1.
Hanover
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At the end of the Napoleonic Wars, the Electorate was enlarged to become a Kingdom with Hanover as its capital. From 1868 to 1946 Hanover was the capital of the Prussian Province of Hanover and it is now the capital of the Land of Lower Saxony. Since 2001 it has been part of the Hanover district, which is a body made up from the former district. With a population of 518,000, Hanover is a centre of Northern Germany. Hanover also hosts annual commercial trade fairs such as the Hanover Fair, every year Hanover hosts the Schützenfest Hannover, the worlds largest marksmens festival, and the Oktoberfest Hannover, the second largest such festival in Germany. In 2000, Hanover hosted the world fair Expo 2000, the Hanover fairground, due to numerous extensions, especially for the Expo 2000, is the largest in the world. Hanover is of importance because of its universities and medical school, its international airport. The city is also a crossing point of railway lines and highways. Hanover is the traditional English spelling, the German spelling is becoming more popular in English, recent editions of encyclopaedias prefer the German spelling, and the local government uses the German spelling on English websites. The traditional English spelling is used in historical contexts, especially when referring to the British House of Hanover. Hanover was founded in times on the east bank of the River Leine. Its original name Honovere may mean high bank, though this is debated, Hanover was a small village of ferrymen and fishermen that became a comparatively large town in the 13th century due to its position at a natural crossroads. As overland travel was difficult, its position on the upper navigable reaches of the river helped it to grow by increasing trade. In the 14th century the churches of Hanover were built. The beginning of industrialization in Germany led to trade in iron and silver from the northern Harz Mountains, in 1636 George, Duke of Brunswick-Lüneburg, ruler of the Brunswick-Lüneburg principality of Calenberg, moved his residence to Hanover. The Dukes of Brunswick-Lüneburg were elevated by the Holy Roman Emperor to the rank of Prince-Elector in 1692, thus the principality was upgraded to the Electorate of Brunswick-Lüneburg, colloquially known as the Electorate of Hanover after Calenbergs capital. Its electors would later become monarchs of Great Britain, the first of these was George I Louis, who acceded to the British throne in 1714. The last British monarch who ruled in Hanover was William IV, semi-Salic law, which required succession by the male line if possible, forbade the accession of Queen Victoria in Hanover
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Kingdom of Prussia
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It was the driving force behind the unification of Germany in 1871 and was the leading state of the German Empire until its dissolution in 1918. Although it took its name from the region called Prussia, it was based in the Margraviate of Brandenburg, the kings of Prussia were from the House of Hohenzollern. Prussia was a power from the time it became a kingdom, through its predecessor, Brandenburg-Prussia. Prussia continued its rise to power under the guidance of Frederick II, more known as Frederick the Great. After the might of Prussia was revealed it was considered as a power among the German states. Throughout the next hundred years Prussia went on to win many battles and it was because of its power that Prussia continuously tried to unify all the German states under its rule. Attempts at creation of a federation remained unsuccessful and the German Confederation collapsed in 1866 when war ensued between its two most powerful states, Prussia and Austria. The North German Confederation which lasted from 1867–1871, created a union between the Prussian-aligned states while Austria and most of Southern Germany remained independent. The North German Confederation was seen as more of an alliance of military strength in the aftermath of the Austro-Prussian War, the German Empire lasted from 1871–1918 with the successful unification of all the German states under Prussian hegemony. This was due to the defeat of Napoleon III in the Franco-Prussian War of 1870–71, in 1871, Germany unified into a single country, minus Austria and Switzerland, with Prussia the dominant power. Prussia is considered the predecessor of the unified German Reich. The Kingdom left a significant cultural legacy, today notably promoted by the Prussian Cultural Heritage Foundation, in 1415 a Hohenzollern Burgrave came from the south to the March of Brandenburg and took control of the area as elector. In 1417 the Hohenzollern was made an elector of the Holy Roman Empire, after the Polish wars, the newly established Baltic towns of the German states including Prussia, suffered many economic setbacks. Many of the Prussian towns could not even afford to attend political meetings outside of Prussia, the towns were poverty stricken, with even the largest town, Danzig, having to borrow money from elsewhere to pay for trade. Poverty in these towns was partly caused by Prussias neighbors, who had established and developed such a monopoly on trading that these new towns simply could not compete and these issues led to feuds, wars, trade competition and invasions. However, the fall of these gave rise to the nobility, separated the east and the west. It was clear in 1440 how different Brandenburg was from the other German territories, not only did it face partition from within but also the threat of its neighbors. It prevented the issue of partition by enacting the Dispositio Achillea which instilled the principle of primogeniture to both the Brandenburg and Franconian territories, the second issue was solved through expansion
3.
German Empire
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The German Empire was the historical German nation state that existed from the unification of Germany in 1871 to the abdication of Kaiser Wilhelm II in 1918, when Germany became a federal republic. The German Empire consisted of 26 constituent territories, with most being ruled by royal families and this included four kingdoms, six grand duchies, five duchies, seven principalities, three free Hanseatic cities, and one imperial territory. Although Prussia became one of kingdoms in the new realm, it contained most of its population and territory. Its influence also helped define modern German culture, after 1850, the states of Germany had rapidly become industrialized, with particular strengths in coal, iron, chemicals, and railways. In 1871, it had a population of 41 million people, and by 1913, a heavily rural collection of states in 1815, now united Germany became predominantly urban. During its 47 years of existence, the German Empire operated as an industrial, technological, Germany became a great power, boasting a rapidly growing rail network, the worlds strongest army, and a fast-growing industrial base. In less than a decade, its navy became second only to Britains Royal Navy, after the removal of Chancellor Otto von Bismarck by Wilhelm II, the Empire embarked on a bellicose new course that ultimately led to World War I. When the great crisis of 1914 arrived, the German Empire had two allies, Italy and the Austro-Hungarian Empire, Italy, however, left the once the First World War started in August 1914. In the First World War, German plans to capture Paris quickly in autumn 1914 failed, the Allied naval blockade caused severe shortages of food. Germany was repeatedly forced to send troops to bolster Austria and Turkey on other fronts, however, Germany had great success on the Eastern Front, it occupied large Eastern territories following the Treaty of Brest-Litovsk. German declaration of unrestricted submarine warfare in early 1917 was designed to strangle the British, it failed, but the declaration—along with the Zimmermann Telegram—did bring the United States into the war. Meanwhile, German civilians and soldiers had become war-weary and radicalised by the Russian Revolution and this failed, and by October the armies were in retreat, Austria-Hungary and the Ottoman Empire had collapsed, Bulgaria had surrendered and the German people had lost faith in their political system. The Empire collapsed in the November 1918 Revolution as the Emperor and all the ruling monarchs abdicated, and a republic took over. The German Confederation had been created by an act of the Congress of Vienna on 8 June 1815 as a result of the Napoleonic Wars, German nationalism rapidly shifted from its liberal and democratic character in 1848, called Pan-Germanism, to Prussian prime minister Otto von Bismarcks pragmatic Realpolitik. He envisioned a conservative, Prussian-dominated Germany, the war resulted in the Confederation being partially replaced by a North German Confederation in 1867, comprising the 22 states north of the Main. The new constitution and the title Emperor came into effect on 1 January 1871, during the Siege of Paris on 18 January 1871, William accepted to be proclaimed Emperor in the Hall of Mirrors at the Palace of Versailles. The second German Constitution was adopted by the Reichstag on 14 April 1871 and proclaimed by the Emperor on 16 April, the political system remained the same. The empire had a parliament called the Reichstag, which was elected by universal male suffrage, however, the original constituencies drawn in 1871 were never redrawn to reflect the growth of urban areas
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Hamburg
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Hamburg, officially Freie und Hansestadt Hamburg, is the second largest city in Germany and the eighth largest city in the European Union. It is the second smallest German state by area and its population is over 1.7 million people, and the wider Hamburg Metropolitan Region covers more than 5.1 million inhabitants. The city is situated on the river Elbe, the official long name reflects Hamburgs history as a member of the medieval Hanseatic League, a free imperial city of the Holy Roman Empire, a city-state, and one of the 16 states of Germany. Before the 1871 Unification of Germany, it was a sovereign state. Prior to the changes in 1919, the civic republic was ruled by a class of hereditary grand burghers or Hanseaten. Though repeatedly destroyed by the Great Fire of Hamburg, the floods and military conflicts including WW2 bombing raids, the city managed to recover and emerge wealthier after each catastrophe. On the river Elbe, Hamburg is a port and a global service, media, logistics and industrial hub, with headquarters and facilities of Airbus, Blohm + Voss, Aurubis, Beiersdorf. The radio and television broadcaster NDR, Europes largest printing and publishing firm Gruner + Jahr, Hamburg has been an important financial centre for centuries, and is the seat of Germanys oldest stock exchange and the worlds second oldest bank, Berenberg Bank. The city is a fast expanding tourist destination for domestic and international visitors. It ranked 16th in the world for livability in 2015, the ensemble Speicherstadt and Kontorhausviertel was declared a World Heritage Site by the UNESCO in 2015. Hamburg is a major European science, research and education hub with several universities and institutes and its creative industries and major cultural venues include the renowned Elbphilharmonie and Laeisz concert halls, various art venues, music producers and artists. It is regarded as a haven for artists, gave birth to movements like Hamburger Schule. Hamburg is also known for theatres and a variety of musical shows. St. Paulis Reeperbahn is among the best known European entertainment districts, Hamburg is on the southern point of the Jutland Peninsula, between Continental Europe to the south and Scandinavia to the north, with the North Sea to the west and the Baltic Sea to the north-east. It is on the River Elbe at its confluence with the Alster, the city centre is around the Binnenalster and Außenalster, both formed by damming the River Alster to create lakes. The island of Neuwerk and two neighbouring islands Scharhörn and Nigehörn, in the Hamburg Wadden Sea National Park, are also part of Hamburg. The neighbourhoods of Neuenfelde, Cranz, Francop and Finkenwerder are part of the Altes Land region, neugraben-Fischbek has Hamburgs highest elevation, the Hasselbrack at 116.2 metres AMSL. Hamburg has a climate, influenced by its proximity to the coast
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West Germany
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West Germany is the common English name for the Federal Republic of Germany or FRG in the period between its creation on 23 May 1949 to German reunification on 3 October 1990. During this Cold War era, NATO-aligned West Germany and Warsaw Pact-aligned East Germany were divided by the Inner German border, after 1961 West Berlin was physically separated from East Berlin as well as from East Germany by the Berlin Wall. This situation ended when East Germany was dissolved and its five states joined the ten states of the Federal Republic of Germany along with the reunified city-state of Berlin. With the reunification of West and East Germany, the Federal Republic of Germany, enlarged now to sixteen states and this period is referred to as the Bonn Republic by historians, alluding to the interwar Weimar Republic and the post-reunification Berlin Republic. The Federal Republic of Germany was established from eleven states formed in the three Allied Zones of occupation held by the United States, the United Kingdom and France, US and British forces remained in the country throughout the Cold War. Its population grew from roughly 51 million in 1950 to more than 63 million in 1990, the city of Bonn was its de facto capital city. The fourth Allied occupation zone was held by the Soviet Union, as a result, West Germany had a territory about half the size of the interbellum democratic Weimar Republic. At the onset of the Cold War, Europe was divided among the Western and Eastern blocs, Germany was de facto divided into two countries and two special territories, the Saarland and divided Berlin. The Federal Republic of Germany claimed a mandate for all of Germany. It took the line that the GDR was an illegally constituted puppet state, though the GDR did hold regular elections, these were not free and fair. For all practical purposes the GDR was a Soviet puppet state, from the West German perspective the GDR was therefore illegitimate. Three southwestern states of West Germany merged to form Baden-Württemberg in 1952, in addition to the resulting ten states, West Berlin was considered an unofficial de facto 11th state. It recognised the GDR as a de facto government within a single German nation that in turn was represented de jure by the West German state alone. From 1973 onward, East Germany recognised the existence of two German countries de jure, and the West as both de facto and de jure foreign country, the Federal Republic and the GDR agreed that neither of them could speak in the name of the other. The first chancellor Konrad Adenauer, who remained in office until 1963, had worked for an alignment with NATO rather than neutrality. He not only secured a membership in NATO but was also a proponent of agreements that developed into the present-day European Union, when the G6 was established in 1975, there was no question whether the Federal Republic of Germany would be a member as well. With the collapse of communism in Central and Eastern Europe in 1989, symbolised by the opening of the Berlin Wall, East Germany voted to dissolve itself and accede to the Federal Republic in 1990. Its five post-war states were reconstituted along with the reunited Berlin and they formally joined the Federal Republic on 3 October 1990, raising the number of states from 10 to 16, ending the division of Germany
6.
