sometimes i wonder why mathematics is working so smooth as it is. for me, this is one of the most intriguing things around, next to the questions on why do we live and on whats the question to the answer 42… based on a small set of axioms, nobody knowing whether they are free of contradiction, an enormous building of constructions and proofs has been built. so huge, that no one can learn about all of it in one lifetime. and inside this building, between lots of dirty corners with ugly computations and hard work, there sit so many beautiful small and big results, sometimes showing surprising connections to completely different parts of mathematics. this connectivity is what surprises me most. every time again. that’s what i like about mathematics, and that’s what’s keeping me doing math. and makes me even more curious about the question on why it is working so smooth.
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comments.
Smooth? It's only "smooth" in your complex analysis... ;-) scnr
But you're right. All the beauty and recurrence of structures and how some areas of math suddenly intertwine are fascinating.
my elliptic curves over finite fields are smooth, too ;)
[...] do you know the feeling when, while doing something completely unrelated, like taking a shower, you get an idea? an idea which is somehow cool, which will change life completely, in some sense? with such ideas, usually lots of endorphines and adrenaline is set free, making you unable to sleep, to rest, to think clearly. then, after spending the day working the idea out, you finally notice a tiny flaw, something that didn't worked as smoothly as you thought it would or should. such tiny, but yet so fatal, killing the whole idea, throwing you back to the ground of the pit, where you continue to lurk around, in search for new ideas. but then, it's not as bad as it sounds. usually you learn something. you get a better understanding of something, the object in question has turned into something which you can see better with your mind, from a bit farer away, not as near as before, so near that you can see every bump but have no clue what these bumps belong to. like a new stack of jigsaw pieces, given to you to plug it into your big world puzzle, to complete it a bit more, to widen your glance on the truth. the universe got a bit smoother. [...]