This counterexample saga reminds me of Lakato’s “Proofs and Refutations”. You have a result that is “essentially true” but you can still find some “counterexamples” to it by conveniently stressing the “obvious setting” in which the result was originally formulated. Note in any case that whereas Euler has been “refuted” he is still credited for his original V—E + F = 2 formula.
This counterexample saga reminds me of Lakato’s “Proofs and Refutations”. You have a result that is “essentially true” but you can still find some “counterexamples” to it by conveniently stressing the “obvious setting” in which the result was originally formulated. Note in any case that whereas Euler has been “refuted” he is still credited for his original V—E + F = 2 formula.