1.
Riedstadt
–
Riedstadt, with its municipal area of 73.76 km² is Groß-Gerau districts biggest town by land area. It lies in Hesse, Germany, about 12 km southwest of Darmstadt, riedstadt is shaped not only by its preserved rural structure, but also by being near several cities, namely Frankfurt am Main, Darmstadt, Wiesbaden, Mainz, and Mannheim. As its name suggests, it lies in the Hessisches Ried, the community practises the structured settlement of environmentally friendly business operations. Local recreation sites near the community include the Kühkopf-Knoblochsaue nature reserve, the Bergstraße, the Odenwald, riedstadt consists of the centres Crumstadt, Erfelden, Goddelau, Leeheim, and Wolfskehlen. The community came into being on 1 January 1977 with Hesses municipal reforms, which merged the independent communities of Goddelau, Wolfskehlen, Erfelden, Crumstadt. Erfelden was first mentioned in a document from the Lorsch Monastery in 779. In the Thirty Years War, King Gustavus Adolphus of Sweden spent two nights at the house in 1631 while his troops were crossing the Rhine. His building master Matthäus Staud built the Schwedensäule at Erfelden which recalls the crossing, Goddelau was first mentioned in a donation document when Count Gundram donated his property in Terminis Gotalohono to Fulda Abbey. Over the centuries, the village was shaped by its dwellers agricultural, in 1588 there were roughly 180 inhabitants in Goddelau. The house in which writer and revolutionary Georg Büchner would later be born was built in 1665, Leeheim was first mentioned in the Lorsch codex in 766 when a man named Dodo made a donation to the Lorsch Monastery. Near the earlier village of Camba, the Salian Conrad II was chosen to be German King in 1024, Leeheim was shaped by several monastic properties, belonging to, among others, St. Albans Monastery in Mainz. The overlords were the Wolfskehlers, and later the Katzenelnbogen family, in 1536, Leeheim became Evangelical, and in the Thirty Years War, more than 70% of the village was destroyed. In 1666, almost half the inhabitants lost their lives to the Plague, in earlier times, Leeheim developed itself from a farming village into a workers residential village with recreational lands on the Riedsee, a nearby lake, and a golf course. Wolfskehlen is Riedstadts northernmost constituent community and it was first mentioned in the document Historia Episcopatus Wormatiensis in 1002 in which Emperor Heinrich II granted Bishop Burchard of Worms the rights in the Forest of Forehahi. In 1252, the Lords of Wolfskehlen, who had taken their name from the village, in 1539, Barbara von Wolfskehlen wed Eberhard von Gemmingen-Hornberg, who introduced the Reformation into Wolfskehlen. In 1579, the Mainz Palatinate ceded its rights to the Landgraves of Hesse, during the Thirty Years War, and through the Plague, almost the whole population was killed, the reconstruction began in the 18th century. From 1868 to 1878, the building of the Mannheim–Frankfurt railway brought the dissolution of the purely agricultural structure. After the Second World War, the village absorbed about 800 refugees, in January 2011, Werner Amend was voted as the new mayor
2.
Grand Duchy of Hesse
–
Hesse lost its independence when it joined the German Empire in 1871. Before 1866, its northern neighbour was its former sister Landgraviate, since 1803 an Electorate, of Hesse-Kassel – for this reason, Hesse-Darmstadt was a member of Napoleons Confederation of the Rhine during the Napoleonic Wars. Rapidly expanding during the mediatizations, Hesse-Darmstadt became an amalgamation of smaller German states, the legal patchwork of the state culminated in a decree issued on 1 October 1806 by Louis I. The old territorial estates were abolished, which altered Hesse-Darmstadt from a mosaic of patrimonial fragments into a centralized, during the Congress of Vienna it was forced to cede the Duchy of Westphalia, which Hesse-Darmstadt had received in 1803, to the Kingdom of Prussia. However, Hesse-Darmstadt received some territory on the bank of the Rhine. The Grand Duchy changed its name to the Grand Duchy of Hesse, in 1867, the northern half of the Grand Duchy became a part of the North German Confederation, while the half of the Grand Duchy south of the Main remained outside. In 1871, it became a constituent state of the German Empire, the last Grand Duke, Ernst Ludwig, was forced from his throne at the end of World War I, and the state was renamed the Peoples State of Hesse. After World War II, the majority of the state combined with Frankfurt am Main, the Waldeck area, excluded were the Montabaur district from Hessen-Nassau and that part of Hessen-Darmstadt on the left bank of the Rhine, which became part of the Rhineland-Palatinate state. Wimpfen—an exclave of Hessen-Darmstadt—became part of Baden-Württemberg, in the district of Sinsheim, after a plebiscite on 29 April 1951, Bad Wimpfen was transferred from Sinsheim district to Heilbronn District. This change to Heilbronn was carried out on 1 May 1952, the Grand Duchy of Hesse was divided into three provinces, Starkenburg, Right bank of the Rhine, south of the Main. Rhenish Hesse, Left bank of the Rhine, territory gained from the Congress of Vienna, upper Hesse, North of the Main, separated from Starkenburg by the Free City of Frankfurt. List of rulers of Hesse Line of succession to the former Hessian throne Hessenlager Constitution of Hesse Das Großherzogtum Hessen 1806–1918 Großherzogtum Hessen 1910
3.
German Empire
–
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
4.
Upper Bavaria
–
Upper Bavaria is one of the seven administrative districts of Bavaria, Germany. Upper Bavaria is located in the portion of Bavaria, and is centered on the city of Munich. It is subdivided into four planning regions, Ingolstadt, Munich, Bayerisches Oberland and it is named Upper Bavaria because the land is higher above sea level than the rest of Bavaria, not because it is farther north. After the reunification in 1340 Bavaria was divided again in 1349, in 1505 Bavaria was permanently reunited. After the founding of the Kingdom of Bavaria the state was reorganised and, in 1808, divided into 15 administrative districts. They were created in the fashion of the French departements, quite even in size and population, in the following years, due to territorial changes, the number of districts was reduced to 8. One of these was the Isarkreis, in 1837 king Ludwig I of Bavaria renamed the Kreise after historical names and tribes. This also involved minor border changes or territorial swaps, thus, the name Isarkreis changed to Upper Bavaria. Featured former residence cities are the capital Munich, Ingolstadt and Neuburg an der Donau, interesting townscapes have especially also Landsberg am Lech and Wasserburg am Inn. The highest mountain in Upper Bavaria, Zugspitze, offers a panoramic view of the Alps. Nestled in forested mountain ranges, the lakes Tegernsee, Schliersee, the larger lakes, like Starnberger See, Ammersee, and Chiemsee further to the east, all situated in the pre-alpine uplands, offer regular Passenger services on steamers. Sacred art treasures can be found in the monasteries Andechs, Benediktbeuern and Ettal, the most important places of pilgrimage are Altoetting and Tuntenhausen. Official website Official website Tourism website
5.
West Germany
–
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.
