Riemann (1826-1866)
George Bernhard Riemann was born in 1826. This time period was the time of development of Non Euclidean geometry. He was the son of a Lutheran priest. He enrolled at the University of Göttingen at the age of 19 to study theology and philosophy in accordance with his father's wishes and to please his father. But he also took math classes and he was committed to math. A few years later he went to Berlin to study with great mathematicians. He went to Berlin to study with mathematicians like Jacobi, Dirichlet, Einstein. He also worked as a guard for the protection of the king for 2 days. He returned to Göttingen in 1849 to complete his studies. He did research on surface over a complex domain. The surface is also called Riemann surface today. This helped establish him as a first-rate mathematician. On whose recommendation Riemann was appointed to the Privandozent, paying a fee for his classes.
In 1857 he was appointed associate professor with salary. After Gauss died in 1855, Diriklet was replaced by Riemann four years later. As he fell ill in the hot climate, he went to Italy late in life to take care of himself. Riemann died in 1866 at the age of 39. While he was a privatdozent, he was hired by Gauss to take classes on complex topics that he found difficult, which he found challenging. Around the year 1854 a discussion was conducted under On the hypotheses that underlie the foundation of Geometry. Riemann's views and propositions regarding geometry were not understood by anyone except Riemann, Legendre, Gauss and Weaver. Later it was organized and published. What he presented was related to the study of matter in space. He referred to the surface of a great circle as a line. He studied the relationship of spheres and mentioned geometry as an empirical science.
Many of Riemann's proposals in geometry were guided by non-Euclidean geometry. He also mentions an alternative to the parallelism postulate which is as follows.
There are no parallel to a line through a point not on a line, in short, a pair of parallel lines meet at a point. This claim led to massive changes in ancient geometry by Gauss, Bolyai, Lobachevsky. Due to this, Axioms started to be seen in contradiction with the sixteenth postulate of Euclid, so that the second Axioms of Euclidean geometry also had to be changed, otherwise the consistency of geometry would be damaged.
Thus, Riemann seems to have made an important contribution to the refinement of Euclidean geometry and the development of non-Euclidean geometry.
Overall, his contributions to the field of mathematics are mentioned under the following points:
• Pursue Euclidean geometry and advance your presentation to assist in the development of Non-Euclidean geometry.
•Developed Complex Analysis using Analytical function.
• Developed the Riemann integral.
• Introduced the concept of Riemann surface.
• Developed Riemannian space and Riemannian geometry.
• Lectured on Riemannian function and Zeta function and advanced further possibilities of mathematics.
• Helped in the development of number theory.
• Complex number series mentioned.
• Contributed to the development of cosmology, general relativity, spherical geometry and celestial mechanics.
Thanks for reading
Study more about
Tags:
MATHEMATICIANS