Euclid’s Elements, read backwards, reduces complex truths to simpler ones, such as the Pythagorean Theorem to the parallelogram area theorem, and that in turn to triangle congruence. How far can this reductive process be taken, and what should be its ultimate goals? Some have advocated that the axiomatic-deductive program in mathematics is best seen in … Continue reading Consequentia mirabilis: the dream of reduction to logic