breadth of mathematical knowledge

[gusl]

I 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)

Comments

[en-ki.livejournal.com]

Betcha there are many little branches of math that have been pruned from general math education, so you might want to restrict it to things that are in the proof chain to results still being cited/used these past few decades.

[gustavolacerda.livejournal.com]

yeah, I agree.

[bhudson.livejournal.com]

(a) is going to be pretty much immediately as soon as anything resembling math started getting written up. For example, there's all this elementary geometry that is not hard to prove, but needs a trick that I learned fifteen years ago and haven't reviewed since. Heck, I wouldn't know off the top of my head how to prove the Pythagorean Theorem, which is ancient.

[gustavolacerda.livejournal.com]

ok, but you don't need to think before deciding that it's true.

[en-ki.livejournal.com]

Ah, but you can cheat and use trig.

[spoonless.livejournal.com]

They proved a lot of stuff about what can be constructed using only a compass and straightedge. Some of it I think would be too non-trivial to guess before sitting down and playing with a compass and straightedge for a while.

http://en.wikipedia.org/wiki/Squaring_the_circle
(squaring the circle wasn't proven until 1882, so I guess it doesn't count as an example of a theorem of the ancient world, however I think there were enough surrounding and similar things they were able to prove that I wouldn't know off the top of my head which ones were true or false.