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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
by curiousHacker 12y ago
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.
- j2kun 12y ago"Institutional faculty" are valuable because they prove new theorems as well.
- curiousHacker 12y agoYou're right and the tone of my message was wrong.
- juliangamble 12y agoI 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 http://vimeo.com/17207564 and Part 2 here: https://www.youtube.com/watch?v=yilkBvVDB_w https://www.youtube.com/watch?v=yilkBvVDB_w
- gosub 12y agoCategory 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 https://www.youtube.com/watch?v=o6L6XeNdd_k [2] http://ncatlab.org/ http://ncatlab.org/