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Hermann Vermeil
Hermann Vermeil (1889–1959) was a German mathematician who produced the first published proof that the scalar curvature is the only absolute invariant among those of prescribed type suitable for Albert Einstein’s theory. The theorem was proved by him in 1917 when he was Hermann Weyl Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is ass ...'s assistant. Notes External links * 1889 births 1959 deaths 20th-century German mathematicians Differential geometers {{Germany-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universität Leipzig
Leipzig University (german: Universität Leipzig), in Leipzig in Saxony, Germany, is one of the world's oldest universities and the second-oldest university (by consecutive years of existence) in Germany. The university was founded on 2 December 1409 by Frederick I, Elector of Saxony and his brother William II, Margrave of Meissen, and originally comprised the four scholastic faculties. Since its inception, the university has engaged in teaching and research for over 600 years without interruption. Famous alumni include Gottfried Wilhelm von Leibniz, Johann Wolfgang von Goethe, Leopold von Ranke, Friedrich Nietzsche, Robert Schumann, Richard Wagner, Tycho Brahe, Georgius Agricola, Angela Merkel and ten Nobel laureates associated with the university. History Founding and development until 1900 The university was modelled on the University of Prague, from which the German-speaking faculty members withdrew to Leipzig after the Jan Hus crisis and the Decree of Kutná H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Otto Ludwig Hölder
Otto is a masculine German given name and a surname. It originates as an Old High German short form (variants ''Audo'', ''Odo'', ''Udo'') of Germanic names beginning in ''aud-'', an element meaning "wealth, prosperity". The name is recorded from the 7th century ( Odo, son of Uro, courtier of Sigebert III). It was the name of three 10th-century German kings, the first of whom was Otto I the Great, the first Holy Roman Emperor, founder of the Ottonian dynasty. The Gothic form of the prefix was ''auda-'' (as in e.g. '' Audaþius''), the Anglo-Saxon form was ''ead-'' (as in e.g. ''Eadmund''), and the Old Norse form was '' auð-''. The given name Otis arose from an English surname, which was in turn derived from ''Ode'', a variant form of ''Odo, Otto''. Due to Otto von Bismarck, the given name ''Otto'' was strongly associated with the German Empire in the later 19th century. It was comparatively frequently given in the United States (presumably in German American families) during ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vermeil's Theorem
In differential geometry, Vermeil's theorem essentially states that the scalar curvature is the only (non-trivial) absolute invariant among those of prescribed type suitable for Albert Einstein’s theory of General Relativity. The theorem was proved by the German mathematician Hermann Vermeil in 1917. Standard version of the theorem The theorem states that the Ricci scalar RLet us recall that Ricci scalar R is linear in the second derivatives of the metric tensor g_, quadratic in the first derivatives and contains the inverse matrix g^, which is a rational function of the components g_. is the only scalar invariant (or absolute invariant) linear in the second derivatives of the metric tensor g_. See also *Scalar curvature *Differential invariant *Einstein–Hilbert action *Lovelock's theorem Lovelock's theorem of general relativity says that from a local gravitational action which contains only second derivatives of the four-dimensional spacetime metric, then the only p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagoreans, Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scalar Curvature
In the mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the geometry of the metric near that point. It is defined by a complicated explicit formula in terms of partial derivatives of the metric components, although it is also characterized by the volume of infinitesimally small geodesic balls. In the context of the differential geometry of surfaces, the scalar curvature is twice the Gaussian curvature, and completely characterizes the curvature of a surface. In higher dimensions, however, the scalar curvature only represents one particular part of the Riemann curvature tensor. The definition of scalar curvature via partial derivatives is also valid in the more general setting of pseudo-Riemannian manifolds. This is significant in general relativity, where scalar curvature of a Lorentzian metric is one o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory of relativity, but he also made important contributions to the development of the theory of quantum mechanics. Relativity and quantum mechanics are the two pillars of modern physics. His mass–energy equivalence formula , which arises from relativity theory, has been dubbed "the world's most famous equation". His work is also known for its influence on the philosophy of science. He received the 1921 Nobel Prize in Physics "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect", a pivotal step in the development of quantum theory. His intellectual achievements and originality resulted in "Einstein" becoming synonymous with "genius". In 1905, a year sometimes described as his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermann Weyl
Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is associated with the University of Göttingen tradition of mathematics, represented by Carl Friedrich Gauss, David Hilbert and Hermann Minkowski. His research has had major significance for theoretical physics as well as purely mathematical disciplines such as number theory. He was one of the most influential mathematicians of the twentieth century, and an important member of the Institute for Advanced Study during its early years. Weyl contributed to an exceptionally wide range of mathematical fields, including works on space, time, matter, philosophy, logic, symmetry and the history of mathematics. He was one of the first to conceive of combining general relativity with the laws of electromagnetism. Freeman Dyson wrote that Weyl alone b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1889 Births
Events January–March * January 1 ** The total solar eclipse of January 1, 1889 is seen over parts of California and Nevada. ** Paiute spiritual leader Wovoka experiences a vision, leading to the start of the Ghost Dance movement in the Dakotas. * January 4 – An Act to Regulate Appointments in the Marine Hospital Service of the United States is signed by President Grover Cleveland. It establishes a Commissioned Corps of officers, as a predecessor to the modern-day U.S. Public Health Service Commissioned Corps. * January 5 – Preston North End F.C. is declared the winner of the inaugural Football League in England. * January 8 – Herman Hollerith receives a patent for his electric tabulating machine in the United States. * January 15 – The Coca-Cola Company is originally incorporated as the Pemberton Medicine Company in Atlanta, Georgia. * January 22 – Columbia Phonograph is formed in Washington, D.C. * January 30 – Rudolf, Crown Prince of Austria a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1959 Deaths
Events January * January 1 - Cuba: Fulgencio Batista flees Havana when the forces of Fidel Castro advance. * January 2 - Lunar probe Luna 1 was the first man-made object to attain escape velocity from Earth. It reached the vicinity of Earth's Moon, and was also the first spacecraft to be placed in heliocentric orbit. * January 3 ** The three southernmost atolls of the Maldive Islands, Maldive archipelago (Addu Atoll, Huvadhu Atoll and Fuvahmulah island) United Suvadive Republic, declare independence. ** Alaska is admitted as the 49th U.S. state. * January 4 ** In Cuba, rebel troops led by Che Guevara and Camilo Cienfuegos enter the city of Havana. ** Léopoldville riots: At least 49 people are killed during clashes between the police and participants of a meeting of the ABAKO Party in Kinshasa, Léopoldville in the Belgian Congo. * January 6 ** Fidel Castro arrives in Havana. ** The International Maritime Organization is inaugurated. * January 7 – The United States rec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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