Why do you like your chosen math field?

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I like topology, differential topology, set theory, differential geometry. But I ask myself why, and I can't give a good answer.

I know that I like abstraction and proofs, but yet I don't like group theory and ring theory, which are quite abstract and deals mainly with proofs. Perhaps I like dealing with derivatives, and hence my preference for differential topology and differential geometry. But yet I don't like differential equations or plain calculus. Do we like something just because we are good at it? Not in my case. I got my highest grade in group theory, ring theory, and number theory, all of which I don't like. Perhaps it's a genetic thing? I don't think so. So what is it then? And why don't I like group theory and ring theory? I don't know.

Can someone explain why you have chosen your math field?
 
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mathwonk
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well i think i alsoiked your chosen fields because of the geometric and visual aspect. also they involve smoothness and continuity, whidch are evry intuitive things to me, unlike finte reasoning in group theory, and the ugliness of the way calculus is often aught.

the older i get the more fields i like. it helps to teach them and learn them better.

if you want to enjoy diff eq, instead of those books like boyce and diprima, read arnol'd.
 
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well i think i alsoiked your chosen fields because of the geometric and visual aspect. also they involve smoothness and continuity, whidch are evry intuitive things to me, unlike finte reasoning in group theory, and the ugliness of the way calculus is often aught.
hmmm... I think you explained it pretty well. I like visual, geometric, continuous, and smooth objects. Group theory, ring theory, and number theory lacks the continuity and smoothness that I lust for. Differential Equations and calculus are too ugly in the sense that there is too much analytic calculation for my taste. I think I got it now.
 
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I used to hate algebra, until I learned some algebraic geometry, which made it seem much more down to earth to me.
 
mathwonk
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i also began to l;ike algebra more afgter learning algebraic geometry. IN AG, one l;earns to vieew every ring as the ring of functions on some geometric space. this adds a lot to the intuition of the dioealas tructure of the ring, i.e. ideals become like (functions vanishing on) subvarieties of the geometric variety.
 

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