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7/16/2025, 12:10:53 AM
7/2/2025, 2:50:39 PM
>>16713250
I’m a transcendental idealist when it comes to math. It’s all forms of Kant’s sensible intuition. No matter how complicated or abstract a topic is, it still relies on our perception of it as space and time. In most abstract setting, spatial intuition corresponds to topology (even very abstract stuff like Grothendieck topology has the intuition of locality and gluing local patches) and temporal intuition corresponds to algebra. The beauty of modern mathematics is that we get this Einsteinesque melding of space and time together. One can speak of locally free modules with intuition behind it drawn from manifold theory via the Serre-Swan duality. Or one can use homological algebra to classify geometric spaces via K-theory.
I’m a transcendental idealist when it comes to math. It’s all forms of Kant’s sensible intuition. No matter how complicated or abstract a topic is, it still relies on our perception of it as space and time. In most abstract setting, spatial intuition corresponds to topology (even very abstract stuff like Grothendieck topology has the intuition of locality and gluing local patches) and temporal intuition corresponds to algebra. The beauty of modern mathematics is that we get this Einsteinesque melding of space and time together. One can speak of locally free modules with intuition behind it drawn from manifold theory via the Serre-Swan duality. Or one can use homological algebra to classify geometric spaces via K-theory.
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