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Find out more about one of the highest honours in maths.

Near the beginning of his 1859 paper Riemann incorrectly assumes that the complex variable s =1/2 +ti is a zeta power. Riemann fails to recognise that an expression containing an imaginary number such as 1/2 +ti cannot be a power unless the base is a log base such as e. The best known example of this is Cotes's formula cosu + isinu equals e^(iu) where it is not possible for e to be meanfully replaced by other values, also e^(1/2) X e^(iu) equals e^[(1/2) +iu]. This means that Riemann is badly wrong in applying as a power s= (1/2) +ti. It also means that practically all the arguments in his 1859 paper are fallacious. submitted by Peter L. Griffiths.