another problem that the Greeks raised without answering. One of the axioms Euclid used in systematizing geometry has to do with parallels. The axiom he adopted is logically equivalent to (though not identical with) the assumption that through a point outside a given line only one parallel to the line can be drawn. For various reasons, this axiom did not appear “self-evident” to the ancients. They sought, therefore, to deduce it from the other Euclidean axioms, which they regarded as clearly self evident.1 Can such a proof of the parallel axiom be given? Generations of mathematicians struggled
...more
I wish I could go back in time and listen to them discuss and argue over logic and proof.
