Some of the Original your Love is Hotenough shirt and by the same token and most powerful ideas in mathematics require subtle violations of symmetry to succeed. The complex sphere is more symmetric than the complex plane, but it hardly supports the analytic function. Seen from this angle, the plane of complexity is a luminous and broken structure: take the perfect sphere, pierce it, and unravel the beauty that emanates from it. The tension between modular forms and modular functions is another example of the same idea.
The definition of a field, one of the Original your Love is Hotenough shirt and by the same token and fundamental objects of algebra, makes addition and multiplication satisfy roughly the same axioms – but only roughly. If you’re forced to have complete symmetry between the two, then nothing matters. There is a spectrum from purely abstract and ethereal to purely natural and material. Mathematics has fields across this spectrum, and people find their personal beauty in many different places.
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