Quantum mechanics
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Quantum mechanics, including quantum field theory, is a branch of physics which is the fundamental theory of nature at small scales and low energies of atoms and subatomic particles. Classical physics, the physics existing before quantum mechanics, derives from quantum mechanics as an approximation valid only at large scales, early quantum theory was profoundly reconceived in the mid-1920s. The reconceived theory is formulated in various specially developed mathematical formalisms, in one of them, a mathematical function, the wave function, provides information about the probability amplitude of position, momentum, and other physical properties of a particle. In 1803, Thomas Young, an English polymath, performed the famous experiment that he later described in a paper titled On the nature of light. This experiment played a role in the general acceptance of the wave theory of light. In 1838, Michael Faraday discovered cathode rays, Plancks hypothesis that energy is radiated and absorbed in discrete quanta precisely matched the observed patterns of black-body radiation. In 1896, Wilhelm Wien empirically determined a distribution law of black-body radiation, ludwig Boltzmann independently arrived at this result by considerations of Maxwells equations. However, it was only at high frequencies and underestimated the radiance at low frequencies. Later, Planck corrected this model using Boltzmanns statistical interpretation of thermodynamics and proposed what is now called Plancks law, following Max Plancks solution in 1900 to the black-body radiation problem, Albert Einstein offered a quantum-based theory to explain the photoelectric effect. Among the first to study quantum phenomena in nature were Arthur Compton, C. V. Raman, robert Andrews Millikan studied the photoelectric effect experimentally, and Albert Einstein developed a theory for it. In 1913, Peter Debye extended Niels Bohrs theory of structure, introducing elliptical orbits. This phase is known as old quantum theory, according to Planck, each energy element is proportional to its frequency, E = h ν, where h is Plancks constant. Planck cautiously insisted that this was simply an aspect of the processes of absorption and emission of radiation and had nothing to do with the reality of the radiation itself. In fact, he considered his quantum hypothesis a mathematical trick to get the right rather than a sizable discovery. He won the 1921 Nobel Prize in Physics for this work, lower energy/frequency means increased time and vice versa, photons of differing frequencies all deliver the same amount of action, but do so in varying time intervals. High frequency waves are damaging to human tissue because they deliver their action packets concentrated in time, the Copenhagen interpretation of Niels Bohr became widely accepted. In the mid-1920s, developments in mechanics led to its becoming the standard formulation for atomic physics. In the summer of 1925, Bohr and Heisenberg published results that closed the old quantum theory, out of deference to their particle-like behavior in certain processes and measurements, light quanta came to be called photons
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Quantum field theory
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QFT treats particles as excited states of the underlying physical field, so these are called field quanta. In quantum field theory, quantum mechanical interactions among particles are described by interaction terms among the corresponding underlying quantum fields and these interactions are conveniently visualized by Feynman diagrams, which are a formal tool of relativistically covariant perturbation theory, serving to evaluate particle processes. The first achievement of quantum theory, namely quantum electrodynamics, is still the paradigmatic example of a successful quantum field theory. Ordinarily, quantum mechanics cannot give an account of photons which constitute the prime case of relativistic particles, since photons have rest mass zero, and correspondingly travel in the vacuum at the speed c, a non-relativistic theory such as ordinary QM cannot give even an approximate description. Photons are implicit in the emission and absorption processes which have to be postulated, for instance, the formalism of QFT is needed for an explicit description of photons. In fact most topics in the development of quantum theory were related to the interaction of radiation and matter. However, quantum mechanics as formulated by Dirac, Heisenberg, and Schrödinger in 1926–27 started from atomic spectra, as soon as the conceptual framework of quantum mechanics was developed, a small group of theoreticians tried to extend quantum methods to electromagnetic fields. A good example is the paper by Born, Jordan & Heisenberg. The basic idea was that in QFT the electromagnetic field should be represented by matrices in the way that position. The ideas of QM were thus extended to systems having a number of degrees of freedom. The inception of QFT is usually considered to be Diracs famous 1927 paper on The quantum theory of the emission and absorption of radiation, here Dirac coined the name quantum electrodynamics for the part of QFT that was developed first. Employing the theory of the harmonic oscillator, Dirac gave a theoretical description of how photons appear in the quantization of the electromagnetic radiation field. Later, Diracs procedure became a model for the quantization of fields as well. These first approaches to QFT were further developed during the three years. P. Jordan introduced creation and annihilation operators for fields obeying Fermi–Dirac statistics and these differ from the corresponding operators for Bose–Einstein statistics in that the former satisfy anti-commutation relations while the latter satisfy commutation relations. The methods of QFT could be applied to derive equations resulting from the treatment of particles, e. g. the Dirac equation, the Klein–Gordon equation. Schweber points out that the idea and procedure of second quantization goes back to Jordan, in a number of papers from 1927, some difficult problems concerning commutation relations, statistics, and Lorentz invariance were eventually solved. The first comprehensive account of a theory of quantum fields, in particular
8.
Jordan algebra
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In abstract algebra, a Jordan algebra is an nonassociative algebra over a field whose multiplication satisfies the following axioms, x y = y x = x. The product of two elements x and y in a Jordan algebra is denoted x ∘ y, particularly to avoid confusion with the product of a related associative algebra. They were originally called r-number systems, but were renamed Jordan algebras by Albert, given an associative algebra A, one can construct a Jordan algebra A+ using the same underlying addition vector space. Notice first that an associative algebra is a Jordan algebra if, if it is not commutative we can define a new multiplication on A to make it commutative, and in fact make it a Jordan algebra. The new multiplication x ∘ y is the anti-commutator, x ∘ y = x y + y x 2 and this defines a Jordan algebra A+, and we call these Jordan algebras, as well as any subalgebras of these Jordan algebras, special Jordan algebras. All other Jordan algebras are called exceptional Jordan algebras, the Shirshov–Cohn theorem states that any Jordan algebra with two generators is special. If is an algebra with an involution σ, then if σ=x. Thus the set of all fixed by the involution form a subalgebra of A+ which is sometimes denoted H.1. The set of self-adjoint real, complex, or quaternionic matrices with multiplication /2 form a special Jordan algebra, the set of 3×3 self-adjoint matrices over the non-associative octonions, again with multiplication /2, is a 27 dimensional, exceptional Jordan algebra. This was the first example of an Albert algebra and its automorphism group is the exceptional Lie group F₄. Since over the numbers this is the only simple exceptional Jordan algebra up to isomorphism. Over the real numbers there are three classes of simple exceptional Jordan algebras. A derivation of a Jordan algebra A is an endomorphism D of A such that D = Dy+xD, the derivations form a Lie algebra der. The Jordan identity implies that if x and y are elements of A, thus the direct sum of A and der can be made into a Lie algebra, called the structure algebra of A, str. A simple example is provided by the Hermitian Jordan algebras H, in this case any element x of A with σ=−x defines a derivation. In many important examples, the algebra of H is A. Derivation and structure algebras also form part of Tits construction of the Freudenthal magic square, a algebra over the real numbers is said to be formally real if it satisfies the property that a sum of n squares can only vanish if each one vanishes individually. In 1932, Jordan attempted to axiomatize quantum theory by saying that the algebra of observables of any quantum system should be a real algebra which is commutative and power-associative
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Theoretical physics
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Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to physics, which uses experimental tools to probe these phenomena. The advancement of science depends in general on the interplay between experimental studies and theory, in some cases, theoretical physics adheres to standards of mathematical rigor while giving little weight to experiments and observations. Conversely, Einstein was awarded the Nobel Prize for explaining the photoelectric effect, a physical theory is a model of physical events. It is judged by the extent to which its predictions agree with empirical observations, the quality of a physical theory is also judged on its ability to make new predictions which can be verified by new observations. A physical theory similarly differs from a theory, in the sense that the word theory has a different meaning in mathematical terms. A physical theory involves one or more relationships between various measurable quantities, archimedes realized that a ship floats by displacing its mass of water, Pythagoras understood the relation between the length of a vibrating string and the musical tone it produces. Other examples include entropy as a measure of the uncertainty regarding the positions and motions of unseen particles, Theoretical physics consists of several different approaches. In this regard, theoretical particle physics forms a good example, for instance, phenomenologists might employ empirical formulas to agree with experimental results, often without deep physical understanding. Modelers often appear much like phenomenologists, but try to model speculative theories that have certain desirable features, some attempt to create approximate theories, called effective theories, because fully developed theories may be regarded as unsolvable or too complicated. Other theorists may try to unify, formalise, reinterpret or generalise extant theories, or create completely new ones altogether. Sometimes the vision provided by pure mathematical systems can provide clues to how a system might be modeled, e. g. the notion, due to Riemann and others. Theoretical problems that need computational investigation are often the concern of computational physics, Theoretical advances may consist in setting aside old, incorrect paradigms or may be an alternative model that provides answers that are more accurate or that can be more widely applied. In the latter case, a correspondence principle will be required to recover the previously known result, sometimes though, advances may proceed along different paths. However, an exception to all the above is the wave–particle duality, Physical theories become accepted if they are able to make correct predictions and no incorrect ones. They are also likely to be accepted if they connect a wide range of phenomena. Testing the consequences of a theory is part of the scientific method, Physical theories can be grouped into three categories, mainstream theories, proposed theories and fringe theories. Theoretical physics began at least 2,300 years ago, under the Pre-socratic philosophy, during the Middle Ages and Renaissance, the concept of experimental science, the counterpoint to theory, began with scholars such as Ibn al-Haytham and Francis Bacon
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University of Hanover
