More later, but just a brief remark – I think that one issue is that the top ~200 mathematicians are of such high
intellectual caliber that they’ve plucked all of the low hanging fruit and that as a result mathematicians outside of that
group have a really hard time doing research that’s both interesting and original.
I disagree with this. I think it is a feature that all the low hanging fruit looks picked, until you pick another one. Also I am not entirely sure if there is a divide between pure math and stuff pure mathematicians would consider “applied” (e.g. causal inference, theoretical economics, ?complexity theory? etc.) other than a cultural divide.
I disagree with this. I think it is a feature that all the low hanging fruit looks picked, until you pick another one.
Maybe our difference here is semantic, or we have different standards in mind for what constitutes “fruit.” Googling you, I see that you seem to be in theoretical CS? My impression from talking with in the field people is that there is in fact a lot more low hanging fruit there.
Also I am not entirely sure if there is a divide between pure math and stuff pure mathematicians would consider “applied” (e.g. causal inference, theoretical economics, ?complexity theory? etc.) other than a cultural divide.
I strongly agree with this, which is one point that I’ll be making later in my sequence.
But the cultural divide is significant, and it seems that in practice the most mathematically talented do skew heavily toward going into “pure math” so that more low hanging fruit has been plucked in the areas that mathematicians in math departments work in. I say this based on knowledge of apples-to-apples comparisons coming from people who work on math within and outside of “pure math.” For example, Razborov’s achievements in TCS have been hugely significant, but he’s also worked in combinatorics and hasn’t had similar success there. This isn’t very much evidence – it could be that the combinatorics problems that he’s worked on are really hard, or that he’s only done it casually – but it’s still evidence, and there are other examples.
I disagree with this. I think it is a feature that all the low hanging fruit looks picked, until you pick another one. Also I am not entirely sure if there is a divide between pure math and stuff pure mathematicians would consider “applied” (e.g. causal inference, theoretical economics, ?complexity theory? etc.) other than a cultural divide.
Maybe our difference here is semantic, or we have different standards in mind for what constitutes “fruit.” Googling you, I see that you seem to be in theoretical CS? My impression from talking with in the field people is that there is in fact a lot more low hanging fruit there.
I strongly agree with this, which is one point that I’ll be making later in my sequence.
But the cultural divide is significant, and it seems that in practice the most mathematically talented do skew heavily toward going into “pure math” so that more low hanging fruit has been plucked in the areas that mathematicians in math departments work in. I say this based on knowledge of apples-to-apples comparisons coming from people who work on math within and outside of “pure math.” For example, Razborov’s achievements in TCS have been hugely significant, but he’s also worked in combinatorics and hasn’t had similar success there. This isn’t very much evidence – it could be that the combinatorics problems that he’s worked on are really hard, or that he’s only done it casually – but it’s still evidence, and there are other examples.
Let’s say I am at an intersection of foundations of statistics and philosophy (?).
The (?) proves you right about the philosophy part.
The (?) was meant to apply to the conjunction, not the latter term alone.