Nobody's making the claim that Euclidean geometry is all of maths. But the part of the universe that Euclidean geometry represents has always, still does, and will continue to work even when the last traces of Euclidean geometry vanish from recorded knowledge and memory.
> ... link to Gödel's incompleteness theorems
That's a proof of some limits of formal systems — particularly those that want to formalise everything under one unified set of axioms — not limits of mathematics. Mathematics / the universe does care one iota if you use this particular set of axioms or another. Or even any. It continues to work without a care for your need to have a grand unified theory. That you cannot discover all of its secrets because you restricted yourself is not its concern.
Maths is how the universe works, whether you understand it or not.
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But thank you for linking to Gödel's theorems. Your link directly answers the topic being discussed. You'll notice the text never says "invented" when talking about these or related theorems; it says "discovered".
> ... link to Gödel's incompleteness theorems
That's a proof of some limits of formal systems — particularly those that want to formalise everything under one unified set of axioms — not limits of mathematics. Mathematics / the universe does care one iota if you use this particular set of axioms or another. Or even any. It continues to work without a care for your need to have a grand unified theory. That you cannot discover all of its secrets because you restricted yourself is not its concern.
Maths is how the universe works, whether you understand it or not.
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But thank you for linking to Gödel's theorems. Your link directly answers the topic being discussed. You'll notice the text never says "invented" when talking about these or related theorems; it says "discovered".