1.
Erhard Schmidt (admiral)
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Ehrhard Schmidt was an Admiral of the Kaiserliche Marine during World War I. At age 15 he entered the navy and saw service at several branches at sea, among them were posts on missions, as a commanding officer and in cadet training. His wish to become commander of a ship was granted in 1901 when he assumed command of the armoured cruiser Prinz Adalbert and he held that command until 1907. From 1908 to 1910 he commanded the Braunschweig-class battleship Hessen and was promoted to Konteradmiral to command the II Squadron of the Offshore Fleet. Later he was commander of the naval artillery, at the beginning of World War I, he was commander of the IV Squadron, made up of old Wittelsbach-class ships. During the Battle of Jutland, Schmidt commanded the I Squadron, in 1917 he led Operation Albion, a special task force for the occupation of the Baltic Sea islands of Saaremaa and Hiiumaa off the Estonian coast. For his achievements he was awarded the Pour le Mérite order. Upon his request, he was retired in 1918 with the rank of Admiral à la Suite and he remained loyal to the spirit of the Imperial Navy. Apart from his nomination as Honorary Chairman of the Munich Naval Association, geschichte der Ritter des Ordens pour le mérite im Weltkrieg, Vol. II, M-Z, Verlag Bernard & Graefe, Berlin 1935, pp. 274–275
Erhard Schmidt (admiral)
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Erhard Schidt (centre) and his staff
2.
Tartu
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Tartu is the second largest city of Estonia, following Estonias political and financial capital Tallinn. Tartu is often considered the centre of the country, especially since it is home to the nations oldest and most renowned university. The city also houses the Supreme Court of Estonia, the Ministry of Education and Research and it is the birthplace of Estonian Song Festivals. Situated 186 kilometres southeast of Tallinn and 245 kilometres northeast of Riga, Tartu lies on the Emajõgi, the city is served by Tartu Airport. Since 1918 the Estonian name Tartu has been used, but as the town has come under control of rulers throughout its history. Most of them derive ultimately from the earliest attested form, the Estonian Tarbatu, in German, Swedish and Polish the town has been known and is sometimes still referred to as Dorpat, a variant of Tarbatu. In Russian, the city has known as Юрьев and as Дерпт. Similarly, the city has known as Tērbata in Latvian. Archaeological evidence of the first permanent settlement on the site of modern Tartu dates to as early as the 5th century AD, by the 7th century, local inhabitants had built a wooden fortification on the east side of Toome Hill. The first documented record of the area was made in 1030 by chroniclers of Kievan Rus, yaroslav I the Wise, Prince of Kiev, invaded the region that year, built his own fort there, and named it Yuryev. Kievan Rus again controlled Tartu from 1133 for an unknown period, in the 12th century Tartu was the most notable Slavic settlement in Chud territory. His views have been criticized by historian Ain Mäesalu, subsequently, known as Dorpat, Tartu became a commercial centre of considerable importance during the later Middle Ages and the capital of the semi-independent Bishopric of Dorpat. In 1262 the army of Prince Dmitri of Pereslavl, son of Alexander Nevsky launched an assault on Dorpat and his troops did not manage to capture the bishops fortress on Toome Hill. In medieval times, after the Livonian Order was subsumed into the Teutonic Knights in 1236, in the 1280s Dorpat joined the Hanseatic League. For example, the hall of Dorpat was designed by an architect from Rostock in Mecklenburg, while the university buildings were designed by Johann Wilhelm Krause. Most Germans left during the first half of the 20th century, in particular as part of the Heim ins Reich program of the Nazis, in 1558 the forces of Muscovy led by tsar Ivan the Terrible invaded the region in what became known as the Livonian War. Dorpat was captured without a fight and the bishop was imprisoned in Moscow. In the effect of the Truce of Jam Zapolski of 1582 the city along with southern regions of Livonian Confederation became part of the Polish–Lithuanian Commonwealth, in 1598 it became the capital of the Dorpat Voivodeship of the Duchy of Livonia
Tartu
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Overlooking Town Hall Square from Toome Hill
Tartu
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University of Tartu main building.
Tartu
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Tartu old town
Tartu
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For other uses, see
Tartu (disambiguation).
3.
Governorate of Livonia
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The Governorate of Livonia, was one of the Baltic governorates of the Russian Empire, now divided between the Republic of Latvia and the Republic of Estonia. Sweden formally ceded Swedish Livonia to Russia in 1721 with the Treaty of Nystad, in 1722 Tartu County was added to Riga Governorate. In 1726 Smolensk Governorate was separated from Governorate, which now had five provinces - Rīga, Cēsis, Tartu, Pärnu, in 1783 the Sloka County was added. On July 3,1783 Catherine the Great reorganized Governorate into Riga Lieutenancy, only in 1796, after the Third Partition of Poland this territory was renamed as the Governorate of Livonia. Until late 19th century the governorate was not ruled by Russian laws but was administered autonomously by the local German Baltic nobility through feudal Landtag, German nobles insisted on preserving their privileges and use of German language. After the Russian February Revolution in 1917, the part of the Governorate of Livonia was combined with the Governorate of Estonia to form a new Autonomous Governorate of Estonia. The Autonomous Governorate of Estonia issued the Estonian Declaration of Independence on 24 February 1918, the Governorate of Livonia was divided into 9 counties. However the new border between the Governments of Estonia and Livland was never properly demarcated, by the Imperial census of 1897. In bold are languages spoken by more people than the state language, administrative divisions of Russia in 1713-1714 Baltic governorates Courland Governorate Estonia Governorate Livonian Confederation
Governorate of Livonia
Governorate of Livonia
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Flag
4.
