Bernhard Riemann

Episode #8 of the course “Greatest Mathematicians”

The contributions Georg Friedrich Bernhard Riemann made to mathematics later enabled the development of Einstein’s general relativity. His lectures on Riemannian geometry in 1854 provided the framework for this. In one of these lectures, he became the first to describe physical reality using dimensions higher than three or four—an idea that was ultimately vindicated with Einstein’s discoveries in the early 1900s.

Riemann was born in Breselenz, Germany in 1826. His work spans the fields of complex analysis, real analysis, number theory, and differential geometry, of which Riemannian geometry is a subset. He never made it to the age of 40, passing away in 1866, but his short career was filled with genuine masterpieces. In his journals are innovative methods, insightful ideas, and extensive imagination—ideas he cultivated under fellow German mathematician Carl Friedrich Gauss.

Often referred to as the most important unproved assumption in present-day mathematics, the Riemann Hypothesis is the product of Riemann’s work. This series of conjectures about properties of the zeta function greatly influenced modern analytic number theory. He is also responsible for Riemann surfaces, which provided the mathematical groundwork for the study of topology. These concepts are still extensively applied in modern mathematical physics.

Riemannian Geometry, however, might be his most important contribution to the world of mathematics. In addition to the lecture in 1854 and the publishing of his findings two years after his death in 1868, Riemann was also developing a collection of numbers at every point in space that would aid in analyzing how much things were curved or bent. This became a popular fundamental construction in geometry, known now as a Riemannian metric.

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