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Jul 12, 2018 at 18:24 comment added David G. Stork Yes, of course the study of irrational numbers is a large and active subfield of Number Theory. But the matter at hand is what new insights were gleaned about the claim that not all real numbers are rational from these new proofs. I would guess the next generalization was to realize that Pythagoras' counter-example applied to any integer containing any prime factor raised to an odd power. But what other proof shed the most light? And my central question: What was it about this (irrationals) problem that kept mathematicians' interest, whereas some other disproved conjectures not?
S Jul 12, 2018 at 3:13 history answered Gerry Myerson CC BY-SA 4.0
S Jul 12, 2018 at 3:13 history made wiki Post Made Community Wiki by Gerry Myerson