Four color problem, odd Goldbach conjecture, and the curse of computing. For over twenty-three hundred years, at least since the publication of Euclid’s Elements, the conjecture and proof of new theorems has been the sine qua non of mathematics.
The method of proof is at “the heart of mathematics, the royal road to creating analytical tools and catalyzing growth” (Rav, 1999; pg 6). Proofs are not mere justifications for theorems; they are the foundations and vessels of mathematical knowledge. Contrary to popular conception, proofs are used for more than supporting new results. Proofs are the results, they are the carriers of mathematical methods, technical tricks, and cross-disciplinary connections. Of course, at its most basic level, a proof convinces us of the validity of a given theorem.
English. Bretgosselin. Chemistry. Physics. Math.