However, several of his students became influential mathematicians, among them Richard Dedekind, Bernhard Riemann, and Friedrich Bessel.

In mathematics, the Cauchy – Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which must be satisfied if we know that a complex function is complex differentiable.

Historically, the concept of fundamental group first emerged in the theory of Riemann surfaces, in the work of Bernhard Riemann, Henri Poincaré and Felix Klein, where it describes the monodromy properties of complex functions, as well as providing a complete topological classification of closed surfaces.

Heine proposed that Cantor solve an open problem that had eluded Dirichlet, Lipschitz, Bernhard Riemann, and Heine himself: the uniqueness of the representation of a function by trigonometric series.

A rigorous mathematical definition of the integral was given by Bernhard Riemann.

Additional impetus to consider continuous groups came from ideas of Bernhard Riemann, on the foundations of geometry, and their further development in the hands of Klein.

* Bernhard Riemann

Some notable mathematicians include Archimedes of Syracuse, Leonhard Euler, Carl Gauss, Johann Bernoulli, Jacob Bernoulli, Aryabhata, Brahmagupta, Bhaskara II, Nilakantha Somayaji, Omar Khayyám, Muhammad ibn Mūsā al-Khwārizmī, Bernhard Riemann, Gottfried Leibniz, Andrey Kolmogorov, Euclid of Alexandria, Jules Henri Poincaré, Srinivasa Ramanujan, Alexander Grothendieck, David Hilbert, Alan Turing, von Neumann, Kurt Gödel, Joseph-Louis Lagrange, Georg Cantor, William Rowan Hamilton, Carl Jacobi, Évariste Galois, Nikolay Lobachevsky, Rene Descartes, Joseph Fourier, Pierre-Simon Laplace, Alonzo Church, Nikolay Bogolyubov and Pierre de Fermat.

Bernhard Riemann in his memoir " On the Number of Primes Less Than a Given Magnitude " published in 1859 extended the Euler definition to a complex variable, proved its meromorphic continuation and functional equation and established a relation between its zeros and the distribution of prime numbers.

In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval.

In the 1850s, Bernhard Riemann developed an equivalent theory of elliptical geometry, in which no parallel lines pass through P. In this geometry, triangles have more than 180 ° and circles have a ratio of circumference-to-diameter that is less than pi.

Tensors were first conceived by Tullio Levi-Civita and Gregorio Ricci-Curbastro, who continued the earlier work of Bernhard Riemann and Elwin Bruno Christoffel and others, as part of the absolute differential calculus.

* September 17 – Bernhard Riemann, German mathematician ( d. 1866 )

* Bernhard Riemann formulates the Riemann hypothesis, one of the most important open problems of contemporary mathematics.

* July 20 – Bernhard Riemann, German mathematician ( b. 1826 )

In the 19th century, Augustin Cauchy finally developed a rigorous theory of limits, and Bernhard Riemann followed up on this by formalizing what is now called the Riemann integral.

In the 19th century, calculus was put on a much more rigorous footing by mathematicians such as Augustin Louis Cauchy ( 1789 – 1857 ), Bernhard Riemann ( 1826 – 1866 ), and Karl Weierstrass ( 1815 – 1897 ).

Bernhard Riemann, in a famous lecture in 1854, founded the field of Riemannian geometry, discussing in particular the ideas now called manifolds, Riemannian metric, and curvature.

In the mathematical field of differential geometry, the Riemann curvature tensor, or Riemann – Christoffel tensor after Bernhard Riemann and Elwin Bruno Christoffel, is the most standard way to express curvature of Riemannian manifolds.

Amati Music also publishes reference works in cello pedagogy under Pricope's editorship, including Duport's Essai sur le doigté du violoncelle et la conduite de l ' archet ( 1809 ) and Bernhard Romberg's Violoncell-Schule ( 1840 ).

He later worked for the company that had produced the special paper for the Operation Bernhard forgeries.

Euler generalised the problem considerably, and his ideas were taken up years later by Bernhard Riemann in his seminal 1859 paper On the Number of Primes Less Than a Given Magnitude, in which he defined his zeta function and proved its basic properties.

" die Anzahl der Primzahlen unter einer gegebenen " ( usual English translation: " On the Number of Primes Less Than a Given Magnitude ") is a seminal 10-page paper by Bernhard Riemann published in the November 1859 edition of the Monatsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin.

Therefore, on 13 September the cabinet dismissed Count Detlev von Einsiedel, followed by Bernhard von Lindenau.

* 1984 – Bernhard Hugo Goetz shoots four African-American would-be muggers on an express train in Manhattan, New York City.

Bernhard ’ s focus on Jungian depth psychology proved to be the single greatest influence on Fellini ’ s mature style and marked the turning point in his work from neorealism to filmmaking that was “ primarily oneiric ”.

Bernhard Riemann's article on the number of primes below a given magnitude.

