If nothing rational designed the universe, and math is the invention of men, why does physical space behave like a mathematical space?

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They had empirical knowledge accumulated in the library of Alexandria.

This knowledge was preserved from before the cataclysm, which ended the antediluvian iceage era civilization. This civilization also built the pyramids and the sphinx (which could not have been built by dynastic Egyptians, who had bronze tools, and fought wars on chariots with wooden wheels.

Plato studied at the library, and refers to the cataclysm flood event, which occurred +9000 years before his time. Plato also refers to more advanced civilizations like Atlantis, etc.