@ava2790 - I'll send you a PM.

Lol. Keynes.

I wish I could pronounce 'abgemacht'.

@abgemacht: but what about subsystems of second order arithmetic (developed in the nineties) which aims to address paradoxes inherent in set theory - a purely metamathenatical objective...or category theory which is supposed to be the next set theory? Or how about the concept of Kolmogorov space which has no purpose but to be a theoretical example that only lives in pure maths papers?

I'm not sure how to respond to that, really...

Just because all new math doesn't have an immediate use doesn't mean that a) no new math does and b) it never will.

A perfectly good response! I am just a little miffed by some of the material I've been coming across recently.

@abgemacht Group theory can be very confusing at times, but it can be very useful and applied in many circumstances. I don't know specifically about the others, but group theory is useful.

@jod

I agree. Group Theory was one of my examples : )

Look guys. The level of abstraction with groups is acceptable for me. But the level of abstraction with homotopy groups? And homeomorphism groups? That's just a kinda pointless (if somewhat interesting) level of theoretical abstraction.

Again, I have to disagree.

Since you mentioned it, homeomorphism is incredibly important. It is required for a number of things in cryptography to work.

I can understand that many things seem pointless in mathematics, but more often than not, they allow other things in math to work. In math, everything is built upon everything else.

An excellent point, and one that I hadn't previously noted. Perhaps this is because the theoretical economics I study mostly uses various functional analytical concepts and is a little more divorced from algebraic topology. I've done a little bit of computability theory in the past few weeks. Some work with Konig's lemma (and WKL, WKLn, etc). It was fascinating.

I read something in a book recently, about a person who invented a topological representation of evolution. It was very interesting.

I'm going to go ahead and take credit for derailing this thread, even though I dropped out of the conversation awhile ago.

Yeah screw you rlumley.

@rlumley

Do you actually dislike MATLAB, or were you just being difficult?

@jodabomb24 - The biological sciences use a lot of functional analysis and non linear dynamics, the predator-prey equation system being the most famous example. As far as evolution is considered, there is a branch of theoretical computer science that works with the omega^omega space (the space of infinite trees with infinitely many branches numbered 1 thru infinity at infinitely many nodes). This is very much a topological space and so I can see where you could go with that. From this point of you, the theorems mentioned above (Konig's lemma, WKL, WKLn, which are statements about the trees themselves, are equivalent to the axiom of choice, compactness theorems, etc in topology).

I wish the apocolypse is tomorrow.

Granted, unfortunately you weren't on the side of right and get to suffer for all eternity.

I wish God would make his presence known to everyone in an obvious, blatant way to where there could be no doubt he exists.

@ abgemacht:

I detest MATLAB...

Granted, but god is a platypus, so everyone rejects the faith.

I wish people would stop talking about math on the corrupt a wish thread

Granted, they start thinking about math and nobody ever posts. I wish that 2 + 2 = 5.

Nobody granted my wish.

Ava, granted. You can now pronounce Abgemacht but can speak no other words at all.I wish I had a new car, that would not kill me or in any way get damaged

Granted, but it won't work.

I still wish 2 + 2 = 5

granted, but four gets mad and kills you because he feels he was abandoned. I wish my car would work while not killing me or getting damaged in any way.

Granted. Your car ceases to kill you, then fails to work.

I wish MATLAB never existed, and that instead, people learned legitimate languages, like C++, or even illegitimate ones, like VBA, that have decent interfaces, ie. Excel.

Granted. Everyone now uses FORTRAN