If people want math posts I’m game. Reply with requests, the more specific the better, not optimized for whether you think anyone can satisfy them; if I can’t maybe someone else can.
I’m sympathetic to this concern (it’s why I don’t like the QM sequence and think thinking about many-worlds is mostly a waste of time), but I also think math has the potential to be a useful toy environment in which to practice good epistemic habits (as suggested by shev’s recent litmustest posts), especially around confusing paradoxes and the like. Many of the complications of reasoning about the real world, like disagreement about complicated empirical facts, are gone, but a few, like the difficulty of telling whether you’ve made an unjustified assumption, remain.
In general I wonder how can anything be proved about prime numbers (other than the fact that they are infinitely many), because they seem to appear quite randomly.
EDIT: I will accept if the inferential distance is simply too large. I am just hoping that maybe it isn’t.
Presumably you mean explaining the proofs? Unfortunately the proof of Dirichlet’s theorem is quite difficult starting from a high-school background, and I don’t even know the proof of Green-Tao. I can try to say something about how one could go about proving nontrivial facts about prime numbers, though; for example, various special cases of Dirichlet’s theorem are much easier to prove.
Thanks; I am not really interested in the theorem per se, but in the tools that are useful for proving it. I guess the special cases use quite different tools, which is what makes them much easier.
In general, I would like to read about things that are not high-school knowledge, but that have a short inferential distance from the high-school knowledge. But I don’t have a strong preference for anything specifically here; mostly because I don’t even know what’s there.
If people want math posts I’m game. Reply with requests, the more specific the better, not optimized for whether you think anyone can satisfy them; if I can’t maybe someone else can.
I don’t think lots of math is a good direction to take the site. And I say this as a person with a mathematics degree.
I think mathematics is a bit too much of a fun distraction for us nerds from the hard problem of “refining the art of human rationality”.
I’m sympathetic to this concern (it’s why I don’t like the QM sequence and think thinking about many-worlds is mostly a waste of time), but I also think math has the potential to be a useful toy environment in which to practice good epistemic habits (as suggested by shev’s recent litmus test posts), especially around confusing paradoxes and the like. Many of the complications of reasoning about the real world, like disagreement about complicated empirical facts, are gone, but a few, like the difficulty of telling whether you’ve made an unjustified assumption, remain.
I don’t know if it is possible, but could you explain Dirichlet’s theorem on arithmetic progressions and Green–Tao theorem to someone with, uhm, good knowledge of high-school math, but not much beyond that?
In general I wonder how can anything be proved about prime numbers (other than the fact that they are infinitely many), because they seem to appear quite randomly.
EDIT: I will accept if the inferential distance is simply too large. I am just hoping that maybe it isn’t.
Presumably you mean explaining the proofs? Unfortunately the proof of Dirichlet’s theorem is quite difficult starting from a high-school background, and I don’t even know the proof of Green-Tao. I can try to say something about how one could go about proving nontrivial facts about prime numbers, though; for example, various special cases of Dirichlet’s theorem are much easier to prove.
Thanks; I am not really interested in the theorem per se, but in the tools that are useful for proving it. I guess the special cases use quite different tools, which is what makes them much easier.
In general, I would like to read about things that are not high-school knowledge, but that have a short inferential distance from the high-school knowledge. But I don’t have a strong preference for anything specifically here; mostly because I don’t even know what’s there.