I cannot resist adding my grain of salt. Maybe we should distinguish between a human proof and a mechanical proof. The goal of a human proof is to convince other peoples of the truthfulness of a proposition. It is by nature explanatory and it can lead to new insights. A mechanical proof can be checked by computer but may not produce new insights. It is establishing a fact. Of course, it is better than none. Mathematics is above all a human activity. The value of a proof depends very much on its method. A new proof may suggest a new method. A method is a kind of toolbox for proving a large class of propositions. Commutative algebra is a method in geometry Category theory is a method in mathematics. proofs --->methods ----> proofs ----> methods ....... André [For admin and other information see: http://www.mta.ca/~cat-dist/ ]