Bernhard Riemann

Introduction

Bernhard Riemann was one of the top mathematicians of the eighteen hundreds. He is most well known for his his development of non-Euclidean geometry which is used today in physics and in the relativity theory.

Summary of Riemann's Life

Georg Friedrich Bernhard Riemann was born on September 17th, 1826 in Breselenz, Germany to Georg Friedrich Bernhard Riemann and Charlotte Ebell. Sadly, his mother died before her children were grown. He had five siblings, four girls and one boy. His father, who was a Lutheran minister and fought in the Napoleonic Wars, taught Bernhard until he was about ten years old. After that, a teacher from a local school named Schulz helped with Bernhard's education. At a very young age, he started to exhibit exceptional skills in math and calculations. In high school, Riemann studied the Bible intensively. But his mind often drifted back to mathematics and he even tried to prove mathematically the correctness of the book of Genesis. His teachers were amazed by his genius and by his ability to solve extremely complicated mathematical operations with ease.

When he was fourteen years of age, he entered into the third class at the Lyceum in Hanover. While he was there, he lived with his grandmother, but in 1842, when she passed away, he moved to the Johanneum Gymnasium in Luneberg. While attending school here, he befriended a teacher who saw his true mathematical abilities. This teacher let him use his private library, allowing him to further advance his mathematical prowess by reading the works of Legendre and Gauss.

In 1846, at the age of 19, he started studying philosophy and theology at Gottingen University. He was hoping to become a priest and help with his family's financial situation. However, he soon realized that theology wasn't for him and, with his father's permission, started to pursue science and mathematics. After this transfer, he started taking classes in mathematics from Moritz Stern and Johann Carl Friedrich Gauss.

After a year at Gottingen, he moved to Berlin. While there, he studied under a few of the greatest mathematicians of all time for about two years. These were Jacobi, Steiner, and Eisenstein. After learning all about the new discoveries in mathematics from these men, he then returned to Gцttingen to finish his doctoral work in 1849.

Two years later, in 1951, he submitted his PhD thesis which had been supervised by Gauss. After Gauss's recommendation, Riemann was appointed to a post in Gцttingen and he worked for his habilitation, the degree which would allow him to become a lecturer. He spent two and a half years working on his habilitation dissertation which was on the representability of functions by trigonometric series. In order to complete his habilitation, Riemann had to present a lecture on geometry. His lecture, On the hypotheses that lie at the foundations of geometry, was delivered on June tenth, 1854 and instantly became a classic of mathematics.

In 1855, Gauss's chair at Gottingen was superseded by Johann Peter Gustav Lejeune Dirichlet, another mathematician who had a