breadth of mathematical knowledge
Jan. 21st, 2010 08:05 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
guslI hereby propose that we measure the breadth of someone's mathematical knowledge as tuple of years:
(a) the earliest year by which someone proved a theorem that you didn't know was true, i.e. you'd need to think before deciding whether it was true / have no idea how to prove it off the top of your head.
(b) the earliest year by which some mathematical concept had been invented that is totally new to you
(c) the earliest year by which some theorem statement was incomprehensible to you, even after reading definitions for 1 or 2 levels.
http://en.wikipedia.org/wiki/History_of_mathematics may be a good guide.
As for myself:
(a) I might know all the math the Ancient Greeks ever knew (though there could be some intricate geometry e.g. in the Elements). However, Aryabhata has something to teach me (though I'd learn it pretty quickly) (a < 550). I'm definitely bounded above by Euler (a < 1783). Feel free to help me tighten this bound.
(b) hm, this is actually difficult to test... I guess I'd have to take a sample from an encyclopedia of mathematics.
(c) I think the Modularity theorem qualifies, though I haven't tried very hard. c < 1967 (I suspect this bound is very loose)
(a) the earliest year by which someone proved a theorem that you didn't know was true, i.e. you'd need to think before deciding whether it was true / have no idea how to prove it off the top of your head.
(b) the earliest year by which some mathematical concept had been invented that is totally new to you
(c) the earliest year by which some theorem statement was incomprehensible to you, even after reading definitions for 1 or 2 levels.
http://en.wikipedia.org/wiki/History_of_mathematics may be a good guide.
As for myself:
(a) I might know all the math the Ancient Greeks ever knew (though there could be some intricate geometry e.g. in the Elements). However, Aryabhata has something to teach me (though I'd learn it pretty quickly) (a < 550). I'm definitely bounded above by Euler (a < 1783). Feel free to help me tighten this bound.
(b) hm, this is actually difficult to test... I guess I'd have to take a sample from an encyclopedia of mathematics.
(c) I think the Modularity theorem qualifies, though I haven't tried very hard. c < 1967 (I suspect this bound is very loose)