the grayness of mathematics

I've finally moved into my new flat for this year.... and I'm not moving again for as long as I can. Its particularly a bitch when you've accumulated truck loads of absolutely futile artifacts and memorabilia ( ie 2 blue straws,an empty mineral water bottle, hotel pens,) Yes, I would be guilty of hogging....massive anything and everything kinda hogging. Anyways, what has this got to do with math...absolutely nothing! I just thought I'd spice this post with some useless neurotic factoid about myself.
Okay ..... so back to the flat.......,along with an amazing kitchen and pretty class rooms, it was furnished with four other students. One is an Archaeology PhD student, another is a Mathematics PhD student who is also a sucker for trashy TV shows (ahhh a kindred spirit indeed eheheh), the third member of the posse is a Philosophy major who did some specialised branch of politics and computer art and physics and history.... and a buisness masters PhD....something or the other student, and then of coure there's yours truly, the boring everyday medic... we're everywhere !!!! (they were temporary fixtures as they're moving out and will be replaced by 4 very unique and somewhat manic individuals who will undoubtedly make this year one heck of a ride:) )
So everynight for the past week, I have found myself engaged in some pretty fascinating conversations ....especially with the philosophy major. Absolutely priceless I'd have to say. Yesterday, was the last night of all of us living in the same flat they moved out .. so after an hour of watching a mind numbing "TV drama" (LOST ...which was actually fairly decent like), we ended up in some random conversation about maths... don't ask me to decribe the genesis of that conversation ... but yeah.... we ( the philosopher, the mathematician, and the medical student) ended up discussing Goldbach's Conjecture.
This theorem is centuries old and is yet to be proven by anyone. Basically it states that any even number greater than 2 is the sum of 2 prime numbers.Sounds basic...fairly straightforward... but alas it is by far one of the most notoriously elusive mathematical theorems.Being the mathematically challenged individual that I am, I asked if it hasn't been proven all these years,could the hypothesis just be wrong etc.According to the mathematician, you have to either prove or disprove a hypothesis that has been proposed.It jsut can't be dismissed.
He also explained how Kurt Godel said that sometimes in mathematics, there not necesssarily has to be a right or wrong... it could be just neutral.... neither of the above.... a concept that I find hard to grapple with.
How can something as objective as mathematics be so elusive at the same time?? The mysticism of math .... that's what Godel was trying to get across. Very very intriguing indeed.
So until a bright spark in this world can come up with a theorem that proves that any odd number greater than 2 is indeed the sum of 2 prime numbers, this hypothesis just stands as it is...... neither false nor definitely true.
Who will be the one to come up with the proof.....I hope I live to see the day!!!