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I think the intuition is that the best mathematicians, autistic or not, tend to be in academia already. So your prior for someone from the general population sh
by azernik 8y ago
I think the intuition is that the best mathematicians, autistic or not, tend to be in academia already. So your prior for someone from the general population should be that they're more likely to be a crank than a genius, ie non-academia has many more cranks than geniuses.
- neilv 8y agoIt's definitely intuitive to me that most all claims from outside the institution will be mistaken/naive. But, for really big wins that have thus far evaded the institution, what's the likelihood that the solution will come from within the institution rather than from outside? (I'm asking sincerely; I'm not a mathematician, and don't know.)
- azernik 8y agoThere's only one example I've heard of (some Russian guy), but generally they tend to involve innovative approaches within the establishment. (As said Russian guy proves, sometimes this heuristic fails; but your prior should be that it's likely correct.)
- schuyler2d 8y agoIf you are thinking of Perelman and the Poincare conjecture then I don't think his career really maps to the kind of "outsider" that is described in this thread: https://en.m.wikipedia.org/wiki/Grigori_Perelman#Early_life_and_education https://en.m.wikipedia.org/wiki/Grigori_Perelman#Early_life_... He had a PhD in math with enough success to be offered faculty positions at Princeton and Stanford. The fact that he recluded from academic life after that doesn't matter.
- Someone 8y agoI was thinking of some Indian guy and (not as nice of an example) some patent officer in the Swiss patent office. There also is the nice example of https://en.wikipedia.org/wiki/Marjorie_Rice https://en.wikipedia.org/wiki/Marjorie_Rice
- dagw 8y agoI was thinking of some Indian Assuming you mean Ramanujan. Although he was self taught in mathematics and did much of his work outside the university setting, the vast majority of his significant discoveries and publications where made within the academic framework.
- jlarocco 8y ago> I think the intuition is that the best mathematicians, autistic or not, tend to be in academia already. Is that a safe assumption, though? Won't it limit the field to people who are happy making a low salary and don't mind teaching?
- tuxxy 8y agoThis is an asinine assumption. What of the incredibly "genius" poor folks who do not have the opportunities to join academia?
- throwawaymath 8y agoThe point is that raw genius is insufficient for replicating Ramanujan-like accomplishments in the 21st century. It's almost irrelevant how brilliant someone is these days - if they haven't had the opportunity to learn a vast amount of theory, they can't really make significant progress towards theoretical problem. The field simply has far less low hanging fruit than it did a century, or even a half-century ago. It's not reasonable to expect that a lone genius with little to no academic background in mathematics could resolve a famous open problem through sheer creativity. For literally generations the field's most intelligent researchers have spent their careers chipping away at this problem.
- jbottoms 8y agoJust yeah, I didn't let Ramunujan into my school, much too messy, over promised, couldn't do proofs right. Not really academic material. He refused to learn LaTex.
- azernik 8y agoI'm not talking about a hard-and-fast policy; I'm talking about a Bayesian, "if a random person off the street sends a proof what should my priors be?"