Heidelberg University
–
Heidelberg University is a public research university in Heidelberg, Baden-Württemberg, Germany. Founded in 1386 on instruction of Pope Urban VI, Heidelberg is Germanys oldest university and it was the third university established in the Holy Roman Empire. Heidelberg has been an institution since 1899. The university consists of twelve faculties and offers programmes at undergraduate, graduate. The language of instruction is usually German, while a number of graduate degrees are offered in English. Associated with 31 Nobel Prize laureates, the university places an emphasis on research, modern scientific psychiatry, psychopharmacology, psychiatric genetics, environmental physics, and modern sociology were introduced as scientific disciplines by Heidelberg faculty. Approximately 1,000 doctorates are completed every year, with more than one third of the students coming from abroad. International students from some 130 countries account for more than 20 percent of the student body. The universitys noted alumni include eleven domestic and foreign Heads of State or Heads of Government, the Great Schism of 1378 made it possible for Heidelberg, a relatively small city and capital of the Electorate of the Palatinate, to gain its own university. The Great Schism was initiated by the election of two popes after the death of Pope Gregory XI in the same year, one successor resided in Avignon and the other in Rome. Rupert I recognized the opportunity and initiated talks with the Curia, as specified in the papal charter, the university was modelled after University of Paris and included four faculties, philosophy, theology, jurisprudence, and medicine. On 18 October 1386 a special Pontifical High Mass in the Heiliggeistkirche was the ceremony that established the university, on 19 October 1386 the first lecture was held, making Heidelberg the oldest university in Germany. In November 1386, Marsilius of Inghen was elected first rector of the university, the rector seal motto was semper apertus—i. e. The book of learning is always open, the university grew quickly and in March 1390,185 students were enrolled at the university. This resulted in establishing a reputation for the university and its professors. Due to the influence of Marsilius, the university initially taught the nominalism or via moderna, the transition from scholastic to humanistic culture was effected by the chancellor and bishop Johann von Dalberg in the late 15th century. Humanism was represented at Heidelberg University particularly by the founder of the older German Humanistic School Rudolph Agricola, Conrad Celtes, Jakob Wimpfeling, and Johann Reuchlin. Æneas Silvius Piccolomini was chancellor of the university in his capacity of provost of Worms, in 1482, Pope Sixtus IV permitted laymen and married men to be appointed professors in the ordinary of medicine through a papal dispensation
7.
Mathematics
–
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
8.
Humboldt University of Berlin
–
The Humboldt university model has strongly influenced other European and Western universities. In 1949, it changed its name to Humboldt-Universität in honour of both its founder Wilhelm and his brother, geographer Alexander von Humboldt. The first semester at the newly founded Berlin university occurred in 1810 with 256 students and 52 lecturers in faculties of law, medicine, theology, du Bois and European unifier Robert Schuman, as well as the influential surgeon Johann Friedrich Dieffenbach in the early half of the 1800s. The structure of German research-intensive universities, such as Humboldt, served as a model for institutions like Johns Hopkins University, Alexander von Humboldt, brother of the founder William, promoted the new learning. With the construction of research facilities in the second half of the 19th Century teaching of the natural sciences began. During this period of enlargement, Berlin University gradually expanded to other previously separate colleges in Berlin. An example would be the Charité, the Pépinière and the Collegium Medico-chirurgicum, in 1717, King Friedrich I had built a quarantine house for Plague at the city gates, which in 1727 was rechristened by the soldier king Friedrich Wilhelm, Es soll das Haus die Charité heißen. By 1829 the site became Berlin Universitys medical campus and remained so until 1927 when the more modern University Hospital was constructed, Berlin University started a natural history collection in 1810, which, by 1889 required a separate building and became the Museum für Naturkunde. The preexisting Tierarznei School, founded in 1790 and absorbed by the university, also the Landwirtschaftliche Hochschule Berlin, founded in 1881 was affiliated with the Agricultural Faculties of the University. After 1933, like all German universities, it was affected by the Nazi regime, the rector during this period was Eugen Fischer. The Law for the Restoration of the Professional Civil Service resulted in 250 Jewish professors and employees being fired during 1933/1934, students and scholars and political opponents of Nazis were ejected from the university and often deported. During this time one third of all of the staff were fired by the Nazis. The Soviet Military Administration in Germany ordered the opening of the university in January 1946, the SMAD wanted a redesigned Berlin University based on the Soviet model, however they insisted on the phrasing newly opened and not re-opened for political reasons. The University of Berlin must effectively start again in almost every way and you have before you this image of the old university. What remains of that is nought but ruins, the teaching was limited to seven departments working in reopened, war-damaged buildings, with many of the teachers dead or missing. However, by the semester of 1946, the Economic. This program existed at Berlin University until 1962, the East-West conflict in post-war Germany led to a growing communist influence in the university. This was controversial, and incited strong protests within the student body, Soviet NKVD secret police arrested a number of students in March 1947 as a response
9.
Goethe University Frankfurt
–
Goethe University is a university located in Frankfurt, Germany. The original name was Universität Frankfurt am Main, in 1932, the universitys name was extended in honour of one of the most famous locals of Frankfurt, the poet and writer Johann Wolfgang von Goethe. It is thus referred to as the Goethe University in both formal and informal settings. The university currently has around 46,000 students, distributed across four campuses within the city. 18 Nobel Prize winners have been affiliated with the university, including Max von Laue, the university is also affiliated with 11 winners of the prestigious Gottfried Wilhelm Leibniz Prize. The university celebrated its 100th anniversary in 2014, the first female president of the university, Birgitta Wolff, was sworn into office in 2015. The University of Frankfurt has at times been considered liberal, or left-leaning, during the Nazi period, almost one third of its academics and many of its students were dismissed for racial and/or political reasons—more than at any other German university. The university also played a part in the German student movement of 1968. Some of the scholars associated with this school include Theodor Adorno, Max Horkheimer, and Jürgen Habermas, as well as Herbert Marcuse, Erich Fromm. The university also has been influential in the sciences and medicine, with Nobel Prize winners including Max von Laue and Max Born. In recent years, the university has focused in particular on law, history, and economics, creating new institutes, such as the Institute for Law and Finance and the Center for Financial Studies. One of the universitys ambitions is to become Germanys leading university for finance and economics, the Goethe Business School offers a M. B. A. program, in cooperation with Duke University’s Fuqua School of Business. Goethe university has established an award for research in financial economics. The university consists of 16 faculties, ordered by their sorting number, these are, ：01. “Campus Westend” of the University is dominated by the IG Farben Building by architect Hans Poelzig, after the university took over the complex, new buildings were added to the campus. On 30 May 2008, the House of Finance relocated to a new building designed by the architects Kleihues+Kleihues, the upper floors of the House of Finance building have several separate offices as well as shared office space for researchers and students. The ground floor is open to the public and welcomes visitors with a spacious, naturally lit foyer that leads to lecture halls, seminar rooms, and the information center, the ground floor also accommodates computer rooms and a café. The floors, walls and ceiling of the foyer are decorated with a design that is continued throughout the entire building
10.
