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I tried to think of any mathematics that used to be canon but isn't anymore. All that comes to mind is the Principia Mathematica, demolished by Gödel. Is there mathematics that has just become unfashionable, not because anybody found anything wrong with it, but just because it turned out not to lead anywhere interesting?

It would be hard to claim that such mathematics existed coeval with (non-avian) dinosaurs.

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Euclid's five axioms.

For one thing we learned to understand "axioms" as something less than self-evidently necessary truths. For another we learned that the original axioms didn't really prove what they were thought to prove -- at least up to modern notions of rigour.

We would now understand the original Euclidean proofs to have been "sneaking in" other, implicit, axioms disguised as obvious deductions, and so modern formulations of the geometry need more elaborate axioms.

Did axiomatic geometry become umfashionable? Or did it just get prettied up?

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