Estonia
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Estonia, officially the Republic of Estonia, is a country in the Baltic region of Northern Europe. It is bordered to the north by the Gulf of Finland, to the west by the Baltic Sea, to the south by Latvia, across the Baltic Sea lies Sweden in the west and Finland in the north. The territory of Estonia consists of a mainland and 2,222 islands and islets in the Baltic Sea, covering 45,339 km2 of land and water, and is influenced by a humid continental climate. The territory of Estonia has been inhabited since at least 6500 BC, in 1988, during the Singing Revolution, the Estonian Supreme Soviet issued the Estonian Sovereignty Declaration in defiance of Soviet rule, and independence was restored on 20 August 1991. Estonia is a parliamentary republic divided into fifteen counties. Its capital and largest city is Tallinn, with a population of 1.3 million, it is one of the least-populous member states of the European Union, Eurozone, North Atlantic Treaty Organization, OECD and Schengen Area. Estonia is a country with an advanced, high-income economy that is among the fastest growing in the EU. Its Human Development Index ranks very highly, and it performs favourably in measurements of economic freedom, civil liberties, the 2015 PISA test places Estonian high school students 3rd in the world, behind Singapore and Japan. Citizens of Estonia are provided with health care, free education. Since independence the country has developed its IT sector, becoming one of the worlds most digitally advanced societies. In 2005 Estonia became the first nation to hold elections over the Internet, in the Estonian language, the oldest known endonym of the Estonians was maarahvas, meaning country people or people of the land. The land inhabited by Estonians was called Maavald meaning Country Parish or Land Parish, one hypothesis regarding the modern name of Estonia is that it originated from the Aesti, a people described by the Roman historian Tacitus in his Germania. The historic Aesti were allegedly Baltic people, whereas the modern Estonians are Finno-Ugric, the geographical areas between Aesti and Estonia do not match, with Aesti being further down south. Ancient Scandinavian sagas refer to a land called Eistland, as the country is called in Icelandic. Early Latin and other ancient versions of the name are Estia and Hestia, esthonia was a common alternative English spelling prior to 1921. Human settlement in Estonia became possible 13,000 to 11,000 years ago, the oldest known settlement in Estonia is the Pulli settlement, which was on the banks of the river Pärnu, near the town of Sindi, in south-western Estonia. According to radiocarbon dating it was settled around 11,000 years ago, the earliest human inhabitation during the Mesolithic period is connected to Kunda culture, which is named after the town of Kunda in northern Estonia. At that time the country was covered with forests, and people lived in communities near bodies of water
Estonia
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Tools made by Kunda culture,
Estonian History Museum
Estonia
Estonia
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Iron Age artifacts of a hoard from
Kumna
Estonia
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A stylised
viking ship on the Estonian 1
Kroon from 1934
5.
Berlin
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Berlin is the capital and the largest city of Germany as well as one of its constituent 16 states. With a population of approximately 3.5 million, Berlin is the second most populous city proper, due to its location in the European Plain, Berlin is influenced by a temperate seasonal climate. Around one-third of the area is composed of forests, parks, gardens, rivers. Berlin in the 1920s was the third largest municipality in the world, following German reunification in 1990, Berlin once again became the capital of all-Germany. Berlin is a city of culture, politics, media. Its economy is based on high-tech firms and the sector, encompassing a diverse range of creative industries, research facilities, media corporations. Berlin serves as a hub for air and rail traffic and has a highly complex public transportation network. The metropolis is a popular tourist destination, significant industries also include IT, pharmaceuticals, biomedical engineering, clean tech, biotechnology, construction and electronics. Modern Berlin is home to world renowned universities, orchestras, museums and its urban setting has made it a sought-after location for international film productions. The city is known for its festivals, diverse architecture, nightlife, contemporary arts. Since 2000 Berlin has seen the emergence of a cosmopolitan entrepreneurial scene, the name Berlin has its roots in the language of West Slavic inhabitants of the area of todays Berlin, and may be related to the Old Polabian stem berl-/birl-. All German place names ending on -ow, -itz and -in, since the Ber- at the beginning sounds like the German word Bär, a bear appears in the coat of arms of the city. It is therefore a canting arm, the first written records of towns in the area of present-day Berlin date from the late 12th century. Spandau is first mentioned in 1197 and Köpenick in 1209, although these areas did not join Berlin until 1920, the central part of Berlin can be traced back to two towns. Cölln on the Fischerinsel is first mentioned in a 1237 document,1237 is considered the founding date of the city. The two towns over time formed close economic and social ties, and profited from the right on the two important trade routes Via Imperii and from Bruges to Novgorod. In 1307, they formed an alliance with a common external policy, in 1415 Frederick I became the elector of the Margraviate of Brandenburg, which he ruled until 1440. In 1443 Frederick II Irontooth started the construction of a new palace in the twin city Berlin-Cölln
Berlin
Berlin
Berlin
Berlin
6.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times
Mathematics
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Euclid (holding
calipers), Greek mathematician, 3rd century BC, as imagined by
Raphael in this detail from
The School of Athens.
Mathematics
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Greek mathematician
Pythagoras (c. 570 – c. 495 BC), commonly credited with discovering the
Pythagorean theorem
Mathematics
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Leonardo Fibonacci, the
Italian mathematician who established the Hindu–Arabic numeral system to the Western World
Mathematics
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Carl Friedrich Gauss, known as the prince of mathematicians
7.
Thesis
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A thesis or dissertation is a document submitted in support of candidature for an academic degree or professional qualification presenting the authors research and findings. In some contexts, the thesis or a cognate is used for part of a bachelors or masters course, while dissertation is normally applied to a doctorate, while in other contexts. The term graduate thesis is used to refer to both masters theses and doctoral dissertations. The required complexity or quality of research of a thesis or dissertation can vary by country, university, or program, the word dissertation can at times be used to describe a treatise without relation to obtaining an academic degree. The term thesis is used to refer to the general claim of an essay or similar work. The term thesis comes from the Greek θέσις, meaning something put forth, Dissertation comes from the Latin dissertātiō, meaning path. A thesis may be arranged as a thesis by publication or a monograph, with or without appended papers, an ordinary monograph has a title page, an abstract, a table of contents, comprising the various chapters, and a bibliography or a references section. They differ in their structure in accordance with the different areas of study. In a thesis by publication, the chapters constitute an introductory, Dissertations normally report on a research project or study, or an extended analysis of a topic. The structure of the thesis or dissertation explains the purpose, the research literature which impinges on the topic of the study, the methods used. Degree-awarding institutions often define their own style that candidates have to follow when preparing a thesis document. Other applicable international standards include ISO2145 on section numbers, ISO690 on bibliographic references, some older house styles specify that front matter uses a separate page-number sequence from the main text, using Roman numerals. They therefore avoid the traditional separate number sequence for front matter, however, strict standards are not always required. Most Italian universities, for example, have only general requirements on the size and the page formatting. A thesis or dissertation committee is a committee that supervises a students dissertation, the committee members are doctors in their field and have the task of reading the dissertation, making suggestions for changes and improvements, and sitting in on the defense. Sometimes, at least one member of the committee must be a professor in a department that is different from that of the student, all the dissertation referees must already have achieved at least the academic degree that the candidate is trying to reach. At English-speaking Canadian universities, writings presented in fulfillment of undergraduate coursework requirements are normally called papers, a longer paper or essay presented for completion of a 4-year bachelors degree is sometimes called a major paper. High-quality research papers presented as the study of a postgraduate consecutive bachelor with Honours or Baccalaureatus Cum Honore degree are called thesis
Thesis
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Doctoral ceremony at
Leiden University (7 July 1721).
