The Great Mathematical Problems by Ian Stewart

Author:Ian Stewart
Language: eng
Format: epub
Publisher: Profile Books
Published: 2013-04-08T04:00:00+00:00

The circumstantial evidence in favour of the truth of the Riemann hypothesis – either the original, or its generalisations – is extensive. Many beautiful things would follow from the truth of the hypothesis. None of these things has ever been disproved: to do so would be to disprove the Riemann hypothesis, but neither proof nor disproof is known. There is a widespread feeling that a proof of the original Riemann hypothesis would open the way to a proof of its generalisations as well. In fact, it might be better to attack the generalised Riemann hypothesis in all its glory, exploiting the wealth of methods now available, and then to deduce the original Riemann hypothesis as a special case.

There is also a vast amount of experimental evidence for the truth of the Riemann hypothesis – or what certainly looks like a vast amount until someone throws cold water on that claim. According to Carl Ludwig Siegel, Riemann calculated the first few zeros of his zeta function numerically but did not publish the results: they are located at

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