Bernhard Riemann (Author of Sulle ipotesi che stanno alla base della geometria e altri scritti scientifici e filosofici)

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Bernhard Riemann

Born

in Germany

September 17, 1826

Died

July 20, 1866

Website

Genre

Science, Mathematics, Number Theory

Influences

Carl Friedrich Gauss, Gotthold Eisenstein, Euclid, Adrien-Marie Legend ...more

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Georg Friedrich Bernhard Riemann [ËˆÊiËman] ( listen) (September 17, 1826 â€� July 20, 1866) was an influential German mathematician who made lasting contributions to analysis, number theory, and differential geometry, some of them enabling the later development of general relativity.

Riemann was born in Breselenz, a village near Dannenberg in the Kingdom of Hanover in what is the Federal Republic of Germany today. His mother, Charlotte Ebell, died before her children had reached adulthood. Riemann was the second of six children, shy and suffering from numerous nervous breakdowns. Riemann exhibited exceptional mathematical skills, such as calculation abilities, from an early age but suffered from timidity and a fear of speaking in public.

Rieman Georg Friedrich Bernhard Riemann [ËˆÊiËman] ( listen) (September 17, 1826 â€� July 20, 1866) was an influential German mathematician who made lasting contributions to analysis, number theory, and differential geometry, some of them enabling the later development of general relativity.

Riemann was born in Breselenz, a village near Dannenberg in the Kingdom of Hanover in what is the Federal Republic of Germany today. His mother, Charlotte Ebell, died before her children had reached adulthood. Riemann was the second of six children, shy and suffering from numerous nervous breakdowns. Riemann exhibited exceptional mathematical skills, such as calculation abilities, from an early age but suffered from timidity and a fear of speaking in public.

Riemann held his first lectures in 1854, which founded the field of Riemannian geometry and thereby set the stage for Einstein's general theory of relativity. In 1857, there was an attempt to promote Riemann to extraordinary professor status at the University of GÃ¶ttingen. Although this attempt failed, it did result in Riemann finally being granted a regular salary. In 1859, following Lejeune Dirichlet's death, he was promoted to head the mathematics department at GÃ¶ttingen. He was also the first to suggest using dimensions higher than merely three or four in order to describe physical realityâ€”an idea that was ultimately vindicated with Albert Einstein's contribution in the early 20th century. In 1862 he married Elise Koch and had a daughter.

Riemann fled GÃ¶ttingen when the armies of Hanover and Prussia clashed there in 1866. He died of tuberculosis during his third journey to Italy in Selasca (now a hamlet of Verbania on Lake Maggiore) where he was buried in the cemetery in Biganzolo (Verbania). Meanwhile, in GÃ¶ttingen his housekeeper discarded some of the papers in his office, including much unpublished work. Riemann refused to publish incomplete work and some deep insights may have been lost forever.

Riemann's published works opened up research areas combining analysis with geometry. These would subsequently become major parts of the theories of Riemannian geometry, algebraic geometry, and complex manifold theory. The theory of Riemann surfaces was elaborated by Felix Klein and particularly Adolf Hurwitz. This area of mathematics is part of the foundation of topology, and is still being applied in novel ways to mathematical physics.

Riemann made major contributions to real analysis. He defined the Riemann integral by means of Riemann sums, developed a theory of trigonometric series that are not Fourier seriesâ€”a first step in generalized function theoryâ€”and studied the Riemannâ€“Liouville differintegral.

He made some famous contributions to modern analytic number theory. In a single short paper (the only one he published on the subject of number theory), he investigated the Riemann zeta function and established its importance for understanding the distribution of prime numbers. He made a series of conjectures about properties of the zeta function, one of which is the well-known Riemann hypothesis.

He applied the Dirichlet principle from variational calculus to great effect; this was later seen to be a powerful heuristic rather than a rigorous method. Its justification took at least a generation. His work on monodromy and the hypergeometric function in the complex domain made a great impression, and established a basic way of working with functions by consideration only of their singularities. ...more

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Average rating: 4.13 · 24 ratings · 2 reviews · 51 distinct works â€� Similar authors

	Sulle ipotesi che stanno alla base della geometria e altri scritti scientifici e filosofici by Bernhard Riemann, Renato Pettoello (Editor) 4.50 avg rating — 12 ratings — published 2010 — 17 editions	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
	Bernhard Riemann Collected Papers 3.86 avg rating — 7 ratings — published 1899 — 2 editions	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
	Bernard Riemann's gesammelte mathematische Werke und wissenschaftlicher Nachlass (Cambridge Library Collection - Mathematics) by Bernhard Riemann, Richard Dedekind (Editor), Heinrich Martin Weber (Editor) really liked it 4.00 avg rating — 4 ratings — 56 editions	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
	Oeuvres Mathematiques de Riemann, Traduites Par L. Langel, Avec Une Preface de M. Hermite Et Un Discours de M. Felix Klein. it was amazing 5.00 avg rating — 1 rating — published 2006 — 3 editions	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
	The Collected Works of Bernhard Riemann (Dover Books on Mathematics) by Bernhard Riemann, Hans Lewy (Introduction), Heinrich Weber (Editor) it was ok 2.00 avg rating — 1 rating	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
	ANIMAUX livre de coloriage 2: Livre de coloriage Ã©tonnant, animaux gÃ©niaux pour les enfants, avec chien, chat, kangourou, Ã©lÃ©phant et plus 0.00 avg rating — 0 ratings — published 1857 — 2 editions	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
	Partielle Differentialgleichungen und Deren Anwendung auf Physikalische Fragen (Classic Reprint): Vorlesungen 0.00 avg rating — 0 ratings — published 1938 — 3 editions	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
	Å’uvres MathÃ©matiques de Riemann 0.00 avg rating — 0 ratings — 19 editions	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
	Grundlagen fÃ¼r eine Allgemeine Theorie der Functionen Einer VerÃ¤nderlichen Complexen GrÃ¶sse 0.00 avg rating — 0 ratings — 11 editions	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
	Antibiotic Policies 0.00 avg rating — 0 ratings	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars

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Quotes by Bernhard Riemann (?)

“It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it.”
― Bernhard Riemann

tags: adrian-marie-legendre, axioms, darkness, definitions, euclid, geometry, legendre, mathematician, mathematics, philosophers, relationships, renown, science, scientist, space

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“Without doubt it would be desirable to have a rigorous proof of this proposition; however I have left this research aside for the time being after some quick unsuccessful attempts, because it appears to be unnecessary for the immediate goal of my study.”
― Bernhard Riemann

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“One can set up a completely self-contained mathematical theory, which proceeds from the elementary laws that are valid for individual points to processes in the actually given continuously filled space, without distinguishing whether it is gravity, electricity, magnetism, or the equilibrium of heat that is being treated.”
― Bernard Riemann

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Bernhard Riemannâ€™s Followers (31)

Bernhard Riemann

Combine EditionsBernhard Riemannâ€™s books

Combine Editions
Bernhard Riemannâ€™s books