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Bernhard Riemann

1826–1866 · mathematics, differential geometry, number theory, complex analysis

Bernhard Riemann was a mathematical genius whose ideas transformed geometry and analysis. His concept of curved space became the mathematical foundation for Einstein's general theory of relativity, and the hypothesis about the zeta function remains the greatest unsolved mystery of mathematics.

Biography

Born in the village of Breselenz (Hanover), studied theology, but soon switched to mathematics under the influence of Gauss in Göttingen. Received his doctorate under Gauss's supervision. Was a professor at the University of Göttingen. Died at age 39 of tuberculosis in Italy, where he had gone for treatment.

Key discoveries

Riemannian geometry: a generalization of Euclidean geometry to curved multidimensional spaces using the metric tensor; without it, modern cosmology and the theory of gravity are inconceivable.
Riemann integral: the first rigorous definition of the definite integral, based on the limit of integral sums; it still forms the basis of calculus courses.
Zeta function and Riemann hypothesis: formulated the famous hypothesis about the distribution of zeros of the zeta function, the proof of which became one of the 'Millennium Problems' and remains open.

💡 Riemann's historic 1854 lecture "On the Hypotheses That Lie at the Foundation of Geometry" was so groundbreaking that only a few listeners attended, among whom was a deeply impressed Gauss. It took more than half a century for Riemann's ideas to be understood and applied by Einstein.

"He viewed mathematics not just as a tool, but as an art that reveals the structure of reality."

Concepts

gravity spacetime curvature tensor

Laws

Einstein field equations

Scientists

Robert Hooke Jacob Bekenstein Karl Schwarzschild Joseph Weber Emmy Noether Kip Thorne Nicolaus Copernicus Isaac Newton

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