[poindexters brother]

We generally don't ask students to 'think critically' about other established scientific laws either. By and large, we regard them as well-established by a large body of experimental work, to which undergraduate students don't have extensive access; and 'critical thinking' about such laws is not a useful pedagogical technique.

Thinking critically about Euclid's 5th postulate has given us the wonders of non-euclidean geometery.

[Right Wing Professor]

Thinking critically about Euclid's 5th postulate has given us the wonders of non-euclidean geometery.

Indeed, but Riemann did that for his habilitation, which is a step after his Ph.D.. If he'd spent math class questioning fundamental postulates, he's have never gotten his primary degree. Research is really only possible when you already know the field.

[edsheppa]

Thinking critically about Euclid's 5th postulate has given us the wonders of non-euclidean geometery.

While I agree that critical thinking is an important and valuable skill, your history is off in this instance. The groundwork for showing the parallel postulate wasn't necessarily so was made unwittingly by folks who accepted it uncritically. For centuries their goal was to show that this "messy" postulate was logically a consequence of the others or maybe of some other less messy but "self-evident" postulate. They never doubted even a moment that the postulate was a true fact of the world - until Gauss et al suddenly realized a possible implication of their failure.

There's a lesson about critical thinking in this story but it's not the one you imply.