5 ms·

A neat comment on the accepted answer: > From OP's point of view this could be viewed as glass half-full rather than glass half-empty. Their dissertation resul

A neat comment on the accepted answer: > From OP's point of view this could be viewed as glass half-full rather than glass half-empty. Their dissertation results hold unequivocally on the sphere and might hold on the torus, though it is an open problem if they do. It is certainly legitimate to study what follows from a given conjecture being true. It could even be spun as a feature rather than a bug of the dissertation. If the results in fact fail on the torus then you know that the conjecture must be false. Potentially, it could open up a fruitful avenue of attack. Kind of reminds me of Terence Tao's post on what solving big problems looks like: https://terrytao.wordpress.com/career-advice/be-sceptical-of-your-own-work/ https://terrytao.wordpress.com/career-advice/be-sceptical-of...

finolex1 6y ago
As an aside, looks like one of the comments in the Math Overflow link above was made by Terence Tao himself
- oconnor663 6y ago
  Oh neat!
theossuary 6y ago
It reminds me of this math overflow answer: https://mathoverflow.net/a/338620 https://mathoverflow.net/a/338620 I suspect the reason OP's thesis worked out okay is because his intuition wrt the problem is correct, even if his formulation was a bit off. Very cool, sounds like a good mathematician to me
thechao 6y ago
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

finolex1 6y ago

As an aside, looks like one of the comments in the Math Overflow link above was made by Terence Tao himself

oconnor663 6y ago
Oh neat!

theossuary 6y ago

It reminds me of this math overflow answer: https://mathoverflow.net/a/338620 https://mathoverflow.net/a/338620 I suspect the reason OP's thesis worked out okay is because his intuition wrt the problem is correct, even if his formulation was a bit off. Very cool, sounds like a good mathematician to me

thechao 6y ago

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