CNet is reporting that a proof for the Riemann Hypothesis has been found by a professor at Purdue. The proof, which is far beyond my ability in math, is a pretty interesting read that covers a large part of the history of prime numbers. It beings:
The Riemann hypothesis is the product of a renaissance in mathematics which began in the seventeenth century after more than a thousand years in which Greek mathematics lay dormant in monasteries. When mathematics is viewed as the science of numbers, two aspects of that science are found to be strikingly present in antiquity.
The ending of the proof:
The proof of the Riemann hypothesis verifes a positivity condition only for those Dirichlet zeta functions which are associated with nonprincipal real characters. The classical zeta function does not satisfy a positivity condition since the condition is not compatible with the singularity of the function. But a weaker condition is satis ed which has the desired implication for zeros.
A curious coincidence needs to be mentioned as part of the chain of events which concluded in the proof of the Riemann hypothesis. The feudal family de Branges originates in a crusader who died in 1199 leaving an emblem of three swords hanging over three coins, surmounted by the traditional crown designating a count, and inscribed with the motto “Nec vi nec numero.”