History of Math

[dshizzle]

People's responses on the Most Important Math thread were really interesting, and got me thinking about the history and development of math. I'd never really spent much time thinking about maths history, or the structure of its development.

1)What pieces of math history do you guys think are really fascinating?
2) Do you think the development of mathematics is primarily linear or chaotic? By this I mean do you think that for the most part math builds on prior developments, or is a series of random discoveries and creations?
3) What do you think about the current state of mathematics compared to what it's been in the past?

[Giallo]

I'm not an expert in maths' history, but my opinion is:

1) I am fascinated by how some people have developed an absurd amount of things even in very short lives (I'm thinking of Galois, Riemann, Cauchy, Ramanjuan...)
2) I think that the development of maths is chaotic, due to the fact that often to further research on topics in a field you need results of some other field, but very often researcher in the first field know "little" of the second. Also you have things that are conjectured and then solved only centuries later (e.g.: Fermat's last theorem).
3) I think maths is advancing faster, primarily because there are many more researchers now than in the past. At the same time, it's becoming more and more difficult for a single person to give large contributions and the amount of study to get to the edge of the known maths is becoming little by little almost impossible to achieve.

[dshizzle]

1) I find cases where multiple people developed what were essentially the same ideas independently like calculus and non-euclidean geometry. Theres something kind of neat about that.
2) I think that math kind of proceeds in cycles, I would imagine most sciences are the same way. Periods of sudden chaotic growth as new fields are born, followed by longer periods of slow linear development of those fields.
3) It feels like math is developing kind of slowly right now, but it also seems that any truly astounding results would take at least a couple of years to filter down to the dum dums like me.