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The University of Hannover, officially the Gottfried Wilhelm Leibniz Universität Hannover, short Leibniz Universität Hannover, is a public university located in Hannover, Germany. Founded in 1831, it is one of the largest and oldest science, in the 2014/15 school year it enrolled 25,688 students, of which 2,121 were from foreign countries. It has nine faculties which offer 190 full and part degree programs in 38 fields of study, the University is named after Gottfried Wilhelm Leibniz, the 18th century mathematician and philosopher. Leibniz Universität Hannover is a member of TU9, an association of the nine leading Institutes of Technology in Germany and it is also a member of the Conference of European Schools for Advanced Engineering Education and Research, a non-profit association of leading engineering universities in Europe. The university sponsors the German National Library of Science and Technology, the roots of the University of Hanover begin in the Higher Vocational College/Polytechnic Institute, founded in 1831. In 1879 the Higher Vocational School moved into the historic Guelph Palace, the Welfenschloss, later, the Higher Vocational School became the Royal College of Technology. In 1899 Kaiser Wilhelm II granted the College of Technology a status equal to that of universities, the College was reconstructed in 1921 with the financial support of the College Patrons’ Association. There were three faculties, Mathematics and Natural Sciences, Civil Engineering, Mechanical Engineering, in 1968 the Faculty of Humanities and Political Science were founded and the College of Technology became the Technische Hochschule. Student numbers exceeded 30,000 for the first time in 1991, on the 175th anniversary of the institution in 2006, the University of Hannover was given the name Gottfried Wilhelm Leibniz Universität Hannover. While 64 pupils first attended the Vocational School, today the university now has around 25.700 students, more than 2.900 academics and scientists, the Senate of the University voted in April 2006 to rename the University of Hannover to Leibniz Universität Hannover. Following agreement by the Leibniz Academy on the use of the name, the brand of the university is Leibniz Universität Hannover. The old logo of the University was inspired by the Massachusetts Institute of Technology, the current logo is a stylized excerpt from a letter to Duke Rudolf August of Wolfenbüttel, in which Leibniz presented binary numbers for the first time. Nine faculties with more than 190 first-degree full-time and part-time degree courses make the university the second-largest institution of education in Lower Saxony. The university staff comprises 2930 research and teaching staff, of whom 321 are professors and it has 1810 additional employees in administrative functions,90 apprentices and some 1400 staff funded by third parties. It expanded into an important collection as the institution evolved from a college into the full University. The removal of the books into storage during the Second World War secured valuable old stocks that became a national collection of scientific. This was the basis on which the library of the Institute of Technology was established in 1959, today the collection forms the heart of the German National Library of Science and Technology, which is the largest institution of its kind in the world. GISMA Business School in Hannover, Germany, was launched in 1999 as a joint initiative by the state of Lower Saxony, GISMA is a privately funded, self-administering institution of higher education
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Max Born
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Max Born was a German physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to physics and optics and supervised the work of a number of notable physicists in the 1920s and 1930s. Born won the 1954 Nobel Prize in Physics for his research in Quantum Mechanics. He wrote his Ph. D. thesis on the subject of Stability of Elastica in a Plane and Space, in 1905, he began researching special relativity with Minkowski, and subsequently wrote his habilitation thesis on the Thomson model of the atom. In the First World War, after originally being placed as a radio operator, in 1921, Born returned to Göttingen, arranging another chair for his long-time friend and colleague James Franck. Under Born, Göttingen became one of the worlds foremost centres for physics, in 1925, Born and Werner Heisenberg formulated the matrix mechanics representation of quantum mechanics. The following year, he formulated the now-standard interpretation of the probability density function for ψ*ψ in the Schrödinger equation and his influence extended far beyond his own research. Max Delbrück, Siegfried Flügge, Friedrich Hund, Pascual Jordan, Maria Goeppert-Mayer, Lothar Wolfgang Nordheim, Robert Oppenheimer, in January 1933, the Nazi Party came to power in Germany, and Born, who was Jewish, was suspended. Max Born became a naturalised British subject on 31 August 1939 and he remained at Edinburgh until 1952. He retired to Bad Pyrmont, in West Germany, and died in a hospital in Göttingen on 5 January 1970. Max Born was born on 11 December 1882 in Breslau, which at the time of Borns birth was part of the Prussian Province of Silesia in the German Empire and she died when Max was four years old, on 29 August 1886. Max had a sister, Käthe, who was born in 1884, Wolfgang later became Professor of Art History at the City College of New York. Initially educated at the König-Wilhelm-Gymnasium in Breslau, Born entered the University of Breslau in 1901, the German university system allowed students to move easily from one university to another, so he spent summer semesters at Heidelberg University in 1902 and the University of Zurich in 1903. Fellow students at Breslau, Otto Toeplitz and Ernst Hellinger, told Born about the University of Göttingen, at Göttingen he found three renowned mathematicians, Felix Klein, David Hilbert and Hermann Minkowski. Very soon after his arrival, Born formed close ties to the two men. Being class scribe put Born into regular, invaluable contact with Hilbert, Hilbert became Borns mentor after selecting him to be the first to hold the unpaid, semi-official position of assistant. Borns introduction to Minkowski came through Borns stepmother, Bertha, as she knew Minkowski from dancing classes in Königsberg, the introduction netted Born invitations to the Minkowski household for Sunday dinners. In addition, while performing his duties as scribe and assistant, Borns relationship with Klein was more problematic
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Physicist
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A physicist is a scientist who has specialized knowledge in the field of physics, the exploration of the interactions of matter and energy across the physical universe. A physicist is a scientist who specializes or works in the field of physics, physicists generally are interested in the root or ultimate causes of phenomena, and usually frame their understanding in mathematical terms. Physicists can also apply their knowledge towards solving real-world problems or developing new technologies, some physicists specialize in sectors outside the science of physics itself, such as engineering. The study and practice of physics is based on a ladder of discoveries. Many mathematical and physical ideas used today found their earliest expression in ancient Greek culture and Asian culture, the bulk of physics education can be said to flow from the scientific revolution in Europe, starting with the work of Galileo and Kepler in the early 1600s. New knowledge in the early 21st century includes an increase in understanding physical cosmology. The term physicist was coined by William Whewell in his 1840 book The Philosophy of the Inductive Sciences, many physicist positions require an undergraduate degree in applied physics or a related science or a Masters degree like MSc, MPhil, MPhys or MSci. In a research oriented level, students tend to specialize in a particular field, Physics students also need training in mathematics, and also in computer science and programming. For being employed as a physicist a doctoral background may be required for certain positions, undergraduate students like BSc Mechanical Engineering, BSc Electrical and Computer Engineering, BSc Applied Physics. etc. With physics orientation are chosen as research assistants with faculty members, the highest honor awarded to physicists is the Nobel Prize in Physics, awarded since 1901 by the Royal Swedish Academy of Sciences. The three major employers of career physicists are academic institutions, laboratories, and private industries, with the largest employer being the last, physicists in academia or government labs tend to have titles such as Assistants, Professors, Sr. /Jr. As per the American Institute for Physics, some 20% of new physics Ph. D. s holds jobs in engineering development programs, while 14% turn to computer software, a majority of physicists employed apply their skills and training to interdisciplinary sectors. For industry or self-employment. and also in science and programming. Hence a majority of Physics bachelors degree holders are employed in the private sector, other fields are academia, government and military service, nonprofit entities, labs and teaching
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Fermion
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In particle physics, a fermion is any subatomic particle characterized by Fermi–Dirac statistics. These particles obey the Pauli exclusion principle, fermions include all quarks and leptons, as well as any composite particle made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics, a fermion can be an elementary particle, such as the electron, or it can be a composite particle, such as the proton. According to the theorem in any reasonable relativistic quantum field theory, particles with integer spin are bosons. Besides this spin characteristic, fermions have another specific property, they possess conserved baryon or lepton quantum numbers, therefore, what is usually referred to as the spin statistics relation is in fact a spin statistics-quantum number relation. As a consequence of the Pauli exclusion principle, only one fermion can occupy a quantum state at any given time. If multiple fermions have the same probability distribution, then at least one property of each fermion, such as its spin. Weakly interacting fermions can also display bosonic behavior under extreme conditions, at low temperature fermions show superfluidity for uncharged particles and superconductivity for charged particles. Composite fermions, such as protons and neutrons, are the key building blocks of everyday matter, the Standard Model recognizes two types of elementary fermions, quarks and leptons. In all, the model distinguishes 24 different fermions, there are six quarks, and six leptons, along with the corresponding antiparticle of each of these. Mathematically, fermions come in three types - Weyl fermions, Dirac fermions, and Majorana fermions, most Standard Model fermions are believed to be Dirac fermions, although it is unknown at this time whether the neutrinos are Dirac or Majorana fermions. Dirac fermions can be treated as a combination of two Weyl fermions, in July 2015, Weyl fermions have been experimentally realized in Weyl semimetals. Composite particles can be bosons or fermions depending on their constituents, more precisely, because of the relation between spin and statistics, a particle containing an odd number of fermions is itself a fermion. Examples include the following, A baryon, such as the proton or neutron, the nucleus of a carbon-13 atom contains six protons and seven neutrons and is therefore a fermion. The atom helium-3 is made of two protons, one neutron, and two electrons, and therefore it is a fermion. The number of bosons within a composite made up of simple particles bound with a potential has no effect on whether it is a boson or a fermion. Fermionic or bosonic behavior of a particle is only seen at large distances. At proximity, where spatial structure begins to be important, a composite particle behaves according to its constituent makeup, fermions can exhibit bosonic behavior when they become loosely bound in pairs
14.
Napoleonic Wars
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The wars resulted from the unresolved disputes associated with the French Revolution and the Revolutionary Wars, which had raged on for years before concluding with the Treaty of Amiens in 1802. Napoleon became the First Consul of France in 1799, then Emperor five years later, inheriting the political and military struggles of the Revolution, he created a state with stable finances, a strong central bureaucracy, and a well-trained army. The British frequently financed the European coalitions intended to thwart French ambitions, by 1805, they had managed to convince the Austrians and the Russians to wage another war against France. At sea, the Royal Navy destroyed a combined Franco-Spanish fleet at Trafalgar in October 1805, Prussian worries about increasing French power led to the formation of the Fourth Coalition in 1806. France then forced the defeated nations of the Fourth Coalition to sign the Treaties of Tilsit in July, although Tilsit signified the high watermark of the French Empire, it did not bring a lasting peace for Europe. Hoping to extend the Continental System and choke off British trade with the European mainland, Napoleon invaded Iberia, the Spanish and the Portuguese revolted with British support. The Peninsular War lasted six years, featured extensive guerrilla warfare, the Continental System caused recurring diplomatic conflicts between France and its client states, especially Russia. Unwilling to bear the consequences of reduced trade, the Russians routinely violated the Continental System. The French launched an invasion of Russia in the summer of 1812. The resulting campaign witnessed the collapse and retreat of the Grand Army along with the destruction of Russian lands. In 1813, Prussia and Austria joined Russian forces in a Sixth Coalition against France, a lengthy military campaign culminated in a large Allied army defeating Napoleon at the Battle of Leipzig in October 1813. The Allies then invaded France and captured Paris in the spring of 1814 and he was exiled to the island of Elba near Rome and the Bourbons were restored to power. However, Napoleon escaped from Elba in February 1815 and took control of France once again, the Allies responded by forming a Seventh Coalition, which defeated Napoleon at the Battle of Waterloo in June. The Congress of Vienna, which started in 1814 and concluded in 1815, established the new borders of Europe and laid out the terms, Napoleon seized power in 1799, creating a de facto military dictatorship. The Napoleonic Wars began with the War of the Third Coalition, Kagan argues that Britain was irritated in particular by Napoleons assertion of control over Switzerland. Furthermore, Britons felt insulted when Napoleon stated that their country deserved no voice in European affairs, for its part, Russia decided that the intervention in Switzerland indicated that Napoleon was not looking toward a peaceful resolution of his differences with the other European powers. The British quickly enforced a blockade of France to starve it of resources. Napoleon responded with economic embargoes against Britain, and sought to eliminate Britains Continental allies to break the coalitions arrayed against him, the so-called Continental System formed a league of armed neutrality to disrupt the blockade and enforce free trade with France
15.
