Which mathematician’s 1859 paper introduced the Riemann hypothesis?

The story behind the answer

Bernhard Riemann introduced the Riemann hypothesis in an 1859 paper.

Riemann presented the idea in “On the Number of Primes Less Than a Given Magnitude,” a short but influential paper concerning the distribution of prime numbers. The hypothesis concerns the nontrivial zeros of the Riemann zeta function and proposes that every such zero has real part one-half.

The statement is closely connected to how regularly primes are distributed among the integers. It has been verified for very many zeros by computation, but no general proof has been accepted. The problem is one of the Clay Mathematics Institute’s seven Millennium Prize Problems.

Riemann’s paper was written in German and published by the Berlin Academy in 1859. The hypothesis is sometimes confused with the prime number theorem, which was proved independently around the end of the 19th century and gives an overall estimate for the density of primes.

Source: Wikipedia · fact-checked Oct. 2026

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