Thesis
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The cover of the thesis presented by
Claude Bernard to obtain his
Doctorate of Medicine (1843).
8.
David Hilbert
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David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th, Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis, Hilbert adopted and warmly defended Georg Cantors set theory and transfinite numbers. A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems set the course for much of the mathematical research of the 20th century. Hilbert and his students contributed significantly to establishing rigor and developed important tools used in mathematical physics. Hilbert is known as one of the founders of theory and mathematical logic. In late 1872, Hilbert entered the Friedrichskolleg Gymnasium, but, after a period, he transferred to. Upon graduation, in autumn 1880, Hilbert enrolled at the University of Königsberg, in early 1882, Hermann Minkowski, returned to Königsberg and entered the university. Hilbert knew his luck when he saw it, in spite of his fathers disapproval, he soon became friends with the shy, gifted Minkowski. In 1884, Adolf Hurwitz arrived from Göttingen as an Extraordinarius, Hilbert obtained his doctorate in 1885, with a dissertation, written under Ferdinand von Lindemann, titled Über invariante Eigenschaften spezieller binärer Formen, insbesondere der Kugelfunktionen. Hilbert remained at the University of Königsberg as a Privatdozent from 1886 to 1895, in 1895, as a result of intervention on his behalf by Felix Klein, he obtained the position of Professor of Mathematics at the University of Göttingen. During the Klein and Hilbert years, Göttingen became the preeminent institution in the mathematical world and he remained there for the rest of his life. Among Hilberts students were Hermann Weyl, chess champion Emanuel Lasker, Ernst Zermelo, john von Neumann was his assistant. At the University of Göttingen, Hilbert was surrounded by a circle of some of the most important mathematicians of the 20th century, such as Emmy Noether. Between 1902 and 1939 Hilbert was editor of the Mathematische Annalen, good, he did not have enough imagination to become a mathematician. Hilbert lived to see the Nazis purge many of the prominent faculty members at University of Göttingen in 1933 and those forced out included Hermann Weyl, Emmy Noether and Edmund Landau. One who had to leave Germany, Paul Bernays, had collaborated with Hilbert in mathematical logic and this was a sequel to the Hilbert-Ackermann book Principles of Mathematical Logic from 1928. Hermann Weyls successor was Helmut Hasse, about a year later, Hilbert attended a banquet and was seated next to the new Minister of Education, Bernhard Rust
David Hilbert
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David Hilbert (1912)
David Hilbert
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The Mathematical Institute in Göttingen. Its new building, constructed with funds from the
Rockefeller Foundation, was opened by Hilbert and Courant in 1930.
David Hilbert
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Hilbert's tomb: Wir müssen wissen Wir werden wissen
9.
Alfred Brauer
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Alfred Theodor Brauer was a German-American mathematician who did work in number theory. He studied at the University of Berlin, as he served Germany in World War I, even being injured in the war, he was able to keep his position longer than many other Jewish academics who had been forced out after Hitlers rise to power. In 1935 he lost his position and in 1938 he tried to leave Germany and he initially worked in the Northeast, but in 1942 he settled into a position at the University of North Carolina at Chapel Hill. A good deal of his works, and the Alfred T. Brauer library, although he occasionally taught at Wake Forest University after he retired from Chapel Hill at 70. He is brother to mathematician Richard Brauer, who was the founder of modular representation theory, Alfred Brauer at the Mathematics Genealogy Project
Alfred Brauer
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Alfred Theodor Brauer
10.
Richard Brauer
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Richard Dagobert Brauer was a leading German and American mathematician. He worked mainly in abstract algebra, but made important contributions to number theory and he was the founder of modular representation theory. Alfred Brauer was Richards brother and seven years older, Alfred and Richard were both interested in science and mathematics, but Alfred was injured in combat in World War I. As a boy, Richard dreamt of becoming an inventor, and he soon transferred to University of Berlin. Except for the summer of 1920 when he studied at University of Freiburg, he studied in Berlin, issai Schur conducted a seminar and posed a problem in 1921 that Alfred and Richard worked on together, and published a result. The problem also was solved by Heinz Hopf at the same time, Richard wrote his thesis under Schur, providing an algebraic approach to irreducible, continuous, finite-dimensional representations of real orthogonal groups. Ilse Karger also studied mathematics at the University of Berlin, she and their sons George Ulrich and Fred Gunther also became mathematicians. Brauer began his career in Königsberg working as Konrad Knopp’s assistant. Brauer expounded central division algebras over a field while in Königsberg. When the Nazi Party took over in 1933, the Emergency Committee in Aid of Displaced Foreign Scholars took action to help Brauer and other Jewish scientists, Brauer was offered an assistant professorship at University of Kentucky. Richard accepted the offer, and by the end of 1933 he was in Lexington, Kentucky, Ilse followed the next year with George and Fred, brother Alfred made it to the USA in 1939, but their sister Alice was killed in The Holocaust. Hermann Weyl invited Richard to assist him at Princetons Institute for Advanced Study in 1934, Richard and Nathan Jacobson edited Weyls lectures Structure and Representation of Continuous Groups. Through the influence of Emmy Noether, Richard was invited to University of Toronto to take up a faculty position, with his graduate student Cecil J. Nesbitt he developed modular representation theory, published in 1937. Robert Steinberg, Stephen Arthur Jennings, and Ralph Stanton were also Brauer’s students in Toronto, Brauer also conducted international research with Tadasi Nakayama on representations of algebras. In 1941 University of Wisconsin hosted visiting professor Brauer, the following year he visited the Institute for Advanced Study and Bloomington, Indiana where Emil Artin was teaching. In 1948 Richard and Ilse moved to Ann Arbor, Michigan where he, with his graduate student K. A. Fowler, Brauer proved the Brauer-Fowler theorem. Donald John Lewis was another of his students at UM, in 1952 Brauer joined the faculty of Harvard University. Before retiring in 1971 he taught aspiring mathematicians such as Donald Passman, the Brauers frequently traveled to see their friends such as Reinhold Baer, Werner Wolfgang Rogosinski, and Carl Ludwig Siegel
Richard Brauer
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Richard and Ilse Brauer in 1970 Photo courtesy MFO
11.
