In Paul Fussell’s book on class (I think), he says that people are really worried about differentiating themselves from the class immediately below them, but largely ignorant of the customs and sometimes even existence of the classes above them. When I found SSC, and then The Motte, and stuff like TLP, I was astonished to find a tier of the internet I had had no idea even existed. The quality of discourse here is . . . usually . . . of the kind that “high brow” (by internet standards) websites THINK they are having, but when you see the best stuff here you realize that those clowns are just flattering themselves. My question is, who is rightly saying the same thing about us? Of what intellectual internet class am I ignorant now? Or does onlineness impose some kind of ceiling on things, and the real galaxy brains are at the equivalent of Davos somewhere?
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Indeed that is a nice heuristic but I feel if this was true for past geniuses (e.g. Euler) however this should be less and less true.
Mathematics have reached a plateau and for all matters has been replaced via the curry Howard correspondence by computer science and software engineering and to some extent machine learning.
There are very few important open problems left and the ones that are left are either non-computable, non provable or false, or are long known, conjectured to be true but can't be proven for all cases because of contrived details.
And that is what mathematics are increasingly, an interest in deeply contrived things.
Many of those contrivations are contingencies, but there's also a lot that shouldn't even exist in the first place under a proper finitist framework.
Do you see genius in the last major proofs?
IIRC what has allowed the Poincaré conjecture millennium prize to be solved for all cases even the many contrived ones, has "simply" or at least essentially been a new way to bruteforce the problem, essentially via a specific software made for it.
Most of the genius we attribute to mathematics is a derivation of a few factors:
Obscurantism as a culture, especially elite notations for denoting trivial things. Notation which mostly have no IDE support btw.
as said lack of IDE tooling/culture
the desire of having fun/ideology such as rejecting finitism. See e.g rational trigonometry. There is a semi-similar parallel with the quantum physics culture.
many historical accidents which alter how we teach maths.
Learning data structures and algorithms in computer science should be enough for someone to demysticize mathematics.
Mathematics have changed the world for the better and many of its concepts are useful for a rationalist mind's, however I'm afraid the lack of non-contrived nor real-world impacting challenges combined with the semi-anti intellectual/contrived culture would limits/bottleneck someone intellectual development instead of strengthening it, as a life main occupation.
Of course this is only a generalization.
Note however that regardless of that, fields medals are like Nobel prizes, a weak signal since they do a very poor job at representing who drove the most progress in a question and only show, allegedly, the last person in the problem solving chain.
IIRC the Russian that solved the millennium problema didn't reject the monetary prize because he was hermit weirdo as depicted by some medias, but as a political act since he didn't deserved most of the recognition.
It's imperfect, sure, but a good starting point if one seeks to compile such a hierarchy. Better than the Nobel Prize, at least, except for maybe physics. The politization of the Nobel Prize has long tainted it.
The prior art in mathematics is enormous. To make progress you have to assimilate all this difficult information, which in and of itself, is indicative of having very high with IQ. Whether or not the results are useful is another matter. Major findings are now on the margins, which I think raises the IQ barriers to entry.
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