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Is that a generic claim? I'm making a specific, counterintuitive, and empirical claim about productivity and work-style of mathematicians, having been on both s

Is that a generic claim? I'm making a specific, counterintuitive, and empirical claim about productivity and work-style of mathematicians, having been on both sides. Even for professional mathematicians, the solution to a problem can come all at once, while one is not even actively pursuing it, which begs the question of the purpose of beating your head against the wall when doing math. For just one example amongst many, see the story of Yitang Zhang, who made his breakthrough in establishing the first finite bound on gaps between prime numbers, while out at a barbeque and having largely given up on the problem after two years of effort.

alew1 8y ago
It seems likely that the two years of effort were essential in getting him to the point where he could have the breakthrough.
- vladislav 8y ago
  Are you confident the majority of the gains weren't made in the first year? It's exactly my point that knowing when to give it a rest is hard to estimate, and those who work on these problems professionally are likely to just keep pushing, potentially just spinning their wheels. Interestingly, the brain keeps working on these problems subconsciously, so you can actually get more done if you work on more things and tend to give up a bit earlier. I've solved hard problems before in an afternoon, a year after being hopelessly stuck on them, and my sincere estimate is that I would have made exactly zero progress had I kept pushing.
barry-cotter 8y ago
It seems unlikely that he would have had the breakthrough without those two years of effort. Step one of the Feynman algorithm is necessary for step two.
- vladislav 8y ago
  I think the counterintuitive aspect of problem solving at that level is how nondeterministic it is. It is no doubt that learning everything you can about a problem is critical to setting yourself up for being able to solve it, but this can happen a lot earlier than when someone burns out on a problem.

alew1 8y ago

It seems likely that the two years of effort were essential in getting him to the point where he could have the breakthrough.

vladislav 8y ago
Are you confident the majority of the gains weren't made in the first year? It's exactly my point that knowing when to give it a rest is hard to estimate, and those who work on these problems professionally are likely to just keep pushing, potentially just spinning their wheels. Interestingly, the brain keeps working on these problems subconsciously, so you can actually get more done if you work on more things and tend to give up a bit earlier. I've solved hard problems before in an afternoon, a year after being hopelessly stuck on them, and my sincere estimate is that I would have made exactly zero progress had I kept pushing.

barry-cotter 8y ago

It seems unlikely that he would have had the breakthrough without those two years of effort. Step one of the Feynman algorithm is necessary for step two.

vladislav 8y ago
I think the counterintuitive aspect of problem solving at that level is how nondeterministic it is. It is no doubt that learning everything you can about a problem is critical to setting yourself up for being able to solve it, but this can happen a lot earlier than when someone burns out on a problem.