Lothar Collatz
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Lothar Collatz was a German mathematician, born in Arnsberg, Westphalia. In 1937 he posed the Collatz conjecture, which remains unsolved, the Collatz–Wielandt formula, for positive matrices important in the Perron–Frobenius theorem, is also named after him. He died in Varna, Bulgaria, while attending a mathematics conference, das Differenzenverfahren mit höherer Approximation für lineare Differentialgleichungen, Leipzig 1935 Eigenwertprobleme und ihre numerische Behandlung. Leipzig 1945 Eigenwertaufgaben mit technischen Anwendungen, Leipzig 1949,1963 Numerische Behandlung von Differentialgleichungen. Berlin 1951,1955 Differentialgleichungen für Ingenieure, stuttgart 1960 with Wolfgang Wetterling, Optimierungsaufgaben Berlin 1966,1971 Funktionalanalysis und Numerische Mathematik. Eine Einführung unter besonderer Berücksichtigung der Anwendungen, stuttgart, Teubner Verlag,1966, 7th edn.1990 with Julius Albrecht, Aufgaben aus der angewandten Mathematik I. Gleichungen in einer und mehreren Variablen, Berlin 1972 Numerische Methoden der Approximationstheorie. Vortragsauszüge der Tagung über Numerische Methoden der Approximationstheorie vom 3. -9, U Eckhardt, Der Einfluss von Lothar Collatz auf die angewandte Mathematik, Numerical mathematics, Sympos. L Elsner and K P Hadeler, Lothar Collatz - on the occasion of his 75th birthday, R B Guenther, Obituary, Lothar Collatz, 1910-1990, Aequationes Math. H Heinrich, Zum siebzigsten Geburtstag von Lothar Collatz, Z. Angew, G Meinardus, G Nürnberger, Th Riessinger and G Walz, In memoriam, the work of Lothar Collatz in approximation theory, J. Approx. G Meinardus and G Nürnberger, In memoriam, Lothar Collatz, J R Whiteman, In memoriam, Lothar Collatz, Internat. OConnor, John J. Robertson, Edmund F. Lothar Collatz, MacTutor History of Mathematics archive, Lothar Collatz at the Mathematics Genealogy Project
Lothar Collatz
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Lothar Collatz
12.
Alexander Dinghas
–
Alexander Dinghas was a Greek mathematician. Dinghas was born on February 9,1908 in Smyrna, Turkey and he did his schooling in Smyrna. He and his moved to Athens in 1922. Dinghas completed his school and entered the National Technical University of Athens in 1925. He graduated with a diploma in electrical and mechanical engineering in 1930, in 1931 Dinghas began his studies at the University of Berlin in Berlin, Germany. He completed his doctorate in mathematics in 1936, Dinghas was not a German and his career during the Nazi years was very difficult. However, after the end of World War II, his luck changed and he became professor of mathematics at the Humboldt University of Berlin in 1947. From 1949 until his death he was a professor of mathematics at the Free University of Berlin, Dinghas died on April 19,1974 in Berlin, Germany. His most important contribution was his work in theory, in particular Nevanlinna theory. Vorlesungen über Funktionentheorie, Springer 1961 Minkowskische Summen und Integrale, Alexander Dinghas at the Mathematics Genealogy Project Alexander Dinghas
Alexander Dinghas
–
Contents
13.
Guido Hoheisel
–
Guido Kark Heinrich Hoheisel was a German mathematician, a professor of mathematics at the University of Cologne. He did his PhD in 1920 from the University of Berlin under the supervision of Erhard Schmidt, Hoheisel is known for a result on gaps between prime numbers. In fact he showed that one may take θ = 32999/33000, Hoheisel contributed to the journal Deutsche Mathematik. During World War II Hoheisel was required to teach classes simultaneously at three universities, in Cologne, Bonn, and Münster and his doctoral students include Arnold Schönhage
Guido Hoheisel
–
Guido Hoheisel (1930)
14.