In fact he exerted enormous influence on the North German School of composers, in particular Georg Anton Benda, Bernhard Joachim Hagen, Ernst Wilhelm Wolf, Johann Gottfried Müthel, Friedrich Wilhelm Rust and many others.

* In 1984, Bernhard Goetz was approached on a New York City subway train by four men intent on mugging him.

Prior to the wedding, on 24 November 1936, Prince Bernhard was granted Dutch citizenship and changed the spelling of his names from German to Dutch.

In 1956, the influence of Miss Hofmans on Juliana's political views would almost bring down the House of Orange in a constitutional crisis that caused the court and the royal family to split in a Bernhard faction set on removing a queen considered religiously fanatic and a threat to NATO, and the queen's pious and pacifist courtiers.

Juliana's husband, Prince Bernhard, died barely eight months after her, on 1 December 2004, aged 93 and his remains were placed next to hers.

Bernhard is number 97 on Comedy Central's list of the 100 greatest standups of all time.

In 1991 Bernhard began playing the role of Nancy Bartlett on the hit sitcom Roseanne.

She also appeared ( as herself ) on Will and Grace in an episode dealing with Will and Grace's spuriously bidding on Sandra's Manhattan apartment in order to become friendly with her and culminates in a diatribe from Bernhard when their ruse is exposed, with obfuscating sounds of a blender ( she was having a smoothie made ) blotting out supposed obscenities.

She gave birth to daughter Cicely Yasin Bernhard on July 4, 1998.

Bernhard was a featured guest singer with children's artist Dan Zane's on the Family Dance album's " Thrift Shop ".

Minerva Mayflower, played by Sandra Bernhard, is sitting on a desk singing the song while it is being played on her headphones.

Dahlgren was born on November 13, 1809 in Philadelphia, the son of Bernhard Ulrik Dahlgren, merchant and Swedish Consul in Philadelphia.

His principal importance was, however, as editor of three scientific journals of great value: Allgemeine Geographische Ephemeriden ( 4 vols., Gotha, 1798-1799 ), Monatliche Correspondenz zur Beförderung der Erd-und Himmels-Kunde ( 28 vols., Gotha, 1800-1813, from 1807 edited by Bernhard von Lindenau ), and ( Genoa, 1818-1826, 14 vols., and one number of the 15th, the suppression of which was instigated by the Jesuits ).

Bernhard Riemann, Johann Peter Gustav Lejeune Dirichlet and a number of significant mathematicians made their contributions to mathematics here.

In 1859 Bernhard Riemann used complex analysis and a special meromorphic function now known as the Riemann zeta function to derive an analytic expression for the number of primes less than or equal to a real number x.

Based on Anne Catherine's growing reputation, during her life a number of figures who were influential in the renewal movement of the Church early in the 19th century came to visit her, among them Clemens von Vischering, the Archbishop of Cologne, Johann Michael Sailer, the Bishop of Ratisbon, Bernhard Overberg and authors Luise Hensel and Friedrich Stolberg.

Interestingly, early Danish jazz was influenced by three classically trained musicians: Erik Tuxen ( 1902 – 1957 ), who created one the country's first jazz bands, Bernhard Christensen ( b. 1906 ), a composer of both jazz and classical music, and Sven Møller Kristensen ( 1909 – 1991 ) who wrote lyrics for Christensen as well as a number of books about jazz.

From 1921 onwards he was in charge of the bird department of the Berlin Zoological Museum, and encouraged a number of young German scientists, including Ernst Mayr and Bernhard Rensch.

This occurs in Professor Martens ' Departure where two different Martens-figures are discussed, legal experts who lived several decades apart, and in Sailing Against the Wind where in one dream sequence the protagonist Bernhard Schmidt meets a number of others named Schmidt.

The white # 22 Martini-entered 917K ( chassis number 053 ) of Helmut Marko and Gijs van Lennep, equipped with a magnesium frame, set an overall distance record that stood until the 2010 win by the Audi R15 TDI of Romain Dumas, Mike Rockenfeller and Timo Bernhard when they set a distance record of at an average speed of 220. 2 km / h ( 137. 6 mph ).

Classic Reprints, number 18: Das Internationale Schachturnier Karlsbad 1923, Kagan, Bernhard, 01-12-1977 ( 1923 ).

Classic Reprints, number 19: Mährisch-Ostrau 1923 Internationales Schachmeister-Turnier, Kagan, Bernhard, 01-12-1978 ( 1923 ).

The first-ever number one, in April 1986, is 1985 Masters Champion Bernhard Langer.

The result provides final confirmation of the recent swing in global dominance away from the American players ; at the end of 1987, only one of the world's top six ( Curtis Strange, in 5th ) is American, while four ( Seve Ballesteros, Bernhard Langer, Sandy Lyle and Ian Woosnam ) are European, while the world number one remains Greg Norman.