Bernhard Riemann
Early Life and Education
Georg Friedrich Bernhard Riemann was born on September 17, 1826, in the village of Breselenz, in the Kingdom of Hanover (now part of Germany). His father, Friedrich Bernhard Riemann, was a Lutheran pastor, and his mother was Charlotte Ebell. Riemann was the second of six children.
Riemann showed exceptional mathematical abilities from an early age. His mathematical talent was recognized by his school teachers, who provided him with advanced mathematical texts including Leonhard Euler's works. He studied these texts independently and developed his own mathematical theories.
In 1846, Riemann enrolled at the University of Göttingen, initially to study theology and philology, in accordance with his father's wishes. However, he soon switched to mathematics, which was his true passion. Here, he was influenced by the teachings of Carl Friedrich Gauss and Peter Gustav Lejeune Dirichlet, two of the leading mathematicians of the time.
Career and Contributions to Mathematics
Riemann's contributions to mathematics are numerous and significant. His work has had a profound impact on both pure and applied mathematics, and his ideas continue to influence many areas of mathematical research.
One of Riemann's most important contributions is the Riemann Hypothesis, which is a conjecture related to the distribution of prime numbers. This hypothesis, which remains unproven, is one of the most famous unsolved problems in mathematics and is one of the seven "Millennium Prize Problems" for which the Clay Mathematics Institute has offered a $1 million prize for a solution.
Riemann also made significant contributions to the field of differential geometry, which has had important implications for the theory of general relativity. His introduction of Riemannian geometry, which deals with curved spaces, was revolutionary and forms the basis for much of modern geometry.
In addition, Riemann made important contributions to the field of complex analysis with his formulation of the Riemann Mapping Theorem, which deals with the conformal mapping of simply-connected domains.
Later Life and Legacy
Riemann's health began to decline in the 1860s, and he died on July 20, 1866, at the age of 39. Despite his short life, his contributions to mathematics have had a lasting impact.
Riemann's work continues to be studied and expanded upon by mathematicians around the world. His ideas have influenced a wide range of fields, from number theory and geometry to physics and engineering. His legacy is evident in the numerous mathematical concepts that bear his name, including Riemann surfaces, Riemann integrals, and the Riemann-Roch theorem.