Eberhard Hopf
–
The Hopf maximum principle is an early result of his that is one of the most important techniques in the theory of elliptic partial differential equations. Eberhard Hopf was born in Salzburg, Austria-Hungary, but his career was divided between Germany and the United States. He received his Ph. D. in Mathematics in 1926, in 1930 he received a fellowship from the Rockefeller Foundation to study classical mechanics with George Birkhoff at Harvard, but his appointment was at the Harvard College Observatory. In late 1931, with the help of Norbert Wiener, Hopf joined the Department of Mathematics of the Massachusetts Institute of Technology, while at MIT, Hopf did much of his work on ergodic theory. In Cambridge Hopf worked on mathematical and astronomical subjects. His book Mathematical problems of radiative equilibrium first appeared in 1934 and was reprinted in 1964, another important contribution from this period is the theory of Wiener-Hopf equations, which he developed in collaboration with Norbert Wiener. By 1960, a version of these equations was being extensively used in electrical engineering and geophysics. During this time, Hopf gained a reputation for his ability of illuminating the most complex subjects for his colleagues, because of this talent, many discoveries and proofs of other mathematicians became easier to understand after they had been described by Hopf. In 1936 Hopf received and accepted an offer of a professorship from the University of Leipzig. Hopf, with his wife Ilse and their infant daughter Barbara, returned to Germany, the book Ergodentheorie, most of which was written when Hopf was still at the Massachusetts Institute of Technology, was published in 1937. In that book, containing only 81 pages, Hopf presented a precise, in 1939 Hopf established ergodicity of the geodesic flow on compact manifolds of constant negative curvature. In 1940 Hopf was on the list of the lecturers to the International Congress of Mathematicians to be held in Cambridge. Because of the start of World War II, however, the Congress was cancelled, in 1942 Hopf was drafted to work in the German Aeronautical Institute. In 1944, one year before the end of World War II, on 22 February 1949 Hopf became a US citizen and joined Indiana University at Bloomington as a Professor of Mathematics. In 1962 he was made Research Professor of Mathematics, staying in position until his death. Hopf was never forgiven by many people for his moving to Germany in 1936, as a result, most of his work in ergodic theory and topology was neglected or even attributed to others in the years following the end of World War II. An example of this was the expulsion of Hopfs name from the version of the Wiener–Hopf equations. In 1971 Hopf was the American Mathematical Society Gibbs Lecturer, in 1981 he received the Leroy P. Steele Prize from the American Mathematical Society for seminal contributions to research
Eberhard Hopf
–
Eberhard Hopf
15.
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
Heinz Hopf
–
Heinz Hopf (on the right) in
Oberwolfach, together with
Hellmuth Kneser
16.
Martin Kneser
–
Martin Kneser was a German mathematician. His father Hellmuth Kneser and grandfather Adolf Kneser were also mathematicians and he obtained his PhD in 1950 from Humboldt University of Berlin with the dissertation, Über den Rand von Parallelkörpern. His name has given to Kneser graphs which he studied in 1955. He also gave a proof of the Fundamental theorem of algebra. His main publications were on quadratic forms and algebraic groups, approximation in algebraic groups Kneser–Tits conjecture Knesers theorem Kneser graphs Martin Kneser at the Mathematics Genealogy Project Martin Kneser’s Work on Quadratic Forms and Algebraic Groups
Martin Kneser
–
Martin Kneser, 1973
17.
Wilhelm Specht
–
Wilhelm Otto Ludwig Specht was a German mathematician who introduced Specht modules. He also proved the Specht criterion for unitary equivalence of matrices, deutscher Verlag der Wissenschaften, Berlin 1956. Algebraische Gleichungen mit reellen oder komplexen Koeffizienten, photos of Wilhelm Specht Wilhelm Specht at the Mathematics Genealogy Project
Wilhelm Specht
–
Wilhelm Specht
18.
Baltic German
–
The Baltic Germans are ethnic German inhabitants of the eastern shores of the Baltic Sea, in what today are Estonia and Latvia. Since their resettling from Estonia and Latvia during the upheavals and aftermath of the Second World War, the largest groups of present-day descendants of the Baltic Germans are found in Germany and Canada. It is estimated that several thousand still reside in Latvia and Estonia, for centuries Baltic Germans and the Baltic nobility were a ruling class over native “Undeutsche” serfs. The emerging Baltic-German middle class was mostly urban and professional, in the 12th and 13th centuries Germans, both traders and crusaders, began settling in the eastern Baltics. After the Livonian Crusade they assumed control of government, politics, economics, education, with the decline of Latin, German became the language of all official documents, commerce, education and government. After 1710 many of these increasingly took high positions in the military, political and civilian life of the Russian Empire, Baltic Germans held citizenship of the Russian Empire until 1918 and Estonian or Latvian citizenship until 1939–40. The Baltic German population never surpassed more than 10% of the total population, in 1881 there were 180,000 Baltic Germans in Russias Baltic provinces, but by 1914 this number had declined to 162,000. In 1881 there were approximately 46,700 Germans in Estonia, according to the Russian Empire Census of 1897, there were 120,191 Germans in Latvia, or 6. 2% of the population. Baltic German history and presence in the Baltics came to an end in late 1939, following the signing of the Molotov–Ribbentrop Pact, almost all the Baltic Germans were resettled by Nazi Germany under the Heim ins Reich program into the newly formed Reichsgaue Wartheland and Danzig-West Prussia. In 1945, most were expelled from these lands by the Soviet army, ethnic Germans from East Prussia and Lithuania are sometimes incorrectly considered Baltic Germans for reasons of cultural, linguistic, and historical affinities. However, the Germans of East Prussia held Prussian, and after 1871, Baltic Germans were not a purely German ethnic group. The early crusaders, tradesmen and craftsmen often married local females, some noble families, like Lievens, even claimed descent from native chieftains. Many of the German Livonian Order soldiers died during the Livonian war, during this time the Low German of the original settlers was replaced by the High German. In those cases where intermarriage occurred, the ethnic group frequently assimilated into German culture, adopting language, customs. They were then considered Germans, leading to the ethnogenesis of the Baltic Germans, barclay de Tolly and George Armitstead, who arrived from the British Isles, became part of the Baltic-German community. Livland, roughly the half of present-day Estonia and the northern and eastern part of todays Latvia, major towns, Riga, Wenden, Wolmar, Walk, Dorpat, Pernau. Kurland, roughly the half of present-day Latvia, major towns. Ösel belonging to present-day Estonia, major town, Arensburg, after the heavy defeat in the 1236 Battle of Saule the Livonian Brothers of the Sword became a part of the Teutonic Order
Baltic German
–
Michael Barclay de Tolly
Baltic German
–
Baltic colours
Baltic German
–
Karl Ernst von Baer
Baltic German
–
Friedrich von Struve
19.
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
Mathematician
–
Euclid (holding
calipers), Greek mathematician, known as the "Father of Geometry"
Mathematician
–
In 1938 in the United States, mathematicians were desired as teachers, calculating machine operators, mechanical engineers, accounting auditor bookkeepers, and actuary statisticians
Mathematician
–
Archimedes, c. 287 – 212 BC
Mathematician
–
Brahmagupta, c. 598 - 670
20.
