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Georg Friedrich RiemannGerman mathematician
Date of Birth: 17.09.1826
Country:  Germany |
Content:
Biography of Georg Friedrich Riemann
Early Life and EducationGeorg Friedrich Riemann was a German mathematician, mechanic, and physicist. He was born on September 17, 1826, in the village of Breselenz near Hanover, into a Lutheran pastor's family. Riemann studied at the gymnasiums in Hanover and Lüneburg. In 1846, he enrolled at the University of Göttingen with the intention of studying theology and philology to become a priest, as his father desired. However, his fascination with mathematics led him to attend lectures on subjects far removed from theology, such as numerical solutions of equations, definite integrals (taught by C. Gauss), terrestrial magnetism, and the method of least squares. Riemann's father eventually relented to his son's persistent requests, allowing him to dedicate himself entirely to mathematics.
Contributions to Mathematics
In 1847, Riemann attended lectures by renowned mathematicians of the time, including C. Jacobi on mechanics and P. Dirichlet on number theory, at the University of Berlin. It was there that the foundation of Riemann's research in the theory of functions of a complex variable was laid. Upon his return to Göttingen in 1849, he developed an interest in physics after connecting with Wilhelm Weber, one of Gauss's collaborators. Riemann became so absorbed in the subject that he only presented his doctoral dissertation, "Foundations for a General Theory of Functions of a Complex Variable" (Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse), which received high praise from Gauss, one of his opponents, in 1851. His dissertation laid the groundwork for the geometric approach to the theory of analytic functions, introducing Riemann surfaces and topological representations into analysis, as well as developing the theory of conformal mappings. In his dissertation, Riemann also provides his definition of a complex function.
In 1854, Riemann made two fundamental contributions: a work on the representability of functions by trigonometric series and "On the Hypotheses that Lie at the Foundations of Geometry" (Über die Hypothesen, welche der Geometrie zu Grunde liegen). The latter work is now considered a classic, where Riemann proposed the general idea of mathematical space as a manifold of arbitrary dimensions and classified all existing types of geometry, including the then-obscure non-Euclidean geometry. He demonstrated the possibility of creating an infinite number of new types of space, many of which were later introduced into geometry and mathematical physics. Riemann also discussed Riemannian spaces and raised the question of the "causes of the metric properties" of physical space, foreshadowing what was later accomplished in Albert Einstein's general theory of relativity.
Career and Legacy
In 1854, Riemann became a private lecturer at the University of Göttingen. He was appointed as an associate professor in 1857 and became the director of the Göttingen Observatory in 1859. In the last years of his short life, Riemann received numerous honors, gained recognition from leading scientists, and was elected as a member of various scientific societies, including the Royal Society of London and the French Academy of Sciences. Despite never having robust health, Riemann contracted pleurisy in 1862 and never fully recovered from the illness. He spent his final four years in Italy and passed away in Selasca on Lake Maggiore on July 20, 1866.
