Are mathematical "beauty" and "abstraction" related in your mind?
When I think of mathematical "beauty" I tend to think of very abstract and unexpected results or theories, like Galois theory, quadratic reciprocity, representation theory of Lie Groups, quarternions, classification of finite abelian groups, etc. I kind of have an inclination to say that more abstraction tends to coincide with more "beauty", but then there are certain topics, like graph theory or algebraic topology, that are very concrete, but they also seem to be "beautiful" in the conventional mathematical sense. Maybe I'm grasping at straws here, or just abusing language in a way that more so reflects my own opinions, rather than standard usage in the mathematical community, but I'm curious for anyone else's perspective.
Is mathematical "beauty" closely and inherently connected with abstraction, or do you think these are really unrelated concepts?
When I think of mathematical "beauty" I tend to think of very abstract and unexpected results or theories, like Galois theory, quadratic reciprocity, representation theory of Lie Groups, quarternions, classification of finite abelian groups, etc. I kind of have an inclination to say that more abstraction tends to coincide with more "beauty", but then there are certain topics, like graph theory or algebraic topology, that are very concrete, but they also seem to be "beautiful" in the conventional mathematical sense. Maybe I'm grasping at straws here, or just abusing language in a way that more so reflects my own opinions, rather than standard usage in the mathematical community, but I'm curious for anyone else's perspective.
Is mathematical "beauty" closely and inherently connected with abstraction, or do you think these are really unrelated concepts?