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
German language
–
Old Frisian (Alt-Friesisch)
German language
–
The widespread popularity of the
Bible translated into German by
Martin Luther helped establish modern German
German language
–
Examples of German language in
Namibian everyday life
German language
–
German-language newspapers in the U.S. in 1922
21.
Ernst Zermelo
–
Ernst Friedrich Ferdinand Zermelo was a German logician and mathematician, whose work has major implications for the foundations of mathematics. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory, Ernst Zermelo graduated from Berlins Luisenstädtisches Gymnasium in 1889. He then studied mathematics, physics and philosophy at the universities of Berlin, Halle and he finished his doctorate in 1894 at the University of Berlin, awarded for a dissertation on the calculus of variations. Zermelo remained at the University of Berlin, where he was appointed assistant to Planck, in 1897, Zermelo went to Göttingen, at that time the leading centre for mathematical research in the world, where he completed his habilitation thesis in 1899. In 1910, Zermelo left Göttingen upon being appointed to the chair of mathematics at Zurich University and he was appointed to an honorary chair at Freiburg im Breisgau in 1926, which he resigned in 1935 because he disapproved of Adolf Hitlers regime. At the end of World War II and at his request, Zermelo began to work on the problems of set theory under Hilberts influence and in 1902 published his first work concerning the addition of transfinite cardinals. By that time he had discovered the so-called Russell paradox. In 1904, he succeeded in taking the first step suggested by Hilbert towards the continuum hypothesis when he proved the well-ordering theorem and this result brought fame to Zermelo, who was appointed Professor in Göttingen, in 1905. Zermelo began to set theory in 1905, in 1908. See the article on Zermelo set theory for an outline of this paper, together with the original axioms, in 1922, Adolf Fraenkel and Thoralf Skolem independently improved Zermelos axiom system. The resulting 8 axiom system, now called Zermelo-Fraenkel axioms, is now the most commonly used system for set theory. Proposed in 1931, the Zermelos navigation problem is an optimal control problem. The problem deals with a boat navigating on a body of water, the boat is capable of a certain maximum speed, and we want to derive the best possible control to reach D in the least possible time. Without considering external forces such as current and wind, the control is for the boat to always head towards D. Its path then is a segment from O to D. With consideration of current and wind, if the force applied to the boat is non-zero the control for no current. Zermelo, Ernst, Ebbinghaus, Heinz-Dieter, Fraser, Craig G. Kanamori, Akihiro, from Frege to Gödel, A Source Book in Mathematical Logic, 1879–1931. Proof that every set can be well-ordered, 139−41, a new proof of the possibility of well-ordering, 183–98
Ernst Zermelo
–
Ernst Zermelo in Freiburg (1953)
Ernst Zermelo
–
Ernst Zermelo in the 1900s
22.
Axiom of choice
–
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty. It states that for every indexed family i ∈ I of nonempty sets there exists an indexed family i ∈ I of elements such that x i ∈ S i for every i ∈ I. The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem. Informally put, the axiom of choice says that any collection of bins, each containing at least one object. One motivation for use is that a number of generally accepted mathematical results, such as Tychonoffs theorem. Contemporary set theorists also study axioms that are not compatible with the axiom of choice, the axiom of choice is avoided in some varieties of constructive mathematics, although there are varieties of constructive mathematics in which the axiom of choice is embraced. A choice function is a function f, defined on a collection X of nonempty sets, each choice function on a collection X of nonempty sets is an element of the Cartesian product of the sets in X. The axiom of choice asserts the existence of elements, it is therefore equivalent to, Given any family of nonempty sets. In this article and other discussions of the Axiom of Choice the following abbreviations are common, ZF – Zermelo–Fraenkel set theory omitting the Axiom of Choice. ZFC – Zermelo–Fraenkel set theory, extended to include the Axiom of Choice, There are many other equivalent statements of the axiom of choice. These are equivalent in the sense that, in the presence of basic axioms of set theory. One variation avoids the use of functions by, in effect. Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains one element in common with each of the sets in X. This guarantees for any partition of a set X the existence of a subset C of X containing exactly one element from each part of the partition. Another equivalent axiom only considers collections X that are essentially powersets of other sets, For any set A, authors who use this formulation often speak of the choice function on A, but be advised that this is a slightly different notion of choice function. With this alternate notion of function, the axiom of choice can be compactly stated as Every set has a choice function. Which is equivalent to For any set A there is a function f such that for any non-empty subset B of A, f lies in B. The negation of the axiom can thus be expressed as, There is a set A such that for all functions f, however, that particular case is a theorem of Zermelo–Fraenkel set theory without the axiom of choice, it is easily proved by mathematical induction
Axiom of choice
23.