House of Hanover
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Upon Victorias death, the British throne passed to her eldest son Edward VII, a member of the House of Saxe-Coburg and Gotha through his father. The House of Hanover was formally named the House of Brunswick-Lüneburg, Hanover line, the senior branch became extinct in 1884, and the House of Hanover is now the only surviving branch of the House of Welf, which is the senior branch of the House of Este. The current head of the House of Hanover is Ernst August, George, Duke of Brunswick-Lüneburg, is considered the first member of the House of Hanover. When the Duchy of Brunswick-Lüneburg was divided in 1635, George inherited the Principality of Calenberg and his son, Christian Louis inherited the Principality of Lüneburg from Georges brother. Calenberg and Lüneburg were then shared between Georges sons until united in 1705 under his grandson, also called George, who subsequently became George I of Great Britain, all held the title Duke of Brunswick-Lüneburg. George died in 1641 and was succeeded by, Christian Louis, 1st son of Duke George, Prince of Calenberg and he relinquished Calenburg when he became Prince of Lüneburg. George William, 2nd son of Duke George, Prince of Calenberg and he relinquished Calenburg when he became Prince of Lüneburg on the death of his brother, Christian Louis. John Frederick, 3rd son of Duke George, Prince of Calenberg, Ernest Augustus, 4th son of Duke George, Prince of Calenberg. He became Prince of Calenberg on the death of his brother John Frederick and he was elevated to prince-elector of the Holy Roman Empire in 1692. Ernest Augustuss wife, Sophia of the Palatinate, was declared heiress of the throne of England by the Act of Settlement of 1701, Sophia was at that time the senior eligible Protestant descendant of James I of England. George Louis, son of Duke Ernest Augustus and Sophia, became Elector and Prince of Calenberg in 1698 and he inherited his mothers claim to the throne of Great Britain when she died in 1714. George Louis became the first British monarch of the House of Hanover as George I in 1714, George I, George II, and George III also served as electors and dukes of Brunswick-Lüneburg, informally, Electors of Hanover. From 1814, when Hanover became a kingdom, the British monarch was also King of Hanover, in 1837, however, the personal union of the thrones of the United Kingdom and Hanover ended. After the death of William IV in 1837, the kings of Hanover continued the dynasty. The 1866 rift between the House of Hanover and the House of Hohenzollern was settled only by the 1913 marriage of Princess Viktoria Luise of Prussia to Ernest Augustus, Duke of Brunswick. At the end of the Thirty Years War, the Peace of Westphalia awarded the Prince-Bishopric of Osnabrück alternately to a Catholic bishop, since the treaty gave cadets priority over heirs and reigning princes, Osnabrück became a form of appanage of the House of Hanover. In 1884, the branch of the House of Welf became extinct. By a law of 1879, the Duchy of Brunswick established a council of regency to take over at the Dukes death
16.
Zoology
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The term is derived from Ancient Greek ζῷον, zōion, i. e. animal and λόγος, logos, i. e. knowledge, study. The history of zoology traces the study of the kingdom from ancient to modern times. This ancient work was developed in the Middle Ages by Muslim physicians. During the Renaissance and early period, zoological thought was revolutionized in Europe by a renewed interest in empiricism. Microscopy revealed the unknown world of microorganisms, laying the groundwork for cell theory. The growing importance of natural theology, partly a response to the rise of mechanical philosophy, over the 18th and 19th centuries, zoology became an increasingly professional scientific discipline. Naturalists began to reject essentialism and consider the importance of extinction, cell theory provided a new perspective on the fundamental basis of life. These developments, as well as the results from embryology and paleontology, were synthesized in Charles Darwins theory of evolution by natural selection. In 1859, Darwin placed the theory of evolution on a new footing, by his discovery of a process by which organic evolution can occur. Darwin gave new direction to morphology and physiology, by uniting them in a biological theory. The end of the 19th century saw the fall of spontaneous generation, cell biology studies the structural and physiological properties of cells, including their behavior, interactions, and environment. This is done on both the microscopic and molecular levels, for single-celled organisms such as bacteria as well as the cells in multicellular organisms such as humans. Understanding the structure and function of cells is fundamental to all of the biological sciences, the similarities and differences between cell types are particularly relevant to molecular biology. Anatomy considers the forms of macroscopic structures such as organs and organ systems and it focuses on how organs and organ systems work together in the bodies of humans and animals, in addition to how they work independently. Anatomy and cell biology are two studies that are related, and can be categorized under structural studies. Physiology studies the mechanical, physical, and biochemical processes of living organisms by attempting to understand how all of the function as a whole. The theme of structure to function is central to biology, for example, what is learned about the physiology of yeast cells can also apply to human cells. The field of animal physiology extends the tools and methods of physiology to non-human species
17.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times
18.
Physics
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Physics is the natural science that involves the study of matter and its motion and behavior through space and time, along with related concepts such as energy and force. One of the most fundamental disciplines, the main goal of physics is to understand how the universe behaves. Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy, Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the mechanisms of other sciences while opening new avenues of research in areas such as mathematics. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs, the United Nations named 2005 the World Year of Physics. Astronomy is the oldest of the natural sciences, the stars and planets were often a target of worship, believed to represent their gods. While the explanations for these phenomena were often unscientific and lacking in evidence, according to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, and all Western efforts in the exact sciences are descended from late Babylonian astronomy. The most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was The Book of Optics, written by Ibn Al-Haitham, in which he was not only the first to disprove the ancient Greek idea about vision, but also came up with a new theory. In the book, he was also the first to study the phenomenon of the pinhole camera, many later European scholars and fellow polymaths, from Robert Grosseteste and Leonardo da Vinci to René Descartes, Johannes Kepler and Isaac Newton, were in his debt. Indeed, the influence of Ibn al-Haythams Optics ranks alongside that of Newtons work of the same title, the translation of The Book of Optics had a huge impact on Europe. From it, later European scholars were able to build the devices as what Ibn al-Haytham did. From this, such important things as eyeglasses, magnifying glasses, telescopes, Physics became a separate science when early modern Europeans used experimental and quantitative methods to discover what are now considered to be the laws of physics. Newton also developed calculus, the study of change, which provided new mathematical methods for solving physical problems. The discovery of new laws in thermodynamics, chemistry, and electromagnetics resulted from greater research efforts during the Industrial Revolution as energy needs increased, however, inaccuracies in classical mechanics for very small objects and very high velocities led to the development of modern physics in the 20th century. Modern physics began in the early 20th century with the work of Max Planck in quantum theory, both of these theories came about due to inaccuracies in classical mechanics in certain situations. Quantum mechanics would come to be pioneered by Werner Heisenberg, Erwin Schrödinger, from this early work, and work in related fields, the Standard Model of particle physics was derived. Areas of mathematics in general are important to this field, such as the study of probabilities, in many ways, physics stems from ancient Greek philosophy
19.
David Hilbert
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David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th, Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis, Hilbert adopted and warmly defended Georg Cantors set theory and transfinite numbers. A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems set the course for much of the mathematical research of the 20th century. Hilbert and his students contributed significantly to establishing rigor and developed important tools used in mathematical physics. Hilbert is known as one of the founders of theory and mathematical logic. In late 1872, Hilbert entered the Friedrichskolleg Gymnasium, but, after a period, he transferred to. Upon graduation, in autumn 1880, Hilbert enrolled at the University of Königsberg, in early 1882, Hermann Minkowski, returned to Königsberg and entered the university. Hilbert knew his luck when he saw it, in spite of his fathers disapproval, he soon became friends with the shy, gifted Minkowski. In 1884, Adolf Hurwitz arrived from Göttingen as an Extraordinarius, Hilbert obtained his doctorate in 1885, with a dissertation, written under Ferdinand von Lindemann, titled Über invariante Eigenschaften spezieller binärer Formen, insbesondere der Kugelfunktionen. Hilbert remained at the University of Königsberg as a Privatdozent from 1886 to 1895, in 1895, as a result of intervention on his behalf by Felix Klein, he obtained the position of Professor of Mathematics at the University of Göttingen. During the Klein and Hilbert years, Göttingen became the preeminent institution in the mathematical world and he remained there for the rest of his life. Among Hilberts students were Hermann Weyl, chess champion Emanuel Lasker, Ernst Zermelo, john von Neumann was his assistant. At the University of Göttingen, Hilbert was surrounded by a circle of some of the most important mathematicians of the 20th century, such as Emmy Noether. Between 1902 and 1939 Hilbert was editor of the Mathematische Annalen, good, he did not have enough imagination to become a mathematician. Hilbert lived to see the Nazis purge many of the prominent faculty members at University of Göttingen in 1933 and those forced out included Hermann Weyl, Emmy Noether and Edmund Landau. One who had to leave Germany, Paul Bernays, had collaborated with Hilbert in mathematical logic and this was a sequel to the Hilbert-Ackermann book Principles of Mathematical Logic from 1928. Hermann Weyls successor was Helmut Hasse, about a year later, Hilbert attended a banquet and was seated next to the new Minister of Education, Bernhard Rust
20.
Arnold Sommerfeld
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He served as PhD supervisor for many Nobel Prize winners in physics and chemistry. He introduced the 2nd quantum number and the 4th quantum number and he also introduced the fine-structure constant and pioneered X-ray wave theory. Sommerfeld studied mathematics and physical sciences at the Albertina University of his city, Königsberg. His dissertation advisor was the mathematician Ferdinand von Lindemann, and he benefited from classes with mathematicians Adolf Hurwitz and David Hilbert. His participation in the student fraternity Deutsche Burschenschaft resulted in a scar on his face. He received his Ph. D. on October 24,1891, after receiving his doctorate, Sommerfeld remained at Königsberg to work on his teaching diploma. He passed the exam in 1892 and then began a year of military service. He completed his military service in September 1893, and for the next eight years continued voluntary eight-week military service. With his turned up moustache, his build, his Prussian bearing. In October, Sommerfeld went to the University of Göttingen, which was the center of mathematics in Germany, Sommerfelds Habilitationsschrift was completed under Klein, in 1895, which allowed Sommerfeld to become a Privatdozent at Göttingen. As a Privatdozent, Sommerfeld lectured on a range of mathematical and mathematical physics topics. Lectures by Klein in 1895 and 1896 on rotating bodies led Klein and Sommerfeld to write a four-volume text Die Theorie des Kreisels – a 13-year collaboration, the first two volumes were on theory, and the latter two were on applications in geophysics, astronomy, and technology. The association Sommerfeld had with Klein influenced Sommerfelds turn of mind to be applied mathematics, while at Göttingen, Sommerfeld met Johanna Höpfner, daughter of Ernst Höpfner, curator at Göttingen. In October,1897 Sommerfeld began the appointment to the Chair of Mathematics at the Bergakademie in Clausthal-Zellerfeld and this appointment provided enough income to eventually marry Johanna. At Kleins request, Sommerfeld took on the position of editor of Volume V of Enzyklopädie der mathematischen Wissenschaften, in 1900, Sommerfeld started his appointment to the Chair of Applied Mechanics at the Königliche Technische Hochschule Aachen as extraordinarius professor, which was arranged through Kleins efforts. At Aachen, he developed the theory of hydrodynamics, which would retain his interest for a long time, later, at the University of Munich, Sommerfelds students Ludwig Hopf and Werner Heisenberg would write their Ph. D. theses on this topic. From 1906 Sommerfeld established himself as professor of physics and director of the new Theoretical Physics Institute at the University of Munich. He was selected for positions by Wilhelm Röntgen, Director of the Physics Institute at Munich
21.
