He was born in Breselenz, a village near Dannenberg in the Kingdom of Hanover in what is today Germany. His father Friedrich Bernhard Riemann was Lutheran pastor in Breselenz. Bernhard was the second of six children.
In 1840 Bernhard went to Hanover to live with his grandmother and visit the Lyceum. After the death of his grandmother in 1842 he went to the Johanneum in Lüneburg. In 1846, at the age of 19, he started studying philology and theology at the University of Göttingen. He attended lectures of Gauss on the method of least squares. In 1847 his father allowed him to stop studying Theology and start studying Mathematics.
In 1847 he moved to Berlin, where Jacobi, Dirichlet and Steiner were teaching. He stayed in Berlin for two years and returned to Göttingen in 1849.
Riemann held his first lectures in 1854, which not only founded the field of Riemannian geometry but set the stage for Einstein's general relativity. He was promoted an extraordinary professor at the University of Göttingen in 1857 and became an ordinary professor in 1859 following Dirichlet's death.
The Riemann zeta function along the critical line is sometimes studied in terms of the Z function, whose real zeros correspond to the zeros of the zeta function on the critical line.
Riemann mentioned the conjecture that became known as the Riemann hypothesis in his 1859 paper On the Number of Primes Less Than a Given Magnitude, but as it was not essential to his central purpose in that paper, he did not attempt a proof.
The zeroes of the Riemann zeta function and the prime numbers satisfy a certain duality property, known as the explicit formulae which show that in the language of Fourier analysis the zeros of the zeta function can be regarded as the harmonic frequencies in the distribution of primes.
Georg Friedrich Bernhard Riemann (September 17, 1826 - July 20, 1866) (pronounced REE mahn) was a German mathematician who made important contributions to analysis and differential geometry, some of them paving the way for the later development of general relativity.
His name is connected with the Riemann zeta function, the Riemann integral, the Riemann lemma, Riemannian manifolds, the Riemann mapping theorem, Riemann-Hilbert problems, Riemann surfaces, the Riemann-Roch theorem, the Riemann sphere, and the Cauchy-Riemann equations.
Riemann held his first lectures in 1854, which not only founded the field of Riemannian geometry but set the stage for Einstein's general relativity.
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