Sunday, July 13, 2003

Riemann's hypothesis

No one knows how prime numbers are distributed. At some places they crowd together and at others they are sparse. Mathematicians have succeded in proving only that prime numbers become rarer as they grow larger. But how exactly they are distributed is still not known.

Riemann observed that the frequency of prime numbers is very closely related to the behaviour of an elaborate function, Zeta(s). It is unproven yet.

Leonhard Euler stated " prime numbers could be a mystery into which the human mind will never penetrate". Contrastingly Hilbert declared " Wir müssen wissen. Wir werden wissen" (We must know. We will know.) and had it carved on his tombstone.

Will we ever know?


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