Felix Klein
–
His 1872 Erlangen Program, classifying geometries by their underlying symmetry groups, was a hugely influential synthesis of much of the mathematics of the day. Felix Klein was born on 25 April 1849 in Düsseldorf, to Prussian parents, his father, Kleins mother was Sophie Elise Klein. He attended the Gymnasium in Düsseldorf, then studied mathematics and physics at the University of Bonn, 1865–1866, at that time, Julius Plücker held Bonns chair of mathematics and experimental physics, but by the time Klein became his assistant, in 1866, Plückers interest was geometry. Klein received his doctorate, supervised by Plücker, from the University of Bonn in 1868, Plücker died in 1868, leaving his book on the foundations of line geometry incomplete. Klein was the person to complete the second part of Plückers Neue Geometrie des Raumes, and thus became acquainted with Alfred Clebsch. Klein visited Clebsch the following year, along with visits to Berlin, in July 1870, at the outbreak of the Franco-Prussian War, he was in Paris and had to leave the country. For a short time, he served as an orderly in the Prussian army before being appointed lecturer at Göttingen in early 1871. Erlangen appointed Klein professor in 1872, when he was only 23, in this, he was strongly supported by Clebsch, who regarded him as likely to become the leading mathematician of his day. Klein did not build a school at Erlangen where there were few students, in 1875 Klein married Anne Hegel, the granddaughter of the philosopher Georg Wilhelm Friedrich Hegel. After five years at the Technische Hochschule, Klein was appointed to a chair of geometry at Leipzig, there his colleagues included Walther von Dyck, Rohn, Eduard Study and Friedrich Engel. Kleins years at Leipzig,1880 to 1886, fundamentally changed his life, in 1882, his health collapsed, in 1883–1884, he was plagued by depression. Nonetheless his research continued, his work on hyperelliptic sigma functions dates from around this period. Klein accepted a chair at the University of Göttingen in 1886, from then until his 1913 retirement, he sought to re-establish Göttingen as the worlds leading mathematics research center. Yet he never managed to transfer from Leipzig to Göttingen his own role as the leader of a school of geometry, at Göttingen, he taught a variety of courses, mainly on the interface between mathematics and physics, such as mechanics and potential theory. The research center Klein established at Göttingen served as a model for the best such centers throughout the world and he introduced weekly discussion meetings, and created a mathematical reading room and library. In 1895, Klein hired David Hilbert away from Königsberg, this appointment proved fateful, under Kleins editorship, Mathematische Annalen became one of the very best mathematics journals in the world. Founded by Clebsch, only under Kleins management did it first rival then surpass Crelles Journal based out of the University of Berlin, Klein set up a small team of editors who met regularly, making democratic decisions. The journal specialized in analysis, algebraic geometry, and invariant theory
11.
Werner Fenchel
–
Moritz Werner Fenchel was a mathematician known for his contributions to geometry and to optimization theory. Fenchel established the basic results of analysis and nonlinear optimization theory which would, in time. A German-born Jew and early refugee from Nazi suppression of intellectuals, fenchels monographs and lecture notes are considered influential. Fenchel was born on 3 May 1905 in Berlin, Germany, Fenchel studied mathematics and physics at the University of Berlin between 1923 and 1928. He wrote his thesis in geometry under Ludwig Bieberbach. From 1928 to 1933, Fenchel was Professor E. Landaus Assistant at the University of Göttingen, during a one-year leave between 1930 and 1931, Fenchel spent time in Rome with Levi-Civita, as well as in Copenhagen with Harald Bohr and Tommy Bonnesen. He visited Denmark again in 1932, Fenchel taught at Göttingen until 1933, when the Nazi discrimination laws led to mass-firings of Jews. Fenchel emigrated to Denmark somewhere between April and September 1933, ultimately obtaining a position at the University of Copenhagen, in December 1933, Fenchel married fellow German refugee mathematician Käte Sperling. When Germany occupied Denmark, Fenchel and roughly eight-thousand other Danish Jews received refuge in Sweden, after the Allied powers liberation of Denmark, Fenchel returned to Copenhagen. In 1946, Fenchel was elected a member of the Royal Danish Academy of Sciences, on leave between 1949 and 1951, Fenchel taught in the U. S. at the University of Southern California, Stanford University, and Princeton University. From 1952 to 1956 Fenchel was the professor in mechanics at the Polytechnic in Copenhagen, from 1956 to 1974 he was the professor in mathematics at the University of Copenhagen. Professor Fenchel died on 24 January 1988, Fenchel lectured on Convex Sets, Cones, and Functions at Princeton University in the early 1950s. His lecture notes shaped the field of analysis, according to the monograph Convex Analysis of R. T. Rockafellar. Werner Fenchel at the Mathematics Genealogy Project Werner Fenchel website – contains CV, biography, links to archive, etc
12.
Maximilian Herzberger
–
Maximilian Jacob Herzberger was a German mathematician and physicist, known for his development of the superachromat lens. Maximilian Herzberger was the son of Leopold Herzberger and Sonja/Sofia Behrendt/Berendt/Berends and he studied mathematics and physics at the Berlin University, where Albert Einstein was one of his professors, and later became a friend and advisor. In 1923, Herzberger finished his Ph. D. thesis Ueber Systeme hyperkomplexer Grössen under Ludwig Bieberbach, in 1925, he married Edith Kaufmann, they had three children, born in Jena, viz. Ruth, Ursula, and Hans. No later than Sep 1930, he was assistant of Hans Boegehold, in 1934, the Nazis deprived him from his professorship at Jena University and his contract with Zeiss. He emigrated with his family to Rochester, where he head of Eastman Kodaks optical research laboratories. In 1940, he and his family became U. S. citizens, in 1945, he got the Cressy Morrison Award of the New York Academy of Sciences. In 1954 he finished the development of the superachromat as the ultimately well-corrected lens for Kodak, in 1962, he was awarded the Frederic Ives Medal of the Optical Society of America. He held patents for an apochromatic telescope objective having three air spaced components, and a superachromatic objective
13.
Heinz Hopf
–
Heinz Hopf was a German mathematician who worked on the fields of topology and geometry. Hopf was born in Gräbschen, Germany, the son of Elizabeth and his father was born Jewish and converted to Protestantism a year after Heinz was born, his mother was from a Protestant family. Hopf attended Dr. Karl Mittelhaus higher boys school from 1901 to 1904 and he showed mathematical talent from an early age. In 1913 he entered the Silesian Friedrich Wilhelm University where he attended lectures by Ernst Steinitz, Kneser, Max Dehn, Erhard Schmidt, when World War I broke out in 1914, Hopf eagerly enlisted. He was wounded twice and received the cross in 1918. In 1920, Hopf moved to Berlin to continue his mathematical education and he studied under Ludwig Bieberbach, receiving his doctorate in 1925. He also studied the indices of zeros of vector fields on hypersurfaces and this theorem is now called the Poincaré–Hopf theorem. Hopf spent the year after his doctorate at Göttingen, where David Hilbert, Richard Courant, Carl Runge, while there he met Paul Alexandrov and began a lifelong friendship. In 1926 Hopf moved back to Berlin, where he gave a course in combinatorial topology and he spent the academic year 1927/28 at Princeton University on a Rockefeller fellowship with Alexandrov. Solomon Lefschetz, Oswald Veblen and J. W. Alexander were all at Princeton at the time, at this time Hopf discovered the Hopf invariant of maps S3 → S2 and proved that the Hopf fibration has invariant 1. In the summer of 1928 Hopf returned to Berlin and began working with Alexandrov, at the suggestion of Courant, three volumes were planned, but only one was finished. In 1929, he declined a job offer from Princeton University, in 1931 Hopf took Hermann Weyls position at ETH, in Zürich. Hopf received another invitation to Princeton in 1940, but he declined it, in 1946/47 and 1955/56 Hopf visited the United States, staying at Princeton and giving lectures at New York University and Stanford University. He served as president of the International Mathematical Union from 1955 to 1958, in October 1928 Hopf married Anja von Mickwitz. He received honorary doctorates from Princeton, Freiburg i, manchester, Sorbonne at Paris, Brussels, and Lausanne. In memory of Hopf, ETH Zürich awards the Heinz Hopf Prize for outstanding work in the field of pure mathematics. Heinz Hopf, History of ICMI web-site Hilton, P. J. Heinz Hopf, doi,10. 1112/blms/4.2.202 OConnor, John J. Robertson, Edmund F. Heinz Hopf, MacTutor History of Mathematics archive, University of St Andrews. On the curvature integra of closed hypersurfaces, transl. by D. H. Delphenich Vector fields in n-dimensional manifolds, transl. by D. H. Delphenich
14.
