I think I understand why people wanted (and still wants of course) to prove some mathematical statements. Example of that would be proof of Pythagorean theorem. People noticed earlier than Pythagoras that there is some correlation between sides of a right triangle. Pythagoras proved the sentence generally for all right triangles so that people no longer had to verify whether the conjecture holds for their right triangle with specific dimensions (again, I only think it was the primary motivation for proving it, I'm not sure of that - please correct me if I'm wrong). However I don't understand the motivation to create some general system of axioms and postulates (like in book Elements) from which we can prove more than just one conjecture. In other words, why to prove Pythagorean theorem from Euclid's primitive axioms and postulates, when Pythagoras's proof has the same conclusion? What is the reason for creating these general axiomatic systems?
2026-02-23 15:18:50.1771859930
What motivated people like Euclid to create such a general axiomatic systems like the one in the book Elements so early in history?
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