File:Georg_Friedrich_Bernhard_Riemann.jpeg · Wikimedia Commons · See Wikimedia Commons

EntityQ42299· pop 110· linked from 510 articles

Bernhard Riemann

Also known as Georg Friedrich Bernhard Riemann

German mathematician (1826–1866)

AI overview

Bernhard Riemann was a German mathematician from the 19th century who made groundbreaking contributions to mathematics before dying at age 39. His work fundamentally shaped modern mathematics, particularly in areas like analysis and geometry, and continues to influence mathematical thinking today.

AI-generated from the Wikipedia summary — may contain errors.

Person · Open Library

Born: 1826
Died: 1866
Works: 17

Top works

Partielle Differentialgleichungen und ihre Anwendungen auf physikalische Fragen
Ueber das Verschwinden der Theta-Functionen
Über die Hypothesen, welche der Geometrie zu Grunde liegen
Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse
Beiträge zur Theorie der durch die Gauss'sche Reihe F([alpha], [beta], [gamma], [chi]) darstellbaren Functionen

via Open Library + Wikidata

Music · MusicBrainz

via MusicBrainz · CC0

Listeners · Last.fm

Listeners: 1
Total plays: 1

via Last.fm · Bernhard Riemann

Recent publications · Crossref

5 total works indexed

Global burden of 369 diseases and injuries in 204 countries and territories, 1990–2019: a systematic analysis for the Global Burden of Disease Study 2019
· 2020 · cited 15,396x
The WEKA data mining software
· 2009 · cited 13,058x
Global, regional, and national incidence, prevalence, and years lived with disability for 354 diseases and injuries for 195 countries and territories, 1990–2017: a systematic analysis for the Global Burden of Disease Study 2017
· 2018 · cited 10,818x
A tutorial on support vector regression
· 2004 · cited 9,935x
2018 ESC/ESH Guidelines for the management of arterial hypertension
· 2018 · cited 8,156x

via Crossref · CC0

Quotes

“Nevertheless, it remains conceivable that the measure relations of space in the infinitely small are not in accordance with the assumptions of our geometry [Euclidean geometry], and, in fact, we should have to assume that they are not if, by doing so, we should ever be enabled to explain phenomena in a more simple way.”
“Magnitude-notions are only possible where there is an antecedent general notion which admits of different specialisations. According as there exists among these specialisations a continuous path from one to another or not, they form a continuous or discrete manifoldness; the individual specialisations are called in the first case points, in the second case elements, of the manifoldness.”
“With every simple act of thinking, something permanent, substantial, enters our soul. This substantial somewhat appears to us as a unit but (in so far as it is the expression of something extended in space and time) it seems to contain an inner manifoldness; I therefore name it "mind-mass." All thinking is, accordingly, formation of new mind masses.”
“Mind-masses entering the soul appear to us as ideas, the quality of the latter depending on the inner state of the former.”
“Forming mind-masses amalgamate, combine or compound themselves in definite degree, partly with each other, partly with older mind-masses. The manner and strength of these combinations depend on conditions which are but imperfectly recognised by Herbart... They depend chiefly upon the inner relationship of the mind-masses.”
“The soul is a compact of mind-masses combined in a most intimate and manifold manner. It grows constantly by accession of mind-masses, and upon these depend its development.”

via Wikiquote · CC BY-SA

Wikidata facts

Image: Georg Friedrich Bernhard Riemann.jpeg

Show 6 more facts

Commons category: Bernhard Riemann
date of birth: 1826-09-17
date of death: 1866-07-20
birth name: Georg Friedrich Bernhard Riemann
Commons gallery: Georg Friedrich Bernhard Riemann
name in native language: Bernhard Riemann

Sources (7)

via Wikidata · CC0

~18 min read

Article

Georg Friedrich Bernhard Riemann (/ˈriːmɑːn/; German: [ˈɡeːɔʁk ˈfʁiːdʁɪç ˈbɛʁnhaʁt ˈʁiːman] ; 17 September 1826 – 20 July 1866) was a German mathematician who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis. His 1859 paper on the prime-counting function, containing the original statement of the Riemann hypothesis, is regarded as a foundational paper of analytic number theory. Through his pioneering contributions to differential geometry, Riemann laid the foundations of the mathematics of general relativity. He is considered by many to be one of the greatest mathematicians of all time.

Biography