Richard Courant
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Richard Courant was a German American mathematician. He is best known by the public for the book What is Mathematics. Courant was born in Lublinitz, in the Prussian Province of Silesia and his parents were Siegmund Courant and Martha Courant née Freund of Oels. Edith Stein was Richards cousin on the paternal side, during his youth his parents moved often, including to Glatz, then to Breslau and in 1905 to Berlin. He stayed in Breslau and entered the university there, then continued his studies at the University of Zürich and he became David Hilberts assistant in Göttingen and obtained his doctorate there in 1910. He was obliged to serve in World War I, but was wounded shortly after enlisting and he continued his research in Göttingen and then engaged a two-year period at the University of Münster as professor of mathematics. There he founded the Mathematical Institute, which he headed as director from 1928 until 1933, Courant left Germany in 1933, earlier than many Jewish escapees. In 1936, after one year at Cambridge, Courant accepted a professorship at New York University in New York City, there he founded an institute for graduate studies in applied mathematics. The Courant Institute of Mathematical Sciences is now one of the most respected research centers in applied mathematics, Courant and David Hilbert authored the influential textbook Methoden der mathematischen Physik which, with its revised editions, is still current and widely used since its publication in 1924. With Herbert Robbins he coauthored a popular overview of mathematics, intended for the general public. Courants name is attached to the finite element method, with his numerical treatment of the plain torsion problem for multiply-connected domains. This method is now one of the ways to solve differential equations numerically. Courant is a namesake of the Courant–Friedrichs–Lewy condition and the Courant minimax principle, Courant died in New Rochelle, New York. Commenting upon his analysis of results from in-laboratory soap film formations. Only a mathematical proof can ensure that the mathematical description of a physical phenomenon is meaningful. In 1919 Courant married Nerina Runge, a daughter of the Göttingen professor for Applied Mathematics, Courant, R. Differential and Integral Calculus, Vol. I, translated by McShane, E. J. New York, Interscience, ISBN 4-87187-838-4 Courant, R. Differential and Integral Calculus, Vol. II, translated by McShane, oxford University Press Medawar, Jean, Pyke, David. Hitlers Gift, The True Story of the Scientists Expelled by the Nazi Regime, Richard Courant at the Mathematics Genealogy Project OConnor, John J. Robertson, Edmund F. Richard Courant, MacTutor History of Mathematics archive, University of St Andrews
22.
Werner Heisenberg
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Werner Karl Heisenberg was a German theoretical physicist and one of the key pioneers of quantum mechanics. He published his work in 1925 in a breakthrough paper, in the subsequent series of papers with Max Born and Pascual Jordan, during the same year, this matrix formulation of quantum mechanics was substantially elaborated. In 1927 he published his uncertainty principle, upon which he built his philosophy, Heisenberg was awarded the Nobel Prize in Physics for 1932 for the creation of quantum mechanics. He was a principal scientist in the Nazi German nuclear weapon project during World War II and he travelled to occupied Copenhagen where he met and discussed the German project with Niels Bohr. Following World War II, he was appointed director of the Kaiser Wilhelm Institute for Physics and he was director of the institute until it was moved to Munich in 1958, when it was expanded and renamed the Max Planck Institute for Physics and Astrophysics. He studied physics and mathematics from 1920 to 1923 at the Ludwig-Maximilians-Universität München, at Munich, he studied under Arnold Sommerfeld and Wilhelm Wien. At Göttingen, he studied physics with Max Born and James Franck and he received his doctorate in 1923, at Munich under Sommerfeld. He completed his Habilitation in 1924, at Göttingen under Born, at the event, Bohr was a guest lecturer and gave a series of comprehensive lectures on quantum atomic physics. There, Heisenberg met Bohr for the first time, and it had a significant, Heisenbergs doctoral thesis, the topic of which was suggested by Sommerfeld, was on turbulence, the thesis discussed both the stability of laminar flow and the nature of turbulent flow. The problem of stability was investigated by the use of the Orr–Sommerfeld equation and he briefly returned to this topic after World War II. Heisenbergs paper on the anomalous Zeeman effect was accepted as his Habilitationsschrift under Max Born at Göttingen, in his youth he was a member and Scoutleader of the Neupfadfinder, a German Scout association and part of the German Youth Movement. In August 1923 Robert Honsell and Heisenberg organized a trip to Finland with a Scout group of this association from Munich, Heisenberg arrived at Munich in 1919 as a member of Freikorps to fight the Bavarian Soviet Republic established a year earlier. Five decades later he recalled those days as youthful fun, like playing cops and robbers and so on, from 1924 to 1927, Heisenberg was a Privatdozent at Göttingen. His seminal paper, Über quantentheoretischer Umdeutung was published in September 1925 and he returned to Göttingen and with Max Born and Pascual Jordan, over a period of about six months, developed the matrix mechanics formulation of quantum mechanics. On 1 May 1926, Heisenberg began his appointment as a university lecturer and it was in Copenhagen, in 1927, that Heisenberg developed his uncertainty principle, while working on the mathematical foundations of quantum mechanics. On 23 February, Heisenberg wrote a letter to fellow physicist Wolfgang Pauli, in his paper on the uncertainty principle, Heisenberg used the word Ungenauigkeit. In 1927, Heisenberg was appointed ordentlicher Professor of theoretical physics and head of the department of physics at the Universität Leipzig, in his first paper published from Leipzig, Heisenberg used the Pauli exclusion principle to solve the mystery of ferromagnetism. Slater, Edward Teller, John Hasbrouck van Vleck, Victor Frederick Weisskopf, Carl Friedrich von Weizsäcker, Gregor Wentzel, in early 1929, Heisenberg and Pauli submitted the first of two papers laying the foundation for relativistic quantum field theory
23.
Cosmology
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Cosmology is the study of the origin, evolution, and eventual fate of the universe. The term cosmology was first used in English in 1656 in Thomas Blounts Glossographia, religious or mythological cosmology is a body of beliefs based on mythological, religious, and esoteric literature and traditions of creation and eschatology. Physical cosmology is studied by scientists, such as astronomers and physicists, as well as philosophers, such as metaphysicians, philosophers of physics, and philosophers of space and time. Because of this scope with philosophy, theories in physical cosmology may include both scientific and non-scientific propositions, and may depend upon assumptions that can not be tested. Cosmology differs from astronomy in that the former is concerned with the Universe as a whole while the latter deals with individual celestial objects. Theoretical astrophysicist David N. Spergel has described cosmology as a science because when we look out in space. Physics and astrophysics have played a role in shaping the understanding of the universe through scientific observation. Physical cosmology was shaped through both mathematics and observation in an analysis of the whole universe, cosmogony studies the origin of the Universe, and cosmography maps the features of the Universe. In Diderots Encyclopédie, cosmology is broken down into uranology, aerology, geology, metaphysical cosmology has also been described as the placing of man in the universe in relationship to all other entities. Physical cosmology is the branch of physics and astrophysics that deals with the study of the physical origins and it also includes the study of the nature of the Universe on a large scale. In its earliest form, it was what is now known as celestial mechanics, greek philosophers Aristarchus of Samos, Aristotle, and Ptolemy proposed different cosmological theories. The geocentric Ptolemaic system was the theory until the 16th century when Nicolaus Copernicus. This is one of the most famous examples of epistemological rupture in physical cosmology, when Isaac Newton published the Principia Mathematica in 1687, he finally figured out how the heavens moved. A fundamental difference between Newtons cosmology and those preceding it was the Copernican principle—that the bodies on earth obey the same laws as all the celestial bodies. This was a crucial advance in physical cosmology. Physicists began changing the assumption that the Universe was static and unchanging, in 1922 Alexander Friedmann introduced the idea of an expanding universe that contained moving matter. In parallel to this approach to cosmology, one long-standing debate about the structure of the cosmos was coming to a climax. This difference of ideas came to a climax with the organization of the Great Debate on 26 April 1920 at the meeting of the U. S. National Academy of Sciences in Washington, D. C
24.
Associative property
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In mathematics, the associative property is a property of some binary operations. In propositional logic, associativity is a rule of replacement for expressions in logical proofs. That is, rearranging the parentheses in such an expression will not change its value, consider the following equations, +4 =2 + =92 × = ×4 =24. Even though the parentheses were rearranged on each line, the values of the expressions were not altered, since this holds true when performing addition and multiplication on any real numbers, it can be said that addition and multiplication of real numbers are associative operations. Associativity is not to be confused with commutativity, which addresses whether or not the order of two operands changes the result. For example, the order doesnt matter in the multiplication of numbers, that is. Associative operations are abundant in mathematics, in fact, many algebraic structures explicitly require their binary operations to be associative, however, many important and interesting operations are non-associative, some examples include subtraction, exponentiation and the vector cross product. Z = x = xyz for all x, y, z in S, the associative law can also be expressed in functional notation thus, f = f. If a binary operation is associative, repeated application of the produces the same result regardless how valid pairs of parenthesis are inserted in the expression. This is called the generalized associative law, thus the product can be written unambiguously as abcd. As the number of elements increases, the number of ways to insert parentheses grows quickly. Some examples of associative operations include the following, the two methods produce the same result, string concatenation is associative. In arithmetic, addition and multiplication of numbers are associative, i. e. + z = x + = x + y + z z = x = x y z } for all x, y, z ∈ R. x, y, z\in \mathbb. }Because of associativity. Addition and multiplication of numbers and quaternions are associative. Addition of octonions is also associative, but multiplication of octonions is non-associative, the greatest common divisor and least common multiple functions act associatively. Gcd = gcd = gcd lcm = lcm = lcm } for all x, y, z ∈ Z. x, y, z\in \mathbb. }Taking the intersection or the union of sets, ∩ C = A ∩ = A ∩ B ∩ C ∪ C = A ∪ = A ∪ B ∪ C } for all sets A, B, C. Slightly more generally, given four sets M, N, P and Q, with h, M to N, g, N to P, in short, composition of maps is always associative. Consider a set with three elements, A, B, and C, thus, for example, A=C = A
25.
Projective geometry
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Projective geometry is a topic of mathematics. It is the study of properties that are invariant with respect to projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, properties meaningful for projective geometry are respected by this new idea of transformation, which is more radical in its effects than can be expressed by a transformation matrix and translations. The first issue for geometers is what kind of geometry is adequate for a novel situation, one source for projective geometry was indeed the theory of perspective. Another difference from elementary geometry is the way in which parallel lines can be said to meet in a point at infinity, again this notion has an intuitive basis, such as railway tracks meeting at the horizon in a perspective drawing. See projective plane for the basics of geometry in two dimensions. While the ideas were available earlier, projective geometry was mainly a development of the 19th century and this included the theory of complex projective space, the coordinates used being complex numbers. Several major types of more abstract mathematics were based on projective geometry and it was also a subject with a large number of practitioners for its own sake, as synthetic geometry. Another topic that developed from axiomatic studies of projective geometry is finite geometry, the topic of projective geometry is itself now divided into many research subtopics, two examples of which are projective algebraic geometry and projective differential geometry. Projective geometry is an elementary form of geometry, meaning that it is not based on a concept of distance. In two dimensions it begins with the study of configurations of points and lines and that there is indeed some geometric interest in this sparse setting was first established by Desargues and others in their exploration of the principles of perspective art. In higher dimensional spaces there are considered hyperplanes, and other linear subspaces, Projective geometry can also be seen as a geometry of constructions with a straight-edge alone. Since projective geometry excludes compass constructions, there are no circles, no angles, no measurements, no parallels and it was realised that the theorems that do apply to projective geometry are simpler statements. For example, the different conic sections are all equivalent in projective geometry, during the early 19th century the work of Jean-Victor Poncelet, Lazare Carnot and others established projective geometry as an independent field of mathematics. Its rigorous foundations were addressed by Karl von Staudt and perfected by Italians Giuseppe Peano, Mario Pieri, Alessandro Padoa, after much work on the very large number of theorems in the subject, therefore, the basics of projective geometry became understood. The incidence structure and the cross-ratio are fundamental invariants under projective transformations, Projective geometry can be modeled by the affine plane plus a line at infinity and then treating that line as ordinary. An algebraic model for doing projective geometry in the style of geometry is given by homogeneous coordinates. In a foundational sense, projective geometry and ordered geometry are elementary since they involve a minimum of axioms and either can be used as the foundation for affine, Projective geometry is not ordered and so it is a distinct foundation for geometry
26.