Germany
–
Germany, officially the Federal Republic of Germany, is a federal parliamentary republic in central-western Europe. It includes 16 constituent states, covers an area of 357,021 square kilometres, with about 82 million inhabitants, Germany is the most populous member state of the European Union. After the United States, it is the second most popular destination in the world. Germanys capital and largest metropolis is Berlin, while its largest conurbation is the Ruhr, other major cities include Hamburg, Munich, Cologne, Frankfurt, Stuttgart, Düsseldorf and Leipzig. Various Germanic tribes have inhabited the northern parts of modern Germany since classical antiquity, a region named Germania was documented before 100 AD. During the Migration Period the Germanic tribes expanded southward, beginning in the 10th century, German territories formed a central part of the Holy Roman Empire. During the 16th century, northern German regions became the centre of the Protestant Reformation, in 1871, Germany became a nation state when most of the German states unified into the Prussian-dominated German Empire. After World War I and the German Revolution of 1918–1919, the Empire was replaced by the parliamentary Weimar Republic, the establishment of the national socialist dictatorship in 1933 led to World War II and the Holocaust. After a period of Allied occupation, two German states were founded, the Federal Republic of Germany and the German Democratic Republic, in 1990, the country was reunified. In the 21st century, Germany is a power and has the worlds fourth-largest economy by nominal GDP. As a global leader in industrial and technological sectors, it is both the worlds third-largest exporter and importer of goods. Germany is a country with a very high standard of living sustained by a skilled. It upholds a social security and universal health system, environmental protection. Germany was a member of the European Economic Community in 1957. It is part of the Schengen Area, and became a co-founder of the Eurozone in 1999, Germany is a member of the United Nations, NATO, the G8, the G20, and the OECD. The national military expenditure is the 9th highest in the world, the English word Germany derives from the Latin Germania, which came into use after Julius Caesar adopted it for the peoples east of the Rhine. This in turn descends from Proto-Germanic *þiudiskaz popular, derived from *þeudō, descended from Proto-Indo-European *tewtéh₂- people, the discovery of the Mauer 1 mandible shows that ancient humans were present in Germany at least 600,000 years ago. The oldest complete hunting weapons found anywhere in the world were discovered in a mine in Schöningen where three 380, 000-year-old wooden javelins were unearthed
15.
Mathematician
–
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, one of the earliest known mathematicians was Thales of Miletus, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, the number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was All is number. It was the Pythagoreans who coined the term mathematics, and with whom the study of mathematics for its own sake begins, the first woman mathematician recorded by history was Hypatia of Alexandria. She succeeded her father as Librarian at the Great Library and wrote works on applied mathematics. Because of a dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked. Science and mathematics in the Islamic world during the Middle Ages followed various models and it was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences, an example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham, the Renaissance brought an increased emphasis on mathematics and science to Europe. As time passed, many gravitated towards universities. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking. ”Thus, seminars, overall, science became the focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. ”Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of an understanding of mathematics, the students, who pass, are permitted to work on a doctoral dissertation. Mathematicians involved with solving problems with applications in life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their knowledge and professional methodology. With professional focus on a variety of problems, theoretical systems
16.
Nazism
–
National Socialism, more commonly known as Nazism, is the ideology and practice associated with the 20th-century German Nazi Party and Nazi Germany, as well as other far-right groups. Nazism subscribed to theories of racial hierarchy and Social Darwinism, identifying Germans as part of what Nazis regarded as an Aryan or Nordic master race and it aimed to overcome social divisions and create a homogeneous society, unified on the basis of racial purity. The term National Socialism arose out of attempts to create a nationalist redefinition of socialism, the Nazi Partys precursor, the Pan-German nationalist and anti-Semitic German Workers Party, was founded on 5 January 1919. By the early 1920s, Adolf Hitler assumed control of the organisation, following the Holocaust and German defeat in World War II, only a few fringe racist groups, usually referred to as neo-Nazis, still describe themselves as following National Socialism. The full name of Adolf Hitlers party was Nationalsozialistische Deutsche Arbeiterpartei, the shorthand Nazi was formed from the first two syllables of the German pronunciation of the word national. The term was in use before the rise of the NSDAP as a colloquial and derogatory word for a peasant, characterizing an awkward. It derived from Ignaz, being a version of Ignatius, a common name in Bavaria. Opponents seized on this and shortened the first word of the name, Nationalsozialistische. The NSDAP briefly adopted the Nazi designation, attempting to reappropriate the term, the use of Nazi Germany, Nazi regime, and so on was popularised by German exiles abroad. From them, the spread into other languages and was eventually brought back to Germany after World War II. In English, Nazism is a name for the ideology the party advocated. The majority of scholars identify Nazism in practice as a form of far-right politics, far-right themes in Nazism include the argument that superior people have a right to dominate over other people and purge society of supposed inferior elements. Adolf Hitler and other proponents officially portrayed Nazism as being neither left- nor right-wing, but the politicians of the Right deserve exactly the same reproach. It was through their miserable cowardice that those ruffians of Jews who came into power in 1918 were able to rob the nation of its arms, a major inspiration for the Nazis were the far-right nationalist Freikorps, paramilitary organisations that engaged in political violence after World War I. The Nazis stated the alliance was purely tactical and there remained substantial differences with the DNVP, the Nazis described the DNVP as a bourgeois party and called themselves an anti-bourgeois party. After the elections in 1932, the alliance broke after the DNVP lost many of its seats in the Reichstag, the Nazis denounced them as an insignificant heap of reactionaries. The DNVP responded by denouncing the Nazis for their socialism, their violence. Kaiser Wilhelm II, who was pressured to abdicate the throne and flee into exile amidst an attempted communist revolution in Germany, there were factions in the Nazi Party, both conservative and radical
17.
Darmstadt
–
Darmstadt is a city in the state of Hesse in Germany, located in the southern part of the Rhine-Main-Area. Darmstadt has a population around 150,000, the Darmstadt Larger Urban Zone has 430,993 inhabitants. Darmstadt holds the official title City of Science as it is a centre of scientific institutions, universities. The existence of the elements were also confirmed at GSI Centre for Heavy Ion Research, nihonium, flerovium, moscovium, livermorium. Darmstadt is also the seat of the worlds oldest pharmaceutical company, Merck, Darmstadt was formerly the capital of a sovereign country, the Grand Duchy of Hesse and its successor, the Peoples State of Hesse, a federal state of Germany. As the capital of an increasingly prosperous duchy, the city gained some international prominence, in the 20th century, industry, as well as large science and electronics sectors became increasingly important, and are still a major part of the citys economy. It is also home to the football club SV Darmstadt 98, Darmstadt, Indiana was named after Darmstadt and for the former Royal Family. The name Darmstadt first appears towards the end of the 11th century, the origins of the name are unknown. Dar-mund in Middle Low German is translated as Boggy Headlands, even locals often believe, incorrectly, that the name derives from the Darmbach. In fact, the received its current name much later, after the city. Darmstadt was chartered as a city by the Holy Roman Emperor Ludwig the Bavarian in 1330, the city, then called Darmstait, became a secondary residence for the counts, with a small castle established at the site of the current, much larger edifice. When the house of Katzenelnbogen became extinct in 1479, the city was passed to the Landgraviate of Hesse, the city grew in population during the 19th century from little over 10,000 to 72,000 inhabitants. A polytechnical school, which became a Technical University now known as TU Darmstadt, was established in 1877. In the beginning of the 20th century, Darmstadt was an important centre for the art movement of Jugendstil, annual architectural competitions led to the building of many architectural treasures of this period. Also during this period, in 1912 the chemist Anton Kollisch, working for the pharmaceutical company Merck, Darmstadts municipal area was extended in 1937 to include the neighbouring localities of Arheilgen and Eberstadt, and in 1938 the city was separated administratively from the surrounding district. Darmstadt was the first city in Germany to force Jewish shops to close in early 1933, the shops were only closed for one day, for endangering communal order and tranquility. In 1942, over 3,000 Jews from Darmstadt were first forced into a camp located in the Liebigschule. Darmstadt was first bombed on 30 July 1940, and 34 other air raids would follow before the wars end, the old city centre was largely destroyed in a British bombing raid on 11 September 1944
18.
