no more patience for any traditional math in a classroom

[gusl]

I have no more patience for set theory class, or any traditional math in a classroom, for that matter.

I keep imagining dynamic definitions popping up to answer my questions... but in general, I'm lacking a reason to learn set theory.

Comments

[mathemajician.livejournal.com]

What is your reason for learning any other part of mathematics?

[gustavolacerda.livejournal.com]

it depends... sometimes for fun, sometimes because it's useful. Set theory is neither. But most content in mathematics classes are useless anyway, so I guess I don't like set theory.... but my definition of "like" boils down to "am I learning interesting stuff at a high enough rate, or am I better off spending my time elsewhere?"

[rdore.livejournal.com]

What sort of stuff is your course covering?

Generally set theory consists of developping a lot of technical material, and then every now and then connecting it back to a philosophically interesting result. Personally I find the technical part interesting, but most people seem to care about the results it gives back. But you need to know a fair ammout of machinery before you get there. (It takes a lot of work to even to, say, get to the point of the undecidability of the continuum hypothesis.)

[gustavolacerda.livejournal.com]

Now we're working on ordinals and proving a lot of obvious things.
One annoying thing about set theory is that it doesn't allow me to use my intuition, which is the only pleasant thing about doing math. Think of things like "prove that two sets have the same size if and only if there is a bijection between them". Since my normal mathematical thought happens above this level (i.e. I normally take this as an axiom), this becomes a game of symbol manipulation. And sometimes, it's not even clear what *can* be assumed. Excuse me, I'm ranting...

It takes a lot of work to even to, say, get to the point of the undecidability of the continuum hypothesis
All such independence results sound pretty advanced to me...

[rdore.livejournal.com]

Now we're working on ordinals and proving a lot of obvious things.

Well the attitude of a professor I know is the best way to prove something hard is to prove a lot of trivial things that together lead to something sophisticated.

And a surprising number of things about ordinals and cardinals are fairly unintuitive the first time you see them. It takes a while to make intuitive sense out of them, and the best way to build that up is just to play with them.

All such independence results sound pretty advanced to me...

Advanced is entirely relative. The ammount of material to prove the independence of CH is probably about two semesters worth. This isn't really any longer than the ammount of algebra one would have to take to get to the proof that the quintic is unsolvable by radicals. (The latter is however more mathematically mainstream, so people see it sooner.)