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Geometry plays an important role in aesthetics (symmetry for instance). (Also math in music.)

That's applied math though. It is categorically on another level in the hierarchy.

Why would one specific application of math, the application of math in beauty be placed by philosophy on the same level as logic fundamentally. Math is derived from logic after all. Why isn't philosophy placing the study of the application of math to origami in the same category? Why does beauty arbitrarily take precedence over origami?

Not historically. Also remember that Pythagoricians were a mystic cult.

That's just a further reason why it makes no sense. The categorization is developed as mysticism.

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