German language
–
German is a West Germanic language that is mainly spoken in Central Europe. It is the most widely spoken and official language in Germany, Austria, Switzerland, South Tyrol, the German-speaking Community of Belgium and it is also one of the three official languages of Luxembourg. Major languages which are most similar to German include other members of the West Germanic language branch, such as Afrikaans, Dutch, English, Luxembourgish and it is the second most widely spoken Germanic language, after English. One of the languages of the world, German is the first language of about 95 million people worldwide. The German speaking countries are ranked fifth in terms of publication of new books. German derives most of its vocabulary from the Germanic branch of the Indo-European language family, a portion of German words are derived from Latin and Greek, and fewer are borrowed from French and English. With slightly different standardized variants, German is a pluricentric language, like English, German is also notable for its broad spectrum of dialects, with many unique varieties existing in Europe and also other parts of the world. The history of the German language begins with the High German consonant shift during the migration period, when Martin Luther translated the Bible, he based his translation primarily on the standard bureaucratic language used in Saxony, also known as Meißner Deutsch. Copies of Luthers Bible featured a long list of glosses for each region that translated words which were unknown in the region into the regional dialect. Roman Catholics initially rejected Luthers translation, and tried to create their own Catholic standard of the German language – the difference in relation to Protestant German was minimal. It was not until the middle of the 18th century that a widely accepted standard was created, until about 1800, standard German was mainly a written language, in urban northern Germany, the local Low German dialects were spoken. Standard German, which was different, was often learned as a foreign language with uncertain pronunciation. Northern German pronunciation was considered the standard in prescriptive pronunciation guides though, however, German was the language of commerce and government in the Habsburg Empire, which encompassed a large area of Central and Eastern Europe. Until the mid-19th century, it was essentially the language of townspeople throughout most of the Empire and its use indicated that the speaker was a merchant or someone from an urban area, regardless of nationality. Some cities, such as Prague and Budapest, were gradually Germanized in the years after their incorporation into the Habsburg domain, others, such as Pozsony, were originally settled during the Habsburg period, and were primarily German at that time. Prague, Budapest and Bratislava as well as cities like Zagreb, the most comprehensive guide to the vocabulary of the German language is found within the Deutsches Wörterbuch. This dictionary was created by the Brothers Grimm and is composed of 16 parts which were issued between 1852 and 1860, in 1872, grammatical and orthographic rules first appeared in the Duden Handbook. In 1901, the 2nd Orthographical Conference ended with a standardization of the German language in its written form
19.
University of Basel
–
The University of Basel is located in Basel, Switzerland. Founded on 3 April 1460, it is Switzerland’s oldest university and is counted among the institutions of the country. The associated University Library of Basel is the largest and among the most important libraries in the whole of Switzerland, in 2016, the University boasted 12852 students and 377 professors. International students accounted for 25 percent of the student body, the University of Basel was founded in connection with the Council of Basel. The deed of foundation given in the form of a Papal bull by Pope Pius II on November 12,1459, originally the University of Basel was decreed to have four faculties—arts, medicine, theology, and jurisprudence. The faculty of arts served until 1818 as the foundation for the three academic subjects. In the eighteenth century as Basel became more commercial, the university, one of the centers of learning in the Renaissance, enrollment which had been over a thousand around 1600, dropped to sixty in 1785 with eighteen professors. The professors themselves were mostly sons of the elite, over the course of centuries as many scholars came to the city, Basel became an early center of book printing and humanism. Around the same time as the university itself, the Basel University Library was founded, today it has over three million books and writings and is the largest library in Switzerland. The city, Basel-Stadt, had to buy back this share, students were expected to continue their education after two years or so at a German university. The Student Advice Center provides advice on academic programs and career opportunities. The Student Administration Office provides information on applications, grants, mobility, exchanges, there are also a variety of organizations that cater to international students, such as local chapters of Toastmasters and AIESEC, and associations that perform community services. There is a foreign affairs association, a Model United Nations team, there are also various religious groups. A number of student groups exist out of formal venues. Such associations include the Akademische Turnerschaft Alemannia zu Basel, AKW Raurica, Helvetia Basel, Jurassia Basiliensis, Schwizerhüsli, membership in many is restricted to men, though A. V. University Sports provides a gym, fitness classes, and sport and dance camps to students, the Studentische Körperschaft der Universität Basel speaks on behalf of the students and represents their needs and interests. It acts as a student representative and has no political or religious affiliations. Information about the university Studierendenstatistik der Universität Basel University Rankings – University of Basel
20.
Complex analysis
–
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
21.
Pierre Fatou
–
Pierre Joseph Louis Fatou was a French mathematician and astronomer. He is known for contributions to several branches of analysis. The Fatou lemma and the Fatou set are named after him, Fatou entered the École Normale Supérieure in Paris in 1898 to study mathematics and graduated in 1901 when he was appointed an observer in the Paris Observatory. Fatou was promoted to assistant astronomer in 1904 and to astronomer in 1928 and he worked in this observatory until his death. Fatou was awarded the Becquerel prize in 1918, he was a knight of the Legion of Honour and he was the president of the French mathematical society in 1927. He was in relations with several contemporary French mathematicians, especially, Maurice René Fréchet. Fatous work had very large influence on the development of analysis in the 20th century, in this work, Fatou studied for the first time the Poisson integral of an arbitrary measure on the unit circle. This work of Fatou is influenced by Henri Lebesgue who invented his integral in 1901, the famous Fatou theorem, which says that a bounded analytic function in the unit disc has radial limits almost everywhere on the unit circle was published in 1906. This theorem was at the origin of a body of research in 20th-century mathematics under the name of bounded analytic functions. See also the Wikipedia article on functions of bounded type, a number of fundamental results on the analytic continuation of a Taylor series belong to Fatou. In 1917–1920 Fatou created the area of mathematics which is called holomorphic dynamics and it deals with a global study of iteration of analytic functions. He was the first to introduce and study the set which is called now the Julia set, some of the basic results of holomorphic dynamics were also independently obtained by Gaston Julia and Samuel Lattes in 1918. Holomorphic dynamics experienced a revival since 1982 because of the new discoveries of Dennis Sullivan, Adrian Douady, John Hubbard. Beautiful pictures illustrating this theory produced by modern computers stimulate great interest not only of mathematicians, in 1926 Fatou pioneered the study of dynamics of transcendental entire functions, a subject which is intensively developing at this time. As a byproduct of his studies in holomorphic dynamics, Fatou discovered what are now called Fatou–Bieberbach domains and these are proper subregions of the complex space of dimension n, which are biholomorphically equivalent to the whole space. Fatou did important work in celestial mechanics and he was the first to prove rigorously a theorem on the averaging of a perturbation produced by a periodic force of short period. This work was continued by Leonid Mandelstam and Nikolay Bogolyubov and his students, Fatous other research in celestial mechanics includes a study of the movement of a planet in a resisting medium. Fatou, P. Séries trigonométriques et séries de Taylor, Fatou, P. Sur les équations fonctionnelles, I
22.
