Caution Advised about Ultra Abstraction in Mathematics


I urge considerable caution about any kind of ultra abstruse mathematics that does not reduce to well known mathematics. For example Cartan geometry is equivalent to Riemann geometry, first formulated in the early nineteenth century and four dimensional Riemann geometry reduces to Minkowski geometry when the connection vanishes. Minkowski geometry reduces to Euclidean space geometry in the non-relativistic limit. So any claim to generalize Cartan is nonsensical if it does not reduce to Euclidean geometry. Contemporary mathematics frequently has no relevance to physics and useless for engineering. Any claim that Cartan is wrong can be dismissed out of hand.


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