The subject founded by this work is Riemannian geometry. Riemann found the correct way to extend into n dimensions the differential geometry of surfaces, which Gauss himself proved in …

Jul 20, 1998 · Riemann argued that the fundamental ingredients for geometry are a space of points (called today a manifold) and a way of measuring distances along curves in the space.

Jul 20, 2011 · Riemann's thesis studied the theory of complex variables and, in particular, what we now call Riemann surfaces. It therefore introduced topological methods into complex …

Bernhard Riemann made profound, far-sighted discoveries with lasting consequences for mathematics and our understanding of space, gravity, and time. Riemannian geometry …

Riemann’s big breakthrough occurred while working on a function in the complex plane called the Riemann zeta function (an extension of the simpler zeta function first explored by Euler in the …

Feb 7, 2024 · Georg Friedrich Bernhard Riemann (German: [ˈɡeːɔʁk ˈfʁiːdʁɪç ˈbɛʁnhaʁt ˈʁiːman] (listen); 17 September 1826 – 20 July 1866) was a German mathematician who made …

Riemann argued that fundamental ingredients of geometry include space of points and it involves measuring distances along lines or curves in that space. As per Riemann, the space does not …

Successfully defending the thesis under questioning by Gauss, Riemann was awarded his doctorate in 1851. Riemann’s mathematical research quickly led him to important discoveries …

Riemann's work led to the idea of a multi-layered surface, later called a Riemann surface, allowing a multi-valued function of a complex variable to be interpreted as a single-valued function. The …

Nov 11, 2025 · One mathematician who found the presence of Dirichlet a stimulus to research was Bernhard Riemann, and his few short contributions to mathematics were among the most …