Holomorphic function
–
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain. Holomorphic functions are the objects of study in complex analysis. The fact that all functions are complex analytic functions. Holomorphic functions are sometimes referred to as regular functions. A holomorphic function whose domain is the complex plane is called an entire function. The phrase holomorphic at a point z0 means not just differentiable at z0, but differentiable everywhere within some neighborhood of z0 in the complex plane. Given a complex-valued function f of a complex variable, the derivative of f at a point z0 in its domain is defined by the limit f ′ = lim z → z 0 f − f z − z 0. This is the same as the definition of the derivative for real functions, in particular, the limit is taken as the complex number z approaches z0, and must have the same value for any sequence of complex values for z that approach z0 on the complex plane. If the limit exists, we say f is complex-differentiable at the point z0. This concept of complex differentiability shares several properties with real differentiability, it is linear and obeys the rule, quotient rule. If f is differentiable at every point z0 in an open set U. We say that f is holomorphic at the point z0 if it is holomorphic on some neighborhood of z0 and we say that f is holomorphic on some non-open set A if it is holomorphic in an open set containing A. The relationship between real differentiability and complex differentiability is the following, if continuity is not given, the converse is not necessarily true. A simple converse is that if u and v have continuous first partial derivatives and satisfy the Cauchy–Riemann equations, the word holomorphic was introduced by two of Cauchys students, Briot and Bouquet, and derives from the Greek ὅλος meaning entire, and μορφή meaning form or appearance. Today, the holomorphic function is sometimes preferred to analytic function. This is also because an important result in complex analysis is that every function is complex analytic. The term analytic is however also in wide use, every holomorphic function can be separated into its real and imaginary parts, and each of these is a solution of Laplaces equation on R2. Here γ is a path in a simply connected open subset U of the complex plane C whose start point is equal to its end point
23.
Complex plane
–
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis. It can be thought of as a modified Cartesian plane, with the part of a complex number represented by a displacement along the x-axis. The concept of the plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors, in particular, multiplication by a complex number of modulus 1 acts as a rotation. The complex plane is known as the Argand plane. These are named after Jean-Robert Argand, although they were first described by Norwegian-Danish land surveyor, Argand diagrams are frequently used to plot the positions of the poles and zeroes of a function in the complex plane. In this customary notation the number z corresponds to the point in the Cartesian plane. In the Cartesian plane the point can also be represented in coordinates as = =. In the Cartesian plane it may be assumed that the arctangent takes values from −π/2 to π/2, and some care must be taken to define the real arctangent function for points when x ≤0. Here |z| is the value or modulus of the complex number z, θ, the argument of z, is usually taken on the interval 0 ≤ θ < 2π. Notice that without the constraint on the range of θ, the argument of z is multi-valued, because the exponential function is periodic. Thus, if θ is one value of arg, the values are given by arg = θ + 2nπ. The theory of contour integration comprises a part of complex analysis. In this context the direction of travel around a curve is important – reversing the direction in which the curve is traversed multiplies the value of the integral by −1. By convention the direction is counterclockwise. Almost all of complex analysis is concerned with complex functions – that is, here it is customary to speak of the domain of f as lying in the z-plane, while referring to the range or image of f as a set of points in the w-plane. In symbols we write z = x + i y, f = w = u + i v and it can be useful to think of the complex plane as if it occupied the surface of a sphere. We can establish a correspondence between the points on the surface of the sphere minus the north pole and the points in the complex plane as follows
24.
Taylor series
–
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the functions derivatives at a single point. The concept of a Taylor series was formulated by the Scottish mathematician James Gregory, a function can be approximated by using a finite number of terms of its Taylor series. Taylors theorem gives quantitative estimates on the error introduced by the use of such an approximation, the polynomial formed by taking some initial terms of the Taylor series is called a Taylor polynomial. The Taylor series of a function is the limit of that functions Taylor polynomials as the degree increases, a function may not be equal to its Taylor series, even if its Taylor series converges at every point. A function that is equal to its Taylor series in an interval is known as an analytic function in that interval. The Taylor series of a real or complex-valued function f that is differentiable at a real or complex number a is the power series f + f ′1. Which can be written in the more compact sigma notation as ∑ n =0 ∞ f n, N where n. denotes the factorial of n and f denotes the nth derivative of f evaluated at the point a. The derivative of order zero of f is defined to be f itself and 0 and 0. are both defined to be 1, when a =0, the series is also called a Maclaurin series. The Maclaurin series for any polynomial is the polynomial itself. The Maclaurin series for 1/1 − x is the geometric series 1 + x + x 2 + x 3 + ⋯ so the Taylor series for 1/x at a =1 is 1 − +2 −3 + ⋯. The Taylor series for the exponential function ex at a =0 is x 00, + ⋯ =1 + x + x 22 + x 36 + x 424 + x 5120 + ⋯ = ∑ n =0 ∞ x n n. The above expansion holds because the derivative of ex with respect to x is also ex and this leaves the terms n in the numerator and n. in the denominator for each term in the infinite sum. The Greek philosopher Zeno considered the problem of summing an infinite series to achieve a result, but rejected it as an impossibility. It was through Archimedess method of exhaustion that a number of progressive subdivisions could be performed to achieve a finite result. Liu Hui independently employed a similar method a few centuries later, in the 14th century, the earliest examples of the use of Taylor series and closely related methods were given by Madhava of Sangamagrama. The Kerala school of astronomy and mathematics further expanded his works with various series expansions, in the 17th century, James Gregory also worked in this area and published several Maclaurin series. It was not until 1715 however that a method for constructing these series for all functions for which they exist was finally provided by Brook Taylor. The Maclaurin series was named after Colin Maclaurin, a professor in Edinburgh, if f is given by a convergent power series in an open disc centered at b in the complex plane, it is said to be analytic in this disc
25.
Louis de Branges de Bourcia
–
Louis de Branges de Bourcia is a French-American mathematician. He is the Edward C. Elliott Distinguished Professor of Mathematics at Purdue University in West Lafayette and he is best known for proving the long-standing Bieberbach conjecture in 1984, now called de Brangess theorem. He claims to have proved several important conjectures in mathematics, including the generalized Riemann hypothesis, born to American parents who lived in Paris, de Branges moved to the U. S. in 1941 with his mother and sisters. He did his studies at the Massachusetts Institute of Technology. His advisors were Wolfgang Fuchs and then-future Purdue colleague Harry Pollard and he spent two years at the Institute for Advanced Study and another two at the Courant Institute of Mathematical Sciences. He was appointed to Purdue in 1962, an analyst, de Branges has made incursions into real, functional, complex, harmonic and Diophantine analyses. As far as particular techniques and approaches are concerned, he is an expert in spectral, de Branges proof of the Bieberbach conjecture was not initially accepted by the mathematical community. The original proof uses hypergeometric functions and innovative tools from the theory of Hilbert spaces of entire functions, actually, the correctness of the Bieberbach conjecture was only the most important consequence of de Branges proof, which covers a more general problem, the Milin conjecture. In June 2004 de Branges announced he had a proof of the Riemann hypothesis, since that time he has released evolving versions of two purported generalizations, following independent but complementary approaches, of his original argument. As of January 2016, his paper entitled A proof of the Riemann Hypothesis is 74 pages long, a commentary on his attempt is available on the Internet. Mathematicians remain skeptical, and neither proof has been subjected to a serious analysis, peter Sarnak also gave contributions to the central argument. He does not cite their paper in his preprints, but both of them cite a 1986 paper of his that was attacked by Li and Conrey and he gave no indication he had actually read the then current version of the purported proof. In a 2003 technical comment, Conrey states he does not believe RH is going to yield to functional analysis tools, somewhat ironically, Li himself released a purported proof of the Riemann Hypothesis in the arXiv in July 2008. It was retracted a few later, after several mainstream mathematicians exposed a crucial flaw. Meanwhile, the Apology has become a diary of sorts, in which he discusses the historical context of the Riemann Hypothesis. He signs his papers and preprints as Louis de Branges, and is always cited this way, however, he does seem interested in his de Bourcia ancestors, and discusses the origins of both families in the Apology. The particular analysis tools he has developed, although successful in tackling the Bieberbach conjecture, have been mastered by only a handful of other mathematicians. During most of his life, he published articles as the sole author
26.
