(no subject)
You wouldn't believe how much effort goes into proving small things that most people would explain by saying "DUH!" I mean, it's not impossible-difficult or even very difficult most of the time... it's just surprising. When I thought of the sorts of proofs a junior-level math major would do, I thought of crazy things that I've never even heard of... not proving "a divides b" in a number of situations. It's sort of mind-blowing when you can take an entire paragraph to explain something like that. I don't know how to put it other than this:
You finish your simple proof and instead of thinking "Ugh. Well I've taken up a third or more of a notebook page when this REALLY should have only required 'Are you kidding? How could this NOT be?!'" you think something along the lines of (a better worded and more intelligent sounding expression equivalent to) "Oh My God. Something is going on with this."
It makes me excited... there's all of this talk of "beauty" and "elegance" in math which I hadn't really found in Calculus. For instance, when I had heard that we would be covering "The Fundamental Theorem of Calculus" in the next class period during freshman year, I seriously felt butterflies... I prepped myself to be blown away and have some sort of life-changing realization. (Whoah. That sounds so religious.) I was dissapointed, to say the least.
Anyway, the point is that I am enjoying my number theory class and that I feel like I've suddenly jumped to the next level of understanding what it means for mathematics to be "beautiful"
Edit: One of my profs called a clever, almost puzzle/game-like method of finding primes "cute" the other day. It hit me - BAM. "Oh My God. He's right. This IS cute. It's almost parlor-trick clever."
You finish your simple proof and instead of thinking "Ugh. Well I've taken up a third or more of a notebook page when this REALLY should have only required 'Are you kidding? How could this NOT be?!'" you think something along the lines of (a better worded and more intelligent sounding expression equivalent to) "Oh My God. Something is going on with this."
It makes me excited... there's all of this talk of "beauty" and "elegance" in math which I hadn't really found in Calculus. For instance, when I had heard that we would be covering "The Fundamental Theorem of Calculus" in the next class period during freshman year, I seriously felt butterflies... I prepped myself to be blown away and have some sort of life-changing realization. (Whoah. That sounds so religious.) I was dissapointed, to say the least.
Anyway, the point is that I am enjoying my number theory class and that I feel like I've suddenly jumped to the next level of understanding what it means for mathematics to be "beautiful"
Edit: One of my profs called a clever, almost puzzle/game-like method of finding primes "cute" the other day. It hit me - BAM. "Oh My God. He's right. This IS cute. It's almost parlor-trick clever."