George friedrich bernard riemann

Bernhard Riemann Facts Bernhard Riemann Facts Georg Friedrich Bernhard Riemann September 17, - July 20, was a leading mathematician who made enduring influences on analysis, number theory, and differential geometry. His contribution to these fields enabled the later development of general relativity. Interesting Bernhard Riemann Facts:

George friedrich bernard riemann

Riemann read the book in a week and then claimed to know it by heart. He then gradually worked his way up the academic profession, through a succession of poorly paid jobs, until he became a full professor in and gained, for the first time in his life, a measure of financial security.

George friedrich bernard riemann

However, inshortly after his marriage to Elise Koch, Riemann fell seriously ill with tuberculosis. Repeated trips to Italy failed to stem the progress of the disease, and he died in Italy in Ill health prevented Riemann from publishing all his work, and some of his best was published only posthumously—e.

His few papers are also difficult to read, but his work won the respect of some of the best mathematicians in Germanyincluding his friend Dedekind and his rival in Berlin, Karl Weierstrass.

Other mathematicians were gradually drawn to his papers by their intellectual depth, and in this way he set an agenda for conceptual thinking over ingenious calculation. In his doctoral thesisRiemann introduced a way of generalizing the study of polynomial equations in two real variables to the case of two complex variables.

Bernhard Riemann Essays

In the real case a polynomial equation defines a curve in the plane. In and in his more widely available paper ofRiemann showed how such surfaces can be classified by a number, later called the genus, that is determined by the maximal number of closed curves that can be drawn on the surface without splitting it into separate pieces.

This is one of the first significant uses of topology in mathematics. Riemann argued that the fundamental ingredients for geometry are a space of points called today a manifold and a way of measuring distances along curves in the space.

He argued that the space need not be ordinary Euclidean space and that it could have any dimension he even contemplated spaces of infinite dimension.

Nor is it necessary that the surface be drawn in its entirety in three-dimensional space. A few years later this inspired the Italian mathematician Eugenio Beltrami to produce just such a description of non-Euclidean geometrythe first physically plausible alternative to Euclidean geometry.

It seems that Riemann was led to these ideas partly by his dislike of the concept of action at a distance in contemporary physics and by his wish to endow space with the ability to transmit forces such as electromagnetism and gravitation.

In Riemann also introduced complex function theory into number theory. He took the zeta function, which had been studied by many previous mathematicians because of its connection to the prime numbers, and showed how to think of it as a complex function.

George friedrich bernard riemann

The Riemann zeta function then takes the value zero at the negative even integers the so-called trivial zeros and also at points on a certain line called the critical line. Standard methods in complex function theory, due to Augustin-Louis Cauchy in France and Riemann himself, would give much information about the distribution of prime numbers if it could be shown that all the nontrivial zeros lie on this line—a conjecture known as the Riemann hypothesis.

All nontrivial zeros discovered thus far have been on the critical line. In fact, infinitely many zeros have been discovered to lie on this line.

Riemann, Georg Friedrich Bernhard

Riemann took a novel view of what it means for mathematical objects to exist. He believed that this approach led to conceptual clarity and prevented the mathematician from getting lost in the details, but even some experts disagreed with such nonconstructive proofs.

Riemann also studied how functions compare with their trigonometric or Fourier series representation, which led him to refine ideas about discontinuous functions. He showed how complex function theory illuminates the study of minimal surfaces surfaces of least area that span a given boundary.

He was one of the first to study differential equations involving complex variables, and his work led to a profound connection with group theory.

He introduced new general methods in the study of partial differential equations and applied them to produce the first major study of shock waves.Bernhard Riemann, as he was called, was the second of six children of a Protestant minister, Friedrich Bernhard Riemann, and the former Charlotte Ebell.

The children received their elementary education from their father, who was later assisted by a local teacher. Bernhard Riemann Georg Friedrich Bernhard Riemann Matemático alemán Nació el 17 de septiembre de en Breselenz.

Su padre, un ministro luterano, se encargó de la educación de sus hijos hasta que cumplieron diez años. George Friedrich Bernard Riemann In high school, Riemann studied the Bible intensively, but math was still a heavier influence on his mind.

As funny as it sounds, he actually tried to prove mathematically the correctness of the book of Genesis. Bernhard Riemann's father, Friedrich Bernhard Riemann, was a Lutheran minister. Friedrich Riemann married Charlotte Ebell when he was in his middle age.

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Bernhard was the second of their six children, two boys and four girls. Friedrich Riemann acted as teacher to his children and he taught Bernhard. Georg Friedrich Bernhard Riemann (September 17, - July 20, ) was a leading mathematician who made enduring influences on analysis, number theory, and differential geometry.

His contribution to these fields enabled the later development of general relativity. Riemann was born in Germany to a. Bernhard Riemann has been one of the greatest mathematicians of all time.

His contributions span from algebra to analysis, from non-euclidean geometry to topology. After the solution of the Last Theorem of Fermat, the Riemann's Hypothesis on the distribution of the Prime Numbers is the last big Born: Sep 17,

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