A reality, often unacknowledged, is that mathematicians proceed largely on the basis of elegance. As Achilles and the Tortoise shows us, basic logic has built-in points of infinite regress, and the only way past them is to agree that the logic is sound.
Mathematicians who must choose between two sets of axioms will pick the one they consider most elegant, every time. The fact that this is ultimately an aesthetic judgement is clear: Erdős Pál, arguably the finest mathematician of the latter half of the 20th century, described proofs that tickled his sensibilities as "Pages from the Book".
Mathematicians who must choose between two sets of axioms will pick the one they consider most elegant, every time. The fact that this is ultimately an aesthetic judgement is clear: Erdős Pál, arguably the finest mathematician of the latter half of the 20th century, described proofs that tickled his sensibilities as "Pages from the Book".