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When Terence Tao writes stuff like this, I'm always very happy that I got to experience the Moore-method for learning math (at UT Austin). A group of us would b

When Terence Tao writes stuff like this, I'm always very happy that I got to experience the Moore-method for learning math (at UT Austin). A group of us would be dumped into a class with a common topic and we'd just have to prove things (topology, algebra, analysis) ... on the blackboard, in front of everyone. The best work we did was when something started going wrong and then we'd all start arguing about the proof, building count-conjectures on the fly and riffing on the math. The worst work was when someone went and found a proof ahead of time and just showed the answer. There's so much to learning where the sharp bits of math are; proofs are the razor-thin path through the briar patch. It was only later that I found out that history, the study of art & literature, and philosophy can all teach you the same thing. The important part is that you're interested in the topic.

truantbuick 6y ago
> There's so much to learning where the sharp bits of math are; proofs are the razor-thin path through the briar patch. This is an excellent metaphor using beautiful language. Did you just coin this yourself or is it pre-existing?
- mslm 6y ago
  Just felt the same way about the portion after the semicolon; it's quite catchy as well! Please give a reference or else if I use this later I'll have to say it came from "some guy on hackernews".
  - AnimalMuppet 6y ago
    Cite it as "thechao on HN", not just as "some guy". (Unless thechao gives you something more specific.)
- thechao 6y ago
  I guess this is mine? I would hesitate to believe I made it up, but I don't remember it from anywhere. If you don't feel comfortable with that, then credit it to Michael Starbird, who was my first Moore-method professor 20-odd years ago.
nicoburns 6y ago
> > There's so much to learning where the sharp bits of math are; proofs are the razor-thin path through the briar patch. As a student representative for my undergraduate mathematics course, I got really pissed off at lecturers for exactly this reason: they'd write out a perfect correct proof on the whiteboard, but wouldn't explain where it had come from or how people had arrived at the solution. We were left to figure that out on our own. They then complained that students were rote-learning for exams, rather than coming to a full understanding of the material. I'm not sure what they were expecting, given that that's exactly how they were teaching it.
- nwallin 6y ago
  My discrete mathematics professor was like that. He would regurgitate a proof onto the whiteboard. Then he'd do it a few more times with proofs of other things. He has an identical twin brother, who is also a math professor at the same college. The regular professor was out for a day, and his brother came in to teach the class. His teaching style was completely different. "Ok, we need to prove X. Where should we start?" and would sit on the table and look at us with an inquisitive look on his face. Then learning happened. Everyone's mind was blown. Most people didn't realize it was a different person. Then on Thursday it was back to same-old same-old. I still don't know shit about discrete math.
  - benibela 6y ago
    I am not getting anywhere with the latter approach when TAing I ask them such a question, and then wait for 15 minutes, and no one says anything.
- llamaz 6y ago
  If you're taking a class with proofs, you're being prepared for research. Doing your own research into, and reverse engineering, proofs is an important skill. Proofs in math journals are given 'as-is' and you learn the intuition through social means and discussions.
  - cclown 6y ago
hackermailman 6y ago
This is what Putnam seminars are like, the whole class goes through problems together. A few of them are on Youtube, maybe more will show up as everything is remote now.
deleted 6y ago
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truantbuick 6y ago

> There's so much to learning where the sharp bits of math are; proofs are the razor-thin path through the briar patch. This is an excellent metaphor using beautiful language. Did you just coin this yourself or is it pre-existing?

mslm 6y ago
Just felt the same way about the portion after the semicolon; it's quite catchy as well! Please give a reference or else if I use this later I'll have to say it came from "some guy on hackernews".
- AnimalMuppet 6y ago
  Cite it as "thechao on HN", not just as "some guy". (Unless thechao gives you something more specific.)
thechao 6y ago
I guess this is mine? I would hesitate to believe I made it up, but I don't remember it from anywhere. If you don't feel comfortable with that, then credit it to Michael Starbird, who was my first Moore-method professor 20-odd years ago.

nicoburns 6y ago

> > There's so much to learning where the sharp bits of math are; proofs are the razor-thin path through the briar patch. As a student representative for my undergraduate mathematics course, I got really pissed off at lecturers for exactly this reason: they'd write out a perfect correct proof on the whiteboard, but wouldn't explain where it had come from or how people had arrived at the solution. We were left to figure that out on our own. They then complained that students were rote-learning for exams, rather than coming to a full understanding of the material. I'm not sure what they were expecting, given that that's exactly how they were teaching it.

nwallin 6y ago
My discrete mathematics professor was like that. He would regurgitate a proof onto the whiteboard. Then he'd do it a few more times with proofs of other things. He has an identical twin brother, who is also a math professor at the same college. The regular professor was out for a day, and his brother came in to teach the class. His teaching style was completely different. "Ok, we need to prove X. Where should we start?" and would sit on the table and look at us with an inquisitive look on his face. Then learning happened. Everyone's mind was blown. Most people didn't realize it was a different person. Then on Thursday it was back to same-old same-old. I still don't know shit about discrete math.
- benibela 6y ago
  I am not getting anywhere with the latter approach when TAing I ask them such a question, and then wait for 15 minutes, and no one says anything.
llamaz 6y ago
If you're taking a class with proofs, you're being prepared for research. Doing your own research into, and reverse engineering, proofs is an important skill. Proofs in math journals are given 'as-is' and you learn the intuition through social means and discussions.
- cclown 6y ago

hackermailman 6y ago

This is what Putnam seminars are like, the whole class goes through problems together. A few of them are on Youtube, maybe more will show up as everything is remote now.

deleted 6y ago

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