Those are both excellent schools with top notch math departments, and the example that he mentioned in the article (about not really grokking the second order ODE and what it meant re: the phase space plot, etc.) indicates that he took a seriously badly taught class. I'm kind of surprised you could get through a diff eq's course at either school without having such basic stuff taught to you...makes me wonder who the teacher was, maybe it was pawned off on a grad student? Edit: whoops...just looked back at the article, turns out he didn't take that diff eq course at Caltech or Berkeley, it was at a local college. That explains a lot. I'm not going to say that there are no good teachers at mediocre schools, nor that there are no bad teachers at the good ones, but on average there's a huge discrepancy in the quality of the classes. I had similar experiences, where I took classes at a local college while in high school, and thought I was stupid or something when I didn't "get" them, only to find that when I took them again at a better school they were, in fact, very easy topics. I blame the textbook writers in part: for one example, Serge Lang's math books are extremely difficult as a rule, and leave a lot of the scaffolding out. Scaffolding which, when he taught classes himself, he always filled in to make for an amazingly smooth and effortless learning experience, but which lesser teachers would never think to talk about (perhaps because they don't understand it themselves, or at least don't understand how important it is to explain). It's really a shame that even now, after so many centuries of teaching math to people, the effectiveness of the process is still so utterly dependent on the teacher. Hopefully things like the Khan Academy will begin to rectify these problems.
  - kragen 15y ago
    > It's really a shame that even now, after so many centuries of teaching math to people, the effectiveness of the process is still so utterly dependent on the teacher. Maybe it's not a shame. Maybe it's just an indication that teaching is hard, like art, science, programming, and discovering new theorems, not easy like answering phones in a call center or being a short-order cook.

by rednum 15y ago

hassy 15y ago

This "guy" studied electrical engineering and computer science at Caltech and UC Berkeley, I am sure his grasp of mathematics is ok. Perhaps you should try to stop feeling offended at his proposal and try to see where he might be coming from. Also as he admits in the article, it is by no means a comprehensive set of thoughts, but rather a few hunches hinting at a bigger idea.

bermanoid 15y ago
This "guy" studied electrical engineering and computer science at Caltech and UC Berkeley I'm actually quite surprised by that. Those are both excellent schools with top notch math departments, and the example that he mentioned in the article (about not really grokking the second order ODE and what it meant re: the phase space plot, etc.) indicates that he took a seriously badly taught class. I'm kind of surprised you could get through a diff eq's course at either school without having such basic stuff taught to you...makes me wonder who the teacher was, maybe it was pawned off on a grad student? Edit: whoops...just looked back at the article, turns out he didn't take that diff eq course at Caltech or Berkeley, it was at a local college. That explains a lot. I'm not going to say that there are no good teachers at mediocre schools, nor that there are no bad teachers at the good ones, but on average there's a huge discrepancy in the quality of the classes. I had similar experiences, where I took classes at a local college while in high school, and thought I was stupid or something when I didn't "get" them, only to find that when I took them again at a better school they were, in fact, very easy topics. I blame the textbook writers in part: for one example, Serge Lang's math books are extremely difficult as a rule, and leave a lot of the scaffolding out. Scaffolding which, when he taught classes himself, he always filled in to make for an amazingly smooth and effortless learning experience, but which lesser teachers would never think to talk about (perhaps because they don't understand it themselves, or at least don't understand how important it is to explain). It's really a shame that even now, after so many centuries of teaching math to people, the effectiveness of the process is still so utterly dependent on the teacher. Hopefully things like the Khan Academy will begin to rectify these problems.
- kragen 15y ago
  > It's really a shame that even now, after so many centuries of teaching math to people, the effectiveness of the process is still so utterly dependent on the teacher. Maybe it's not a shame. Maybe it's just an indication that teaching is hard, like art, science, programming, and discovering new theorems, not easy like answering phones in a call center or being a short-order cook.