[curiousHacker]

I completely agree about the interconnectedness of different branches of mathematics and think it is difficult to visualize and intuit because we don't yet have the language.

My guess: Eventually, as we begin to understand mathematics better, we will elucidate the underlying properties of theorems and there will be better "tagging"; the underlying language must also change. This will not happen for a minimum of 30+ years as new advances must be made and institutional faculty will object lest their life be rendered irrelevant.

[juliangamble]

I saw a talk that said the branch of Mathematics that dealt with the interconnectedness of Mathematics was called 'Category Theory'. You can see it here: http://vimeo.com/17207564 and Part 2 here: https://www.youtube.com/watch?v=yilkBvVDB_w

[gosub]

Category theory by Tom LaGatta[1] is also a nice introduction. He suggests taking a look at the nLab website[2], a wiki of Maths and Physics from the categorical point of view.

[1] https://www.youtube.com/watch?v=o6L6XeNdd_k [2] http://ncatlab.org/

[j2kun]

"Institutional faculty" are valuable because they prove new theorems as well.

[curiousHacker]

You're right and the tone of my message was wrong.