World War II
–
World War II, also known as the Second World War, was a global war that lasted from 1939 to 1945, although related conflicts began earlier. It involved the vast majority of the worlds countries—including all of the great powers—eventually forming two opposing alliances, the Allies and the Axis. It was the most widespread war in history, and directly involved more than 100 million people from over 30 countries. Marked by mass deaths of civilians, including the Holocaust and the bombing of industrial and population centres. These made World War II the deadliest conflict in human history, from late 1939 to early 1941, in a series of campaigns and treaties, Germany conquered or controlled much of continental Europe, and formed the Axis alliance with Italy and Japan. Under the Molotov–Ribbentrop Pact of August 1939, Germany and the Soviet Union partitioned and annexed territories of their European neighbours, Poland, Finland, Romania and the Baltic states. In December 1941, Japan attacked the United States and European colonies in the Pacific Ocean, and quickly conquered much of the Western Pacific. The Axis advance halted in 1942 when Japan lost the critical Battle of Midway, near Hawaii, in 1944, the Western Allies invaded German-occupied France, while the Soviet Union regained all of its territorial losses and invaded Germany and its allies. During 1944 and 1945 the Japanese suffered major reverses in mainland Asia in South Central China and Burma, while the Allies crippled the Japanese Navy, thus ended the war in Asia, cementing the total victory of the Allies. World War II altered the political alignment and social structure of the world, the United Nations was established to foster international co-operation and prevent future conflicts. The victorious great powers—the United States, the Soviet Union, China, the United Kingdom, the Soviet Union and the United States emerged as rival superpowers, setting the stage for the Cold War, which lasted for the next 46 years. Meanwhile, the influence of European great powers waned, while the decolonisation of Asia, most countries whose industries had been damaged moved towards economic recovery. Political integration, especially in Europe, emerged as an effort to end pre-war enmities, the start of the war in Europe is generally held to be 1 September 1939, beginning with the German invasion of Poland, Britain and France declared war on Germany two days later. The dates for the beginning of war in the Pacific include the start of the Second Sino-Japanese War on 7 July 1937, or even the Japanese invasion of Manchuria on 19 September 1931. Others follow the British historian A. J. P. Taylor, who held that the Sino-Japanese War and war in Europe and its colonies occurred simultaneously and this article uses the conventional dating. Other starting dates sometimes used for World War II include the Italian invasion of Abyssinia on 3 October 1935. The British historian Antony Beevor views the beginning of World War II as the Battles of Khalkhin Gol fought between Japan and the forces of Mongolia and the Soviet Union from May to September 1939, the exact date of the wars end is also not universally agreed upon. It was generally accepted at the time that the war ended with the armistice of 14 August 1945, rather than the formal surrender of Japan
World War II
–
Clockwise from top left: Chinese forces in the
Battle of Wanjialing, Australian
25-pounder guns during the
First Battle of El Alamein, German
Stuka dive bombers on the
Eastern Front in December 1943, a U.S. naval force in the
Lingayen Gulf,
Wilhelm Keitel signing the
German Instrument of Surrender, Soviet troops in the
Battle of Stalingrad
World War II
–
The
League of Nations assembly, held in
Geneva,
Switzerland, 1930
World War II
–
Adolf Hitler at a German
National Socialist political rally in
Weimar, October 1930
World War II
–
Italian soldiers recruited in 1935, on their way to fight the
Second Italo-Abyssinian War
24.
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
University of Berlin
–
Monument to Wilhelm von Humboldt in front of the main building. Artist: Paul Otto
University of Berlin
–
Seal of the Universitas Humboldtiana Berolinensis (
Latin)
University of Berlin
–
Statue of
Alexander von Humboldt outside Humboldt University, from 1883 by artist Reinhold Begas. Note the Spanish inscription describing him as "the second discoverer of Cuba".
University of Berlin
–
The Berlin University in 1850.
25.
Nazi
–
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
Nazi
–
Foreground, left to right: Führer
Adolf Hitler;
Hermann Göring; Minister of Propaganda
Joseph Goebbels;
Rudolf Hess
Nazi
–
Nazis alongside members of the far-right
reactionary and
monarchist German National People's Party (DNVP), during the brief Nazi-DNVP alliance in the
Harzburg Front from 1931 to 1932
Nazi
–
Johann Gottlieb Fichte, considered one of the fathers of German nationalism
26.
Hans Freudenthal
–
Hans Freudenthal was a German-born Dutch mathematician. He made substantial contributions to topology and also took an interest in literature, philosophy, history. Freudenthal was born in Luckenwalde, Brandenburg, on 17 September 1905 and he was interested in both mathematics and literature as a child, and studied mathematics at the University of Berlin beginning in 1923. He met Brouwer in 1927, when Brouwer came to Berlin to give a lecture and he completed his thesis work with Heinz Hopf at Berlin, defended a thesis on the ends of topological groups in 1930, and was officially awarded a degree in October 1931. After defending his thesis in 1930, he moved to Amsterdam to take up a position as assistant to Brouwer, in this pre-war period in Amsterdam, he was promoted to lecturer at the University of Amsterdam, and married his wife, Suus Lutter, a Dutch teacher. Although he was a German Jew, Freudenthals position in the Netherlands insulated him from the laws that had been passed in Germany beginning with the Nazi rise to power in 1933. However, in 1940 the Germans invaded the Netherlands, following which Freudenthal was suspended from duties at the University of Amsterdam by the Nazis. In 1943 Freudenthal was sent to a camp in the village of Havelte in the Netherlands. During this period Freudenthal occupied his time in literary pursuits, including winning first prize under a name in a novel-writing contest. He served as the 8th president of the International Commission on Mathematical Instruction from 1967 to 1970, in 1972 he founded and became editor-in-chief of the journal Geometriae Dedicata. He retired from his professorship in 1975 and from his editorship in 1981. He died in Utrecht in 1990, sitting on a bench in a park where he took a morning walk. In his thesis work, published as an article in 1931. Ends remain of great importance in topological group theory, Freudenthals motivating application, in 1936, while working with Brouwer, Freudenthal proved the Freudenthal spectral theorem on the existence of uniform approximations by simple functions in Riesz spaces. The Freudenthal magic square is a construction in Lie algebra developed by Freudenthal in the 1950s and 1960s, later in his life, Freudenthal focused on elementary mathematics education. In the 1970s, his single-handed intervention prevented the Netherlands from following the trend of new math. He was also a fervent critic of one of the first international school achievement studies, Freudenthal published the Impossible Puzzle, a mathematical puzzle that appears to lack sufficient information for a solution, in 1969. He also designed a constructed language, Lincos, to make communication with extraterrestrial intelligence
Hans Freudenthal
–
Hans Freudenthal
27.
