Bernhard Riemann formulates the Riemann hypothesis, one…
1859 CE
Riemann's published works open up research areas combining analysis with geometry.
These will subsequently become major parts of the theories of Riemannian geometry, algebraic geometry, and complex manifold theory.
The theory of Riemann surfaces will be elaborated by Felix Klein and particularly Adolf Hurwitz.
This area of mathematics is part of the foundation of topology and is still being applied in novel ways to mathematical physics.
Riemann was born on September 17, 1826 in Breselenz, a village near Dannenberg in the Kingdom of Hanover.
His father, Friedrich Bernhard Riemann, was a poor Lutheran pastor in Breselenz who fought in the Napoleonic Wars.
His mother, Charlotte Ebell, died before her children had reached adulthood.
Riemann was the second of six children, shy and suffering from numerous nervous breakdowns.
Riemann exhibited exceptional mathematical skills, such as calculation abilities, from an early age but suffered from timidity and a fear of speaking in public.
During 1840, Riemann went to Hanover to live with his grandmother and attend lyceum (middle school).
After the death of his grandmother in 1842, he attended high school at the Johanneum Lüneburg.
In high school, Riemann studied the Bible intensively, but he was often distracted by mathematics.
His teachers were amazed by his adept ability to perform complicated mathematical operations, in which he often outstripped his instructor's knowledge.
In 1846, at the age of nineteen, he started studying philology and Christian theology in order to become a pastor and help with his family's finances.
During the spring of 1846, his father, after gathering enough money, had sent Riemann to the University of Göttingen, where he planned to study towards a degree in Theology.
However, once there, he began studying mathematics under Carl Friedrich Gauss (specifically his lectures on the method of least squares).
Gauss recommended that Riemann give up his theological work and enter the mathematical field; after getting his father's approval, Riemann transferred to the University of Berlin in 1847.
During his time of study, Carl Gustav Jacob Jacobi, Peter Gustav, Lejeune Dirichlet, Jakob Steiner, and Gotthold Eisenstein were teaching.
He stayed in Berlin for two years and returned to Göttingen in 1849.
Riemann had held his first lectures in 1854, which had founded the field of Riemannian geometry and thereby set the stage for Albert Einstein's general theory of relativity
In 1857, there had been an attempt to promote Riemann to extraordinary professor status at the University of Göttingen.
Although this attempt failed, it did result in Riemann finally being granted a regular salary.
In 1859, following Dirichlet's death, he is promoted to head the mathematics department at the University of Göttingen.
He is also the first to suggest using dimensions higher than merely three or four in order to describe physical reality.