Number theory
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Number theory or, in older usage, arithmetic is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called The Queen of Mathematics because of its place in the discipline. Number theorists study prime numbers as well as the properties of objects out of integers or defined as generalizations of the integers. Integers can be considered either in themselves or as solutions to equations, questions in number theory are often best understood through the study of analytical objects that encode properties of the integers, primes or other number-theoretic objects in some fashion. One may also study real numbers in relation to rational numbers, the older term for number theory is arithmetic. By the early century, it had been superseded by number theory. The use of the arithmetic for number theory regained some ground in the second half of the 20th century. In particular, arithmetical is preferred as an adjective to number-theoretic. The first historical find of a nature is a fragment of a table. The triples are too many and too large to have been obtained by brute force, the heading over the first column reads, The takiltum of the diagonal which has been subtracted such that the width. The tables layout suggests that it was constructed by means of what amounts, in language, to the identity 2 +1 =2. If some other method was used, the triples were first constructed and then reordered by c / a, presumably for use as a table. It is not known what these applications may have been, or whether there could have any, Babylonian astronomy, for example. It has been suggested instead that the table was a source of examples for school problems. While Babylonian number theory—or what survives of Babylonian mathematics that can be called thus—consists of this single, striking fragment, late Neoplatonic sources state that Pythagoras learned mathematics from the Babylonians. Much earlier sources state that Thales and Pythagoras traveled and studied in Egypt, Euclid IX 21—34 is very probably Pythagorean, it is very simple material, but it is all that is needed to prove that 2 is irrational. Pythagorean mystics gave great importance to the odd and the even, the discovery that 2 is irrational is credited to the early Pythagoreans. This forced a distinction between numbers, on the one hand, and lengths and proportions, on the other hand, the Pythagorean tradition spoke also of so-called polygonal or figurate numbers
27.
Complex analysis
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Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. As a differentiable function of a variable is equal to the sum of its Taylor series. Complex analysis is one of the branches in mathematics, with roots in the 19th century. Important mathematicians associated with complex analysis include Euler, Gauss, Riemann, Cauchy, Weierstrass, Complex analysis, in particular the theory of conformal mappings, has many physical applications and is also used throughout analytic number theory. In modern times, it has very popular through a new boost from complex dynamics. Another important application of analysis is in string theory which studies conformal invariants in quantum field theory. A complex function is one in which the independent variable and the dependent variable are complex numbers. More precisely, a function is a function whose domain. In other words, the components of the f, u = u and v = v can be interpreted as real-valued functions of the two real variables, x and y. The basic concepts of complex analysis are often introduced by extending the elementary real functions into the complex domain, holomorphic functions are complex functions, defined on an open subset of the complex plane, that are differentiable. In the context of analysis, the derivative of f at z 0 is defined to be f ′ = lim z → z 0 f − f z − z 0, z ∈ C. Although superficially similar in form to the derivative of a real function, in particular, for this limit to exist, the value of the difference quotient must approach the same complex number, regardless of the manner in which we approach z 0 in the complex plane. Consequently, complex differentiability has much stronger consequences than usual differentiability, for instance, holomorphic functions are infinitely differentiable, whereas most real differentiable functions are not. For this reason, holomorphic functions are referred to as analytic functions. Such functions that are holomorphic everywhere except a set of isolated points are known as meromorphic functions. On the other hand, the functions z ↦ ℜ, z ↦ | z |, an important property that characterizes holomorphic functions is the relationship between the partial derivatives of their real and imaginary components, known as the Cauchy-Riemann conditions. If f, C → C, defined by f = f = u + i v, here, the differential operator ∂ / ∂ z ¯ is defined as. In terms of the real and imaginary parts of the function, u and v, this is equivalent to the pair of equations u x = v y and u y = − v x, where the subscripts indicate partial differentiation
28.
Mathematical optimization
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In mathematics, computer science and operations research, mathematical optimization, also spelled mathematical optimisation, is the selection of a best element from some set of available alternatives. The generalization of optimization theory and techniques to other formulations comprises an area of applied mathematics. Such a formulation is called a problem or a mathematical programming problem. Many real-world and theoretical problems may be modeled in this general framework, typically, A is some subset of the Euclidean space Rn, often specified by a set of constraints, equalities or inequalities that the members of A have to satisfy. The domain A of f is called the space or the choice set. The function f is called, variously, a function, a loss function or cost function, a utility function or fitness function, or, in certain fields. A feasible solution that minimizes the objective function is called an optimal solution, in mathematics, conventional optimization problems are usually stated in terms of minimization. Generally, unless both the function and the feasible region are convex in a minimization problem, there may be several local minima. While a local minimum is at least as good as any nearby points, a global minimum is at least as good as every feasible point. In a convex problem, if there is a minimum that is interior, it is also the global minimum. Optimization problems are often expressed with special notation, consider the following notation, min x ∈ R This denotes the minimum value of the objective function x 2 +1, when choosing x from the set of real numbers R. The minimum value in case is 1, occurring at x =0. Similarly, the notation max x ∈ R2 x asks for the value of the objective function 2x. In this case, there is no such maximum as the function is unbounded. This represents the value of the argument x in the interval, John Wiley & Sons, Ltd. pp. xxviii+489. (2008 Second ed. in French, Programmation mathématique, Théorie et algorithmes, Editions Tec & Doc, Paris,2008. Nemhauser, G. L. Rinnooy Kan, A. H. G. Todd, handbooks in Operations Research and Management Science. Amsterdam, North-Holland Publishing Co. pp. xiv+709, J. E. Dennis, Jr. and Robert B
29.
Dirac large numbers hypothesis
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The Dirac large numbers hypothesis is an observation made by Paul Dirac in 1937 relating ratios of size scales in the Universe to that of force scales. The ratios constitute very large, dimensionless numbers, some 40 orders of magnitude in the present cosmological epoch, neither of these two features has gained wide acceptance in mainstream physics. LNH was Diracs personal response to a set of large number coincidences that had intrigued other theorists of his time. The coincidence was further developed by Arthur Eddington who related the above ratios to N, in addition to the examples of Weyl and Eddington, Dirac was influenced also by the primeval-atom hypothesis of Georges Lemaître, who lectured on the topic in Cambridge in 1933. The notion of a varying-G cosmology first appears in the work of Edward Arthur Milne a few years before Dirac formulated LNH, Milne was inspired not by large number coincidences but by a dislike of Einsteins general theory of relativity. According to this relation, G increases over time, hence, in units where c=1 and re =1, the age of the universe is about 1040 units of time. This is the order of magnitude as the ratio of the electrical to the gravitational forces between a proton and an electron, e 24 π ϵ0 G m p m e ≈1040. Dirac interpreted this to mean that G varies with time as G ≈1 / t, although George Gamov noted that such a temporal variation does not necessarily follow from Diracs assumptions, a corresponding change of G has not been found. According to general relativity, however, G is constant, otherwise the law of conserved energy is violated, Dirac met this difficulty by introducing into the Einstein field equations a gauge function β that describes the structure of spacetime in terms of a ratio of gravitational and electromagnetic units. He also provided alternative scenarios for the creation of matter, one of the other significant issues in LNH, additive creation. Diracs theory has inspired and continues to inspire a significant body of literature in a variety of disciplines. However, George Gamow demonstrated in 1962 how a simple revision of the parameters can invalidate Tellers conclusions. The debate is complicated by the choice of LNH cosmologies, In 1978, G. Blake argued that paleontological data is consistent with the multiplicative scenario. Arguments both for and against LNH are also made from astrophysical considerations, for example, D. Falik argued that LNH is inconsistent with experimental results for microwave background radiation whereas Canuto and Hsieh argued that it is consistent. One argument that has created significant controversy was put forward by Robert Dicke in 1961, various authors have introduced new sets of numbers into the original coincidence considered by Dirac and his contemporaries, thus broadening or even departing from Diracs own conclusions. Several authors have identified and pondered the significance of yet another large number. Naturalness Time-variation of physical constants P. A. M. Dirac, proceedings of the Royal Society of London A.165, 199–208. Cosmological Models and the Large Numbers Hypothesis, proceedings of the Royal Society of London A.338, 439–446
30.
