Bernhard Riemann

On 3 June 1862, Bernhard Riemann married Elise Koch from Körchow, Mecklenburg-Schwerin. She was his sister’s friend. The couple had a daughter, named Ida, born in Pisa in 1863.

In the autumn of 1862, shortly after his marriage, Riemann caught a severe cold, which turned into pleuritis. As was the custom those days, he went to Italy to cure his illness but in spite of periodic recovery, his health started deteriorating.

By the middle of 1866, he became very sick. In June, he left for the Italian village of Selasca on the shores of Lake Maggiore, reaching the place on 16th. On 19 July he sat under a fig tree, enjoying the landscape and working on his last paper on natural philosophy, which he left unfinished.

Georg Friedrich Bernhard Riemann was born on 17 September 1826 in Breselenz, now a part of Jameln municipality in the district Lüchow-Dannenberg, Germany. At the time of his birth, it was a separate village under the Kingdom of Hanover.

His father, Friedrich Bernhard Riemann, was a poor Lutheran minister in Breselenz. He and his wife, Charlotte nee Ebell, had six children, out of which Georg was born second. From his childhood, he was very shy and introverted.

Georg lost his mother early in his life. He had his elementary education under his father until the age of ten. Thereafter, somebody named Schulz, who taught at the local school, came to help his father in educating them.

Even at that time, he exhibited astonishing skills in mathematics, especially in calculus. Therefore, in the Easter of 1840, he was sent to live with his grandmother in Hanover and there he entered directly into the third class at the Lyceum (middle school).

He studied in the Hanover lyceum until grandmother’s death in 1842. Thereafter, he entered Johanneum Lüneburg, a traditional gymnasium (high school) in Lüneburg. He was a hardworking and good student, taking special interest in Hebrew and theology; but mathematics remained his favorite subject.

In 1852, on the recommendation of Gauss, Riemann began his career as a Privatdozent at the University of Göttingen. Concurrently, he also worked for Weber without any pay. At the same time, he started preparing for his Habilitation, which would entitle him to obtain appointment as a lecturer.

For his Habilitationsschrift (probationary essay), he chose the Fourier series on heat-flow, submitting it at the end of 1853. It was a masterpiece, which made great progress towards solving some of the foundational issues left unsolved by French mathematician Joseph Fourier in his work, ‘Théorie analytique de la chaleur’.

He also submitted a list of three possible subjects for his Habilitationsvortrag (probationary lecture), out of which Gauss chose the third. It was titled ‘Über die Hypothesen, welche der Geometrie zu Grunde liegen’ (On the hypotheses that underline geometry).

The lecture, given on June 10, 1854, not only introduced what today is known as n-dimensional Riemannian manifold, but also its curvature tensor and discussed the relation between mathematical space and actual space. However, the last was left as a theory for sixty years until it was proved by Einstein.

Even after his habilitation was complete, Riemann continued to work as a privatdozent. The position did not entail any kind of salary; but he was able to collect fees from his students. His first course was on partial differential equations with applications to physics and he had very few students.

Bernhard Riemann is best remembered for his novel approaches to the study of geometry. He argued that space could have infinite dimension and it was not necessary that a surface be drawn only in three-dimensional space.

He is also famous for his contributions to the theory of functions, complex analysis, and number theory. His works inspired Eugenio Beltrami to produce a description of non-Euclidean geometry and provided the mathematical foundation for Albert Einstein’s theory of relativity.