Space group
–
In mathematics, physics and chemistry, a space group is the symmetry group of a configuration in space, usually in three dimensions. In three dimensions, there are 219 distinct types, or 230 if chiral copies are considered distinct, Space groups are also studied in dimensions other than 3 where they are sometimes called Bieberbach groups, and are discrete cocompact groups of isometries of an oriented Euclidean space. In crystallography, space groups are called the crystallographic or Fedorov groups. A definitive source regarding 3-dimensional space groups is the International Tables for Crystallography, in 1879 Leonhard Sohncke listed the 65 space groups whose elements preserve the orientation. More accurately, he listed 66 groups, but Fedorov and Schönflies both noticed that two of them were really the same, the space groups in 3 dimensions were first enumerated by Fedorov, and shortly afterwards were independently enumerated by Schönflies. The correct list of 230 space groups was found by 1892 during correspondence between Fedorov and Schönflies, burckhardt describes the history of the discovery of the space groups in detail. The space groups in three dimensions are made from combinations of the 32 crystallographic point groups with the 14 Bravais lattices, the combination of all these symmetry operations results in a total of 230 different space groups describing all possible crystal symmetries. The elements of the space group fixing a point of space are rotations, reflections, the identity element, the translations form a normal abelian subgroup of rank 3, called the Bravais lattice. There are 14 possible types of Bravais lattice, the quotient of the space group by the Bravais lattice is a finite group which is one of the 32 possible point groups. Translation is defined as the moves from one point to another point. A glide plane is a reflection in a plane, followed by a parallel with that plane. This is noted by a, b or c, depending on which axis the glide is along. There is also the n glide, which is a glide along the half of a diagonal of a face, and the d glide, the latter is called the diamond glide plane as it features in the diamond structure. In 17 space groups, due to the centering of the cell, the glides occur in two directions simultaneously, i. e. the same glide plane can be called b or c, a or b. For example, group Abm2 could be also called Acm2, group Ccca could be called Cccb, in 1992, it was suggested to use symbol e for such planes. The symbols for five groups have been modified, A screw axis is a rotation about an axis. These are noted by a number, n, to describe the degree of rotation, the degree of translation is then added as a subscript showing how far along the axis the translation is, as a portion of the parallel lattice vector. So,21 is a rotation followed by a translation of 1/2 of the lattice vector
27.
Issai Schur
–
Issai Schur was a mathematician who worked in Germany for most of his life. He obtained his doctorate in 1901, became lecturer in 1903 and, after a stay at Bonn, as a student of Frobenius, he worked on group representations, but also in combinatorics and number theory and even theoretical physics. He is perhaps best known today for his result on the existence of the Schur decomposition, Schur published under the name of both I. Schur, and J. Schur, the latter especially in Journal für die reine und angewandte Mathematik and this has led to some confusion. Issai Schur was the son of the businessman Moses Schur and his wife Golde Schur and he was born in Mogilev on the Dnieper River in what was then the Russian Empire. Schur used the name Schaia rather than Issai up in his middle twenties, Schurs father may have been a wholesale merchant. In 1888, at the age of 13, Schur went to Liepāja, kurland was one of the three Baltic governorates of Tsarist Russia, and since the Middle Ages the Baltic Germans were the trend-setting social class. The local Jewish community spoke mostly German and not Yiddish, Schur attended the German-speaking Nicolai Gymnasium in Libau from 1888-1894 and reached the top grade in his final examination, and received a gold medal. Here he became fluent in German, in October 1894, Schur attended the University of Berlin in mathematics and physics. According to Vogt, he began to use the name Issai at this time, Schur thought that his chance of success in the Russian Empire was rather poor, and because he spoke German so perfectly, he remained in Berlin. He graduated in 1903 and was a lecturer at the University of Berlin, Schur held a position as professor at the Berlin University for the ten years from 1903 to 1913. In 1913 he accepted an appointment as professor and successor of Felix Hausdorff in Bonn. In the following years Frobenius tried various ways to get Schur back to Berlin, among other things, Schurs name was mentioned in a letter dated June 27,1913 from Frobenius to Robert Gnehm as a possible successor to Carl Friedrich Geiser. Frobenius complained that they had never followed his advice before and then said, hes too good for Zurich, and should be my successor in Berlin. Hermann Weyl got the job in Zurich, the efforts of Frobenius were finally successful in 1916, when Schur succeeded Johannes Knoblauch as adjunct professor. Frobenius died a year later, on August 3,1917, Schur and Carathéodory were both named as the frontrunners for his successor. But they chose Constantin Carathéodory in the end, in 1919 Schur finally received a personal professorship, and in 1921 he took over the chair of the retired Friedrich Hermann Schottky. In 1922, he was added to the Prussian Academy of Sciences
28.
Sturmabteilung
–
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
29.
NSDAP
–
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
30.
Edmund Landau
–
Edmund Georg Hermann Landau was a German born mathematician who worked in the fields of number theory and complex analysis. Edmund Landau was born to Jewish family in Berlin and his father was Leopold Landau, a gynecologist and his mother was Johanna Jacoby. Landau studied mathematics at the University of Berlin, receiving his doctorate in 1899 and his doctoral thesis was 14 pages long. He taught at the University of Berlin from 1899 to 1909 and he married Marianne Ehrlich, the daughter of the Nobel Prize-winning biologist Paul Ehrlich, in 1905. During the 1920s, Landau was instrumental in establishing the Mathematics Institute at the nascent Hebrew University of Jerusalem and he negotiated with the Universitys president, Judah Magnes, regarding a position at the University and the building that was to house the Mathematics Institute. Landau and his emigrated to Palestine in 1927 and he began teaching at the Hebrew University. The family had difficulty adjusting to the living standards then available in Jerusalem. In addition, Landau became a pawn in a struggle for control of the University between Magnes and Chaim Weizmann and Albert Einstein, Magnes suggested that Landau be appointed Rector of the University, but Einstein and Weizmann supported Selig Brodetsky. Landau was disgusted by the dispute and decided to return to Göttingen, thereafter, he lectured only outside Germany. He moved to Berlin in 1934, where he died in early 1938 of natural causes and he also made important contributions to complex analysis. G. H. Hardy wrote that no one was ever more devoted to mathematics than Landau. Foundations of Analysis, Chelsea Pub Co, differential and Integral Calculus, American Mathematical Society. Elementary Number Theory, American Mathematical Society, journal of the London Mathematical Society. Obituary and review of work and books. OConnor, John J. Robertson, Edmund F. Edmund Landau, MacTutor History of Mathematics archive, Edmund Landau at the Mathematics Genealogy Project Edmund Landau, The Master Rigorist by Eli Maor, Trigonometric Delights, page 192. Translation of his thesis, Neuer Beweis der Gleichung ∑ k =1 ∞ μ k =0
31.