Gravity
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Gravity, or gravitation, is a natural phenomenon by which all things with mass are brought toward one another, including planets, stars and galaxies. Since energy and mass are equivalent, all forms of energy, including light, on Earth, gravity gives weight to physical objects and causes the ocean tides. Gravity has a range, although its effects become increasingly weaker on farther objects. The most extreme example of this curvature of spacetime is a hole, from which nothing can escape once past its event horizon. More gravity results in time dilation, where time lapses more slowly at a lower gravitational potential. Gravity is the weakest of the four fundamental interactions of nature, the gravitational attraction is approximately 1038 times weaker than the strong force,1036 times weaker than the electromagnetic force and 1029 times weaker than the weak force. As a consequence, gravity has an influence on the behavior of subatomic particles. On the other hand, gravity is the dominant interaction at the macroscopic scale, for this reason, in part, pursuit of a theory of everything, the merging of the general theory of relativity and quantum mechanics into quantum gravity, has become an area of research. While the modern European thinkers are credited with development of gravitational theory, some of the earliest descriptions came from early mathematician-astronomers, such as Aryabhata, who had identified the force of gravity to explain why objects do not fall out when the Earth rotates. Later, the works of Brahmagupta referred to the presence of force, described it as an attractive force. Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th and this was a major departure from Aristotles belief that heavier objects have a higher gravitational acceleration. Galileo postulated air resistance as the reason that objects with less mass may fall slower in an atmosphere, galileos work set the stage for the formulation of Newtons theory of gravity. In 1687, English mathematician Sir Isaac Newton published Principia, which hypothesizes the inverse-square law of universal gravitation. Newtons theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted for by the actions of the other planets. Calculations by both John Couch Adams and Urbain Le Verrier predicted the position of the planet. A discrepancy in Mercurys orbit pointed out flaws in Newtons theory, the issue was resolved in 1915 by Albert Einsteins new theory of general relativity, which accounted for the small discrepancy in Mercurys orbit. The simplest way to test the equivalence principle is to drop two objects of different masses or compositions in a vacuum and see whether they hit the ground at the same time. Such experiments demonstrate that all objects fall at the rate when other forces are negligible
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Earth
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Earth, otherwise known as the World, or the Globe, is the third planet from the Sun and the only object in the Universe known to harbor life. It is the densest planet in the Solar System and the largest of the four terrestrial planets, according to radiometric dating and other sources of evidence, Earth formed about 4.54 billion years ago. Earths gravity interacts with objects in space, especially the Sun. During one orbit around the Sun, Earth rotates about its axis over 365 times, thus, Earths axis of rotation is tilted, producing seasonal variations on the planets surface. The gravitational interaction between the Earth and Moon causes ocean tides, stabilizes the Earths orientation on its axis, Earths lithosphere is divided into several rigid tectonic plates that migrate across the surface over periods of many millions of years. About 71% of Earths surface is covered with water, mostly by its oceans, the remaining 29% is land consisting of continents and islands that together have many lakes, rivers and other sources of water that contribute to the hydrosphere. The majority of Earths polar regions are covered in ice, including the Antarctic ice sheet, Earths interior remains active with a solid iron inner core, a liquid outer core that generates the Earths magnetic field, and a convecting mantle that drives plate tectonics. Within the first billion years of Earths history, life appeared in the oceans and began to affect the Earths atmosphere and surface, some geological evidence indicates that life may have arisen as much as 4.1 billion years ago. Since then, the combination of Earths distance from the Sun, physical properties, in the history of the Earth, biodiversity has gone through long periods of expansion, occasionally punctuated by mass extinction events. Over 99% of all species that lived on Earth are extinct. Estimates of the number of species on Earth today vary widely, over 7.4 billion humans live on Earth and depend on its biosphere and minerals for their survival. Humans have developed diverse societies and cultures, politically, the world has about 200 sovereign states, the modern English word Earth developed from a wide variety of Middle English forms, which derived from an Old English noun most often spelled eorðe. It has cognates in every Germanic language, and their proto-Germanic root has been reconstructed as *erþō, originally, earth was written in lowercase, and from early Middle English, its definite sense as the globe was expressed as the earth. By early Modern English, many nouns were capitalized, and the became the Earth. More recently, the name is simply given as Earth. House styles now vary, Oxford spelling recognizes the lowercase form as the most common, another convention capitalizes Earth when appearing as a name but writes it in lowercase when preceded by the. It almost always appears in lowercase in colloquial expressions such as what on earth are you doing, the oldest material found in the Solar System is dated to 4. 5672±0.0006 billion years ago. By 4. 54±0.04 Gya the primordial Earth had formed, the formation and evolution of Solar System bodies occurred along with the Sun
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Crust (geology)
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In geology, the crust is the outermost solid shell of a rocky planet or natural satellite, which is chemically distinct from the underlying mantle. The crust of the Earth is composed of a variety of igneous, metamorphic. The crust is underlain by the mantle, the upper part of the mantle is composed mostly of peridotite, a rock denser than rocks common in the overlying crust. The boundary between the crust and mantle is conventionally placed at the Mohorovičić discontinuity, a boundary defined by a contrast in seismic velocity, the crust occupies less than 1% of Earths volume. The crust of the Earth is of two types, oceanic and continental. The oceanic crust is 5 km to 10 km thick and is composed primarily of basalt, diabase, the continental crust is typically from 30 km to 50 km thick and is mostly composed of slightly less dense rocks than those of the oceanic crust. Some of these less dense rocks, such as granite, are common in the continental crust, both the continental and oceanic crust float on the mantle. Because the continental crust is thicker, it both to greater elevations and greater depth than the oceanic crust. The slightly lower density of continental rock compared to basaltic oceanic rock contributes to the higher relative elevation of the top of the continental crust. As the top of the continental crust reaches elevations higher than that of the oceanic, the temperature of the crust increases with depth, reaching values typically in the range from about 200 °C to 400 °C at the boundary with the underlying mantle. The crust and underlying relatively rigid uppermost mantle make up the lithosphere, because of convection in the underlying plastic upper mantle and asthenosphere, the lithosphere is broken into tectonic plates that move. The temperature increases by as much as 30 °C for every kilometer locally in the part of the crust. Earth has probably always had some form of basaltic crust, in contrast, the bulk of the continental crust is much older. The oldest continental crustal rocks on Earth have ages in the range from about 3.7 to 4, some zircon with age as great as 4.3 billion years has been found in the Narryer Gneiss Terrane. The average age of the current Earths continental crust has been estimated to be about 2.0 billion years, most crustal rocks formed before 2.5 billion years ago are located in cratons. Such old continental crust and the underlying mantle asthenosphere are less dense than elsewhere in Earth, formation of new continental crust is linked to periods of intense orogeny, these periods coincide with the formation of the supercontinents such as Rodinia, Pangaea and Gondwana. The continental crust has a composition similar to that of andesite. The most abundant minerals in Earths continental crust are feldspars, which make up about 41% of the crust by weight, followed by quartz at 12%, Continental crust is enriched in incompatible elements compared to the basaltic ocean crust and much enriched compared to the underlying mantle
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Sial
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In geology, the sial refers to the composition of the upper layer of the Earths crust, namely rocks rich in silicates and aluminium minerals. It is sometimes equated with the continental crust because it is absent in the oceanic basins. As these elements are less dense than the majority of the earths elements, geologists often refer to the rocks in this layer as felsic, because they contain high levels of feldspar, an aluminium silicate mineral series. However, the sial actually has quite a diversity of rock types, the name sial was taken from the first two letters of silica and of aluminium. The sial is often contrasted to the sima, the lower layer in the Earth, which is often exposed in the ocean basins. These geochemical divisions of the Earths interior were first proposed by Eduard Suess in the 19th century and this model of the outer layers of the earth has been confirmed by petrographic, gravimetric, and seismic evidence. Sial has a lower density than sima, which is due to increased amounts of aluminium. The base of the sial is not a boundary, the sial grades into the denser rocks of the sima. The Conrad discontinuity has been proposed as the boundary, but little is known about it, instead, the boundary has been arbitrarily set at a mean density of 2800 kg/m3. Because of the pressures, over geologic time, the sima flows like a very viscous liquid, so, in a real sense. Mountains extend down as well as up, much like icebergs on the ocean, sial has a mean density of 2. 7-2.8 grams per cubic centimeter
34.
Plate tectonics
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The theoretical model builds on the concept of continental drift developed during the first few decades of the 20th century. The geoscientific community accepted plate-tectonic theory after seafloor spreading was validated in the late 1950s, the lithosphere, which is the rigid outermost shell of a planet, is broken up into tectonic plates. The Earths lithosphere is composed of seven or eight major plates, where the plates meet, their relative motion determines the type of boundary, convergent, divergent, or transform. Earthquakes, volcanic activity, mountain-building, and oceanic trench formation occur along plate boundaries. The relative movement of the plates typically ranges from zero to 100 mm annually, tectonic plates are composed of oceanic lithosphere and thicker continental lithosphere, each topped by its own kind of crust. Along convergent boundaries, subduction carries plates into the mantle, the material lost is balanced by the formation of new crust along divergent margins by seafloor spreading. In this way, the surface of the lithosphere remains the same. This prediction of plate tectonics is also referred to as the conveyor belt principle, earlier theories, since disproven, proposed gradual shrinking or gradual expansion of the globe. Tectonic plates are able to move because the Earths lithosphere has greater strength than the underlying asthenosphere. Lateral density variations in the result in convection. Plate movement is thought to be driven by a combination of the motion of the seafloor away from the ridge and drag, with downward suction. Another explanation lies in the different forces generated by forces of the Sun. The relative importance of each of these factors and their relationship to other is unclear. The outer layers of the Earth are divided into the lithosphere and asthenosphere and this is based on differences in mechanical properties and in the method for the transfer of heat. Mechanically, the lithosphere is cooler and more rigid, while the asthenosphere is hotter, in terms of heat transfer, the lithosphere loses heat by conduction, whereas the asthenosphere also transfers heat by convection and has a nearly adiabatic temperature gradient. The key principle of plate tectonics is that the lithosphere exists as separate and distinct tectonic plates, Plate motions range up to a typical 10–40 mm/year, to about 160 mm/year. The driving mechanism behind this movement is described below, tectonic lithosphere plates consist of lithospheric mantle overlain by either or both of two types of crustal material, oceanic crust and continental crust. Average oceanic lithosphere is typically 100 km thick, its thickness is a function of its age, as passes, it conductively cools
35.
Nazi Party
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Its precursor, the German Workers Party, existed from 1919 to 1920. The party emerged from the German nationalist, racist, and populist Freikorps paramilitary culture, the party was created as a means to draw workers away from communism and into völkisch nationalism. Pseudo-scientific racism theories were central to Nazism, the Nazis propagated the idea of a peoples community. Their aim was to unite racially desirable Germans as national comrades, while excluding those deemed either to be political dissidents, to maintain the supposed purity and strength of the Aryan race, the Nazis sought to exterminate Jews, Romani, and the physically and mentally handicapped. They imposed exclusionary segregation on homosexuals, Africans, Jehovahs Witnesses, the partys leader since 1921, Adolf Hitler, was appointed Chancellor of Germany by President Paul von Hindenburg on 30 January 1933. Hitler rapidly established a regime known as the Third Reich. The term Nazi derives from the name given in German to a party member Nationalsozialist and was coined in response to the German term Sozi, members of the party referred to themselves as Nationalsozialisten, rarely as Nazis. The term Parteigenosse was commonly used among Nazis, with the feminine form Parteigenossin used when it was appropriate, the term was in use before the rise of the party as a colloquial and derogatory word for a backward peasant, characterising an awkward and clumsy person. It derived from Ignaz, being a version of Ignatius, a common name in Bavaria. Opponents seized on this and shortened the name in intentional association to the long-time existing Sozi to the dismissive Nazi. In 1933, when Adolf Hitler assumed power of the German government, usage of the designation Nazi diminished in Germany, the use of Nazi Germany, and Nazi regime, was popularised by anti-Nazis and German exiles abroad. Thereafter, the spread into other languages and eventually was brought back to Germany after the Second World War. The party grew out of political groups with a nationalist orientation that formed in the last years of World War I. In 1918, a called the Freien Arbeiterausschuss für einen guten Frieden was created in Bremen. On 7 March 1918, Anton Drexler, an avid German nationalist, Drexler saw the situation of political violence and instability in Germany as the result of the new Weimar Republic being out-of-touch with the masses, especially the lower classes. These were all well-known themes popular with various Weimar paramilitary groups such as the Freikorps, though very small, Drexlers movement did receive attention and support from some influential figures. Supporter Dietrich Eckhart brought military figure Count Felix Graf von Bothmer, later in 1918, Karl Harrer, convinced Drexler and several others to form the Politischer Arbeiterzirkel. The members met periodically for discussions with themes of nationalism and racism directed against the Jews and they became one of many völkisch movements that existed in Germany at the time
36.
Philipp Lenard
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Philipp Eduard Anton von Lenard was a German physicist and the winner of the Nobel Prize for Physics in 1905 for his research on cathode rays and the discovery of many of their properties. Notably, he had labeled Albert Einsteins contributions to science as constituting Jewish physics, Philipp Lenard was born in Pressburg, on 7 June 1862. The Lenard family had come from Tyrol in the 17th century. His father, Philipp von Lenardis, was a wine-merchant in Pressburg, the young Lenard studied at the Pozsonyi Királyi Katolikus Főgymnasium and as he writes it in his autobiography, this made a big impression on him. In 1880 he studied physics and chemistry in Vienna and in Budapest, in 1882 Lenard left Budapest and returned to Pressburg, but in 1883 moved to Heidelberg after his tender for an assistants position in the University of Budapest was refused. In Heidelberg he studied under the illustrious Robert Bunsen, interrupted by one semester in Berlin with Hermann von Helmholtz, in 1887 he worked again in Budapest under Loránd Eötvös as a demonstrator. After posts at Aachen, Bonn, Breslau, Heidelberg, and Kiel, in 1905 Lenard became a member of the Royal Swedish Academy of Sciences and in 1907 of the Hungarian Academy of Sciences. His early work included studies of phosphorescence and luminescence and the conductivity of flames, as a physicist, Lenards major contributions were in the study of cathode rays, which he began in 1888. Prior to his work, cathode rays were produced in primitive, partially evacuated tubes that had metallic electrodes in them. Cathode rays were difficult to study using this arrangement, because they were inside sealed glass tubes, difficult to access, having made a window for the rays, he could pass them out into the laboratory, or, alternatively, into another chamber that was completely evacuated. These windows have come to be known as Lenard windows and he was able to conveniently detect the rays and measure their intensity by means of paper sheets coated with phosphorescent materials. Lenard observed that the absorption of the rays was, to first order and this appeared to contradict the idea that they were some sort of electromagnetic radiation. Thomsons work, which arrived at the understanding that cathode rays were streams of negatively charged energetic particles. He called them quanta of electricity or for short quanta, after Helmholtz, thomson proposed the name corpuscles, but eventually electrons became the everyday term. He proposed that every atom consists of empty space and electrically neutral corpuscules called dynamids, each consisting of an electron and an equal positive charge. As a result of his Crookes tube investigations, he showed that the produced by irradiating metals in a vacuum with ultraviolet light were similar in many respects to cathode rays. His most important observations were that the energy of the rays was independent of the light intensity and these latter observations were explained by Albert Einstein as a quantum effect. This theory predicted that the plot of the cathode ray energy versus the frequency would be a line with a slope equal to Plancks constant
37.
