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Mathematics is generally categorized as a science, but I don't think it is only that. I admit that mathematics has contributed to the realms of physical science, and has itself been reinforced by its interactions with them, but mathematical discoveries are made regardless of their applicability or utility to the physical world. Mathematics has evolved purely for itself, with the greatest contributions to the field being those theories that put value on the beauty of the adopted logic. A theory contrived for purposes other than itself lacks natural beauty. What is mysterious is that a great theory possessed of inherent beauty transcends the subject and finds applicability in other fields.
It is impossible to put in words the intrinsic grace of a theorem. It is highly abstract and complex. I can only describe it as being akin to a perfect piece of music in which each note is irreplaceable or to a haiku in which no syllable can be changed. The beauty I speak of is like the exquisite tension that holds together aspects of a work of art; a fragile serenity that cements its perfection. And so the magnetic force that draws art—and therefore literature—to mathematics is the dignified beauty of its pure logic.
Kevin Kunstadt, Asymptote
