The Riemann Hypothesis and the Call for Maps in Place of Proofs
Modern mathematics still has with it a sense of Holy Grail, a sense that a possible solution is available for a given conjecture, and if it is available, such a solution is best as a proof in the absolute sense. But should such proof should be pursued as an unqualified good in itself? Indeed, this sense of proof is, in terms of history, much like the Greek predilection for rational numbers at the expense of the irrational, a belief which had both religious implication and deadly consequence. Such belief does not diminish the greatness of Greek mathematics, but it somewhat limited Greek mathematicians from further developments (as death is wont to do). Mapping out the range of applicability for a given solution, an act which is often amazing in itself, may one day win out over the absolute quest for proof. And n ote that maps in place of proofs serves to qualify proofs as absolutely descriptive and maps as not necessarily fully determinant in the sense of a...