Johannes Stark
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Johannes Stark was a German physicist and Physics Nobel Prize laureate, who was closely involved with the Deutsche Physik movement under the Nazi regime. Born in Schickenhof, Kingdom of Bavaria, Stark was educated at the Bayreuth Gymnasium and his collegiate education began at the University of Munich, where he studied physics, mathematics, chemistry, and crystallography. His tenure at that college began in 1894, he graduated in 1897, with his dissertation titled Untersuchung über einige physikalische. Stark worked in positions at the Physics Institute of his alma mater until 1900. An extraordinary professor at Hanover by 1906, in 1908 he became professor at the RWTH Aachen University and he worked and researched at physics departments of several universities, including the University of Greifswald, until 1922. In 1919, he won the Nobel Prize in Physics for his discovery of the Doppler effect in canal rays, from 1933 until his retirement in 1939, Stark was elected President of the Physikalisch-Technische Reichsanstalt, while also President of the Deutsche Forschungsgemeinschaft. It was Stark who, as the editor of Jahrbuch der Radioaktivität und Elektronik, asked in 1907, then rather unknown. While working on his article, Einstein began a line of thought that would lead to his generalized theory of relativity. This is heavily ironic, given Starks later work as an anti-Einstein, Stark published more than 300 papers, mainly regarding electricity and other such topics. Probably his best known contribution to the field of physics is the Stark effect and he married Luise Uepler, and they had five children. His hobbies were the cultivation of fruit trees and forestry and he worked in his private laboratory on his country estate in Upper Bavaria after the war. There he studied the deflection of light in an electric field, during the Nazi regime, Stark attempted to become the Führer of German physics through the Deutsche Physik movement against the Jewish physics of Albert Einstein and Werner Heisenberg. After Werner Heisenberg defended Albert Einsteins theory of relativity Stark wrote an article in the SS newspaper Das Schwarze Korps. On August 21,1934 Stark wrote to physicist and fellow Nobel laureate Max von Laue to toe the party line or else, the letter was signed off with a Heil Hitler. He attacked theoretical physics as Jewish and stressed that scientific positions in Nazi Germany should only be held by pure-blooded Germans. In 1947, following the defeat of Germany in World War II, Stark was classified as a Major Offender, die Entladung der Elektricität von galvanisch glühender Kohle in verdünntes Gas. Leipzig,1899 Der elektrische Strom zwischen galvanisch glühender Kohle und einem Metall durch verdünntes Gas, leipzig,1899 Aenderung der Leitfähigkeit von Gasen durch einen stetigen elektrischen Strom. Leipzig,1900 Ueber den Einfluss der Erhitzung auf das elektrische Leuchten eines verdünnten Gases, leipzig,1900 Ueber elektrostatische Wirkungen bei der Entladung der Elektricität in verdünnten Gasen
38.
Sturmabteilung
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The Sturmabteilung, literally Storm Detachment, functioned as the original paramilitary wing of the Nazi Party. It played a significant role in Adolf Hitlers rise to power in the 1920s and 1930s, the SA have been known in contemporary times as Brownshirts from the color of their uniform shirts, similar to Benito Mussolinis blackshirts. The SA developed pseudo-military titles for its members, the SA ranks were adopted by several other Nazi Party groups, chief amongst them the Schutzstaffel, which originated as a branch of the SA before being separated. The SA became disempowered after Adolf Hitler ordered the purge of 1934. This event became known as the Night of the Long Knives, the SA was effectively superseded by the SS, although it was not formally dissolved until after the Third Reichs final capitulation to the Allied powers in 1945. The term Sturmabteilung predates the founding of the Nazi Party in 1919, originally it was applied to the specialized assault troops of Imperial Germany in World War I who used Hutier infiltration tactics. Instead of large mass assaults, the Sturmabteilung were organised into small squads of a few soldiers each, on 2 October 1916, Generalquartiermeister Erich Ludendorff ordered all German armies in the west to form a battalion of stormtroops. They were first used during the 8th Armys siege of Riga, wider use followed on the Western Front in the Spring Offensive in March 1918, where Allied lines were successfully pushed back tens of kilometers. The DAP was formed in Munich in January 1919 and Adolf Hitler joined it in September of that year. His talents for speaking, publicity and propaganda were quickly recognized, and by early 1920 he had gained authority in the party, the precursor to the SA had acted informally and on an ad hoc basis for some time before this. Some 70 people attended, and a second meeting was advertised for 13 November in the Eberlbrau beer hall. Some 130 people attended, there were hecklers, but Hitlers military friends promptly ejected them by force, the next year, on 24 February, he announced the partys Twenty-Five Point program at a mass meeting of some 2000 people at the Hofbräuhaus. Protesters tried to shout Hitler down, but his former companions, armed with rubber truncheons. The basis for the SA had been formed, a permanent group of party members who would serve as the ruffian Saalschutzabteilung for the DAP gathered around Emil Maurice after the February 1920 incident at the Hofbräuhaus. There was little organization or structure to this group, the group was also called the Ordnertruppen around this time. More than a later, on 3 August 1921, Hitler redefined the group as the Gymnastic and Sports Division of the party. It was by now recognized as an appropriate, even necessary. By September 1921 the name Sturmabteilung was being used informally for the group, Hitler was the official head of the Nazi Party by this time
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Luftwaffe
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The Luftwaffe was the aerial warfare branch of the combined German Wehrmacht military forces during World War II. During the interwar period, German pilots were trained secretly in violation of the treaty at Lipetsk Air Base, with the rise of the Nazi Party and the repudiation of the Versailles Treaty, the Luftwaffe was officially established on 26 February 1935. The Condor Legion, a Luftwaffe detachment sent to aid Nationalist forces in the Spanish Civil War, provided the force with a testing ground for new doctrines. By the summer of 1939, the Luftwaffe had twenty-eight Geschwaders, during World War II, German pilots claimed roughly 70,000 aerial victories, while over 75,000 Luftwaffe aircraft were destroyed or significantly damaged. Of these, nearly 40,000 were lost entirely, the Luftwaffe proved instrumental in the German victories across Poland and Western Europe in 1939 and 1940. From 1942, Allied bombing campaigns gradually destroyed the Luftwaffes fighter arm, in addition to its service in the West, the Luftwaffe operated over the Soviet Union, North Africa and Southern Europe. In January 1945, during the stages of the Battle of the Bulge, the Luftwaffe made a last-ditch effort to win air superiority. After the defeat of Germany, the Luftwaffe was disbanded in 1946, the Luftwaffe had only two commanders-in-chief throughout its history, Hermann Göring and later Generalfeldmarschall Robert Ritter von Greim. Throughout the war, the force was responsible for war crimes, one of the forerunners of the Luftwaffe, the Imperial German Army Air Service, was founded in 1910 with the name Die Fliegertruppen des deutschen Kaiserreiches, most often shortened to Fliegertruppe. It was renamed Luftstreitkräfte on 8 October 1916, after the defeat of Germany, the service was dissolved on 8 May 1920 under the conditions of the Treaty of Versailles, which also mandated the destruction of all German military aircraft. Since the Treaty of Versailles forbade Germany to have an air force, to train its pilots on the latest combat aircraft, Germany solicited the help of its future enemy, the Soviet Union, which was also isolated in Europe. This base was known as 4th squadron of the 40th wing of the Red Army. Hundreds of Luftwaffe pilots and technical personnel visited, studied and were trained at Soviet air force schools in locations in Central Russia. The first steps towards the Luftwaffes formation were undertaken just months after Adolf Hitler came to power, in April 1933 the Reichsluftfahrtministerium was established. Görings control over all aspects of aviation became absolute, on 25 March 1933 the Deutschen Luftsportverband absorbed all private and national organizations, while retaining its sports title. On 15 May 1933, all military organizations in the RLM were merged, forming the Luftwaffe. The |Nationalsozialistisches Fliegerkorps was formed in 1937 to give pre-military flying training to male youths, military-age members of the NSFK were drafted to the Luftwaffe. As all such prior NSFK members were also Nazi Party members, the absence of Göring in planning and production matters was fortunate
40.
Wolfgang Pauli
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Wolfgang Ernst Pauli was an Austrian-born Swiss and American theoretical physicist and one of the pioneers of quantum physics. The discovery involved spin theory, which is the basis of a theory of the structure of matter, Pauli was born in Vienna to a chemist Wolfgang Joseph Pauli and his wife Bertha Camilla Schütz, his sister was Hertha Pauli, the writer and actress. Paulis middle name was given in honor of his godfather, physicist Ernst Mach, Paulis paternal grandparents were from prominent Jewish families of Prague, his great-grandfather was the Jewish publisher Wolf Pascheles. Paulis father converted from Judaism to Roman Catholicism shortly before his marriage in 1899, Paulis mother, Bertha Schütz, was raised in her own mothers Roman Catholic religion, her father was Jewish writer Friedrich Schütz. Pauli was raised as a Roman Catholic, although eventually he and he is considered to have been a deist and a mystic. Pauli attended the Döblinger-Gymnasium in Vienna, graduating with distinction in 1918, only two months after graduation, he published his first paper, on Albert Einsteins theory of general relativity. He attended the Ludwig-Maximilians University in Munich, working under Arnold Sommerfeld, Sommerfeld asked Pauli to review the theory of relativity for the Encyklopädie der mathematischen Wissenschaften. Two months after receiving his doctorate, Pauli completed the article and it was praised by Einstein, published as a monograph, it remains a standard reference on the subject to this day. From 1923 to 1928, he was a lecturer at the University of Hamburg, during this period, Pauli was instrumental in the development of the modern theory of quantum mechanics. In particular, he formulated the principle and the theory of nonrelativistic spin. In 1928, he was appointed Professor of Theoretical Physics at ETH Zurich in Switzerland where he made significant scientific progress and he held visiting professorships at the University of Michigan in 1931, and the Institute for Advanced Study in Princeton in 1935. He was awarded the Lorentz Medal in 1931, at the end of 1930, shortly after his postulation of the neutrino and immediately following his divorce and the suicide of his mother, Pauli experienced a personal crisis. He consulted psychiatrist and psychotherapist Carl Jung who, like Pauli, Jung immediately began interpreting Paulis deeply archetypal dreams, and Pauli became one of the depth psychologists best students. He soon began to criticize the epistemology of Jungs theory scientifically, a great many of these discussions are documented in the Pauli/Jung letters, today published as Atom and Archetype. Jungs elaborate analysis of more than 400 of Paulis dreams is documented in Psychology, the German annexation of Austria in 1938 made him a German citizen, which became a problem for him in 1939 after the outbreak of World War II. In 1940, he tried in vain to obtain Swiss citizenship, Pauli moved to the United States in 1940, where he was employed as a professor of theoretical physics at the Institute for Advanced Study. In 1946, after the war, he became a citizen of the United States and subsequently returned to Zurich. In 1949, he was granted Swiss citizenship, in 1958, Pauli was awarded the Max Planck medal