Theodor Vahlen
–
Karl Theodor Vahlen was an Austrian-born mathematician who was an ardent supporter of the Nazi Party. He was a member of both the SA and SS, Vahlen studied in Berlin from 1889 and received his doctorate there in 1893. From 1883, Vahlen was a Privatdozent in mathematics at the Königsberg Albertina University, in 1904, he began teaching at the University of Greifswald, and in 1911 he became an ordinarius professor there. Vahlen had joined the Nazi Party in 1922, from 1924, he was the first Pomeranian district leader of the NSDAP. In 1924, Vahlen incited a crowd at the University against the Weimar Republic, the University placed him on leave for political abuse of his function, and in 1927 he was dismissed without a pension. Upon his dismissal, Friedrich Schmidt-Ott increased the funding Vahlen had been receiving for his work for the German Navy since 1922, Vahlen worked briefly as an assistant in Johannes Stark’s private physics laboratory. In 1930 Vahlen returned to his birthplace and became a lecturer of mathematics at the Technische Hochschule Wien, once Adolf Hitler became Chancellor of Germany on 30 January 1933, Vahlen’s career gained momentum and flourished in Germany as a result of his support for the NSDAP. From 1934, he was professor at the University of Berlin. During the period 1933 to 1937, Vahlen served as vice president of the Kaiser-Wilhelm Gesellschaft. From May 1934, he was Assistant Secretary and head of the Science Office at the Reichserziehungsministerium, actually, the Science Office was split into two components, WI, a continuation of the Prussian department, and WII, the army office for research. Vahlen was head of WI, but, in actuality, the deputy chief, on 1 January 1937 Vahlen was relieved of his duties at the REM. Through a manipulation of the process by Vahlen and his supporters. It was in 1933 that Vahlen joined the Sturmabteilung, and in 1936 he switched to the Schutzstaffel, Theodor Vahlen was the son of the German philologist Johannes Vahlen. Vahlen gained his doctorate with Beiträge zu einer additiven Zahlentheorie, and continued to specialise in number theory, Theodor Vahlen was an early proponent of geometric algebra. His 1902 paper in Mathematische Annalen recounts William Kingdon Cliffords construction of his 2n dimensional algebra with n −1 anti-commuting square roots of −1, Vahlen also recounts split-biquaternions and parabolic biquaternions originated by Clifford. But Vahlen cites Eduard Study most of all since Study also focussed on the geometric motions as implicit in algebra, since Vahlen explores some of the fractional-linear transformations of Clifford algebras, he is sometimes remembered for the Vahlen matrices. These are 2 ×2 matrices with coefficients in a Clifford algebra that act on a line over a ring. The subject of relativity was an issue in Nazi Germany
32.
Deutsche Mathematik
–
Deutsche Mathematik was a mathematics journal founded by Ludwig Bieberbach and Theodor Vahlen in 1936. Vahlen was publisher on behalf of the German Research Foundation, Bieberbach was chief editor, in Feb 1936, the journal was declared the official organ of the German Student Union by its Reichsführer, all local DSt mathematics departments were requested to subscribe and to actively contribute. As well as articles on mathematics, the journal also published propaganda articles giving the Nazi viewpoint on the relation between mathematics and race, as a result of this many mathematics libraries outside Germany did not subscribe to it, so copies of the journal can be hard to find. This caused some problems in Teichmüller theory, as Oswald Teichmüller published several of his papers in the journal. Mehrtens, Herbert, Ludwig Bieberbach and Deutsche Mathematik, in Phillips, studies in the history of mathematics, MAA Stud. America, pp. 195–241, ISBN 978-0-88385-128-9, MR913104 M. A. H. N, moritz Epple and Volker Remmert and Norbert Schappacher, ed. History of Mathematics in Germany, 1920—1960, in particular, Philipp Kranz, The journal Deutsche Mathematik, p. 132—134
33.
Deutsche Physik
–
The term was taken from the title of a 4-volume physics textbook by Nobel Laureate Philipp Lenard in the 1930s. A pseudoscientific movement, it won the support of many eminent physicists in Germany. This movement began as an extension of a German nationalistic movement in the community which went back as far as World War I. On 25 August 1914, during the German invasion of Belgium and they claimed that German character had been misinterpreted and that attempts made over many years to reach an understanding between the two countries had obviously failed. Therefore, they opposed the use of the English language by German scientific authors, editors of books, on the German side it was suggested to avoid an unnecessary use of English language in scientific texts. It was stressed, however, that this measure should not be misunderstood as a rejection of British scientific thought, ideas and stimulations. When on January 26,1920, the young soldier Oltwig von Hirschfelde tried to assassinate German Finance minister Matthias Erzberger, Lenard sent him a telegram of congratulation. After the 1922 assassination, of politician Walther Rathenau, the government ordered flags flown at half mast on the day of his funeral, Socialist students organized a demonstration against Lenard, who on the occasion was taken into protective custody by state prosecutor Hugo Marx. During the early years of the century, Albert Einsteins Theory of Relativity was met with much bitter controversy within the physics communities of the world. There were many physicists, especially the old guard, who were suspicious of the meanings of Einsteins theories. The leading theoretician of the Deutsche Physik type of movement was Rudolf Tomaschek who had re-edited the famous physics textbook Grimsehls Lehrbuch der Physik, in that book, which consists of several volumes, the Lorentz transformation was accepted as well as quantum theory. However, Einsteins interpretation of the Lorentz transformation was not mentioned, many of these classical physicists resented Einsteins dismissal of the notion of a luminiferous aether, which had been a mainstay of their work for the majority of their productive lives. Many of these doubters were very distinguished experimental physicists—Lenard was himself a Nobel laureate in Physics, when the Nazis entered the political scene, Lenard quickly attempted to ally himself with them, joining the party at an early stage. With another physics Nobel laureate, Johannes Stark, Lenard began a campaign to label Einsteins Relativity as Jewish Physics. Lenard and Stark benefitted considerably from this Nazi support, under the rallying cry that physics should be more German and Aryan, Lenard and Stark embarked on a Nazi-endorsed plan to replace physicists at German universities with Aryan Physicists. By 1935, though, this campaign was superseded by the Nuremberg Laws of 1935, there were no longer any Jewish physics professors in Germany, since under the Nuremberg Laws, Jews were not allowed to work in universities. Stark in particular tried to install himself as the national authority on German physics under the principle of Gleichschaltung applied to other professional disciplines. Under this Nazi-era paradigm, academic disciplines and professional fields followed a linear hierarchy created along ideological lines
34.
Alexander Ostrowski
–
Alexander Markowich Ostrowski was a mathematician. His father Mark having been a merchant, Alexander Ostrowski attended the Kiev College of Commerce, not a high school, however, his talent did not remain undetected, Ostrowskis mentor, Dmitry Grave, wrote to Landau and Hensel for help. Subsequently, Ostrowski began to study mathematics at Marburg University under Hensels supervision in 1912, after World War I had ended Ostrowski moved on to Göttingen where he wrote his doctoral dissertation and was influenced by Hilbert, Klein and Landau. In 1920, after having obtained his doctorate, Ostrowski moved to Hamburg where he worked as Heckes assistant and finished his habilitation in 1922, Alexander Ostrowski at the Mathematics Genealogy Project Gautschi, Walter, Alexander M. Ostrowski, His life, work, and students