Hitler
–
Adolf Hitler was a German politician who was the leader of the Nazi Party, Chancellor of Germany from 1933 to 1945, and Führer of Nazi Germany from 1934 to 1945. As dictator of the German Reich, he initiated World War II in Europe with the invasion of Poland in September 1939 and was central to the Holocaust, Hitler was born in Austria, then part of Austria-Hungary, and raised near Linz. He moved to Germany in 1913 and was decorated during his service in the German Army in World War I and he joined the German Workers Party, the precursor of the NSDAP, in 1919 and became leader of the NSDAP in 1921. In 1923 he attempted a coup in Munich to seize power, the failed coup resulted in Hitlers imprisonment, during which he dictated the first volume of his autobiography and political manifesto Mein Kampf. Hitler frequently denounced international capitalism and communism as being part of a Jewish conspiracy, by 1933, the Nazi Party was the largest elected party in the German Reichstag, which led to Hitlers appointment as Chancellor on 30 January 1933. Hitler aimed to eliminate Jews from Germany and establish a New Order to counter what he saw as the injustice of the post-World War I international order dominated by Britain, Hitler sought Lebensraum for the German people in Eastern Europe. His aggressive foreign policy is considered to be the cause of the outbreak of World War II in Europe. He directed large-scale rearmament and on 1 September 1939 invaded Poland, resulting in British, in June 1941, Hitler ordered an invasion of the Soviet Union. By the end of 1941 German forces and the European Axis powers occupied most of Europe, failure to defeat the Soviets and the entry of the United States into the war forced Germany onto the defensive and it suffered a series of escalating defeats. In the final days of the war, during the Battle of Berlin in 1945, Hitler married his long-time lover, on 30 April 1945, less than two days later, the two killed themselves to avoid capture by the Red Army, and their corpses were burned. Hitler and the Nazi regime were also responsible for the killing of an estimated 19.3 million civilians, in addition,29 million soldiers and civilians died as a result of military action in the European Theatre of World War II. The number of civilians killed during the Second World War was unprecedented in warfare, Hitlers father Alois Hitler Sr. was the illegitimate child of Maria Anna Schicklgruber. The baptismal register did not show the name of his father, in 1842, Johann Georg Hiedler married Aloiss mother Maria Anna. Alois was brought up in the family of Hiedlers brother, Johann Nepomuk Hiedler, in 1876, Alois was legitimated and the baptismal register changed by a priest to register Johann Georg Hiedler as Aloiss father. Alois then assumed the surname Hitler, also spelled Hiedler, Hüttler, the Hitler surname is probably based on one who lives in a hut. Nazi official Hans Frank suggested that Aloiss mother had been employed as a housekeeper by a Jewish family in Graz, and that the familys 19-year-old son Leopold Frankenberger had fathered Alois. No Frankenberger was registered in Graz during that period, and no record has been produced of Leopold Frankenbergers existence, Adolf Hitler was born on 20 April 1889 in Braunau am Inn, a town in Austria-Hungary, close to the border with the German Empire. He was one of six born to Alois Hitler and Klara Pölzl
Hitler
–
Hitler in 1938
Hitler
–
Adolf Hitler as an infant (c. 1889–90).
Hitler
–
Hitler's mother,
Klara
Hitler
–
Hitler's father,
Alois
28.
Kristallnacht
–
German authorities looked on without intervening. The name Kristallnacht comes from the shards of glass that littered the streets after the windows of Jewish-owned stores, buildings. Estimates of the number of fatalities caused by the pogrom have varied, early reporting estimated that 91 Jewish people were murdered during the attacks. Modern analysis of German scholarly sources by historians such as Richard J. Evans puts the number much higher, when deaths from post-arrest maltreatment and subsequent suicides are included, the death toll climbs into the hundreds. Additionally,30,000 Jewish men were arrested and incarcerated in Nazi concentration camps, Jewish homes, hospitals, and schools were ransacked, as the attackers demolished buildings with sledgehammers. Over 1,000 synagogues were burned and over 7,000 Jewish businesses were destroyed or damaged. The event which caused the attacks was the assassination of the Nazi German diplomat Ernst vom Rath by Herschel Grynszpan, in the 1920s, most German Jews were fully integrated into German society as German citizens. They served in the German army and navy and contributed to every field of German business, science, from its inception, Hitlers régime moved quickly to introduce anti-Jewish policies. Nazi propaganda singled out the 500,000 Jews in Germany, the subsequent 1935 Nuremberg Laws stripped German Jews of their citizenship and forbade Jews to marry non-Jewish Germans. These laws resulted in the exclusion of Jews from German social and political life, the international Évian Conference on 6 July 1938 addressed the issue of Jewish and Gypsy immigration to other countries. As the number of Jews and Gypsies wanting to leave increased, by 1938, Germany had entered a new radical phase in anti-Semitic activity. In a 1997 interview, the German historian Hans Mommsen claimed that a motive for the pogrom was the desire of the Gauleiters of the NSDAP to seize Jewish property. In the fall of 1938, the pressure on Jewish property nourished the partys ambition. This, however, was one aspect of the origin of the November 1938 pogrom. The Polish government threatened to extradite all Jews who were Polish citizens, the immediate reaction by the Gestapo was to push the Polish Jews—16,000 persons—over the borderline, but this measure failed due to the stubbornness of the Polish customs officers. The loss of prestige as a result of this abortive operation called for some sort of compensation, thus, the overreaction to Herschel Grynszpans attempt against the diplomat Ernst vom Rath came into being and led to the November pogrom. The background of the pogrom was signified by a sharp cleavage of interests between the different agencies of party and state, Heydrich and Himmler were interested in fostering Jewish emigration. In August 1938 the German authorities announced that permits for foreigners were being cancelled
Kristallnacht
–
The interior of the
Fasanenstrasse Synagogue in Berlin after Kristallnacht
Kristallnacht
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Polish Jews expelled from Germany in late October 1938
Kristallnacht
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Herschel Grynszpan, 7 November 1938
Kristallnacht
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Ernst vom Rath
29.
Issai Schur
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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
Issai Schur
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Issai Schur
30.
University of St Andrews
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The University of St Andrews is a British public research university in St Andrews, Fife, Scotland. It is the oldest of the four ancient universities of Scotland, St Andrews was founded between 1410 and 1413, when the Avignon Antipope Benedict XIII issued a papal bull to a small founding group of Augustinian clergy. St Andrews is made up from a variety of institutions, including three constituent colleges and 18 academic schools organised into four faculties, the university occupies historic and modern buildings located throughout the town. The academic year is divided into two terms, Martinmas and Candlemas, in term time, over one-third of the towns population is either a staff member or student of the university. It is ranked as the third best university in the United Kingdom in national league tables, the Times Higher Education World Universities Ranking names St Andrews among the worlds Top 50 universities for Social Sciences, Arts and Humanities. St Andrews has the highest student satisfaction amongst all multi-faculty universities in the United Kingdom, St Andrews has many notable alumni and affiliated faculty, including eminent mathematicians, scientists, theologians, philosophers, and politicians. Six Nobel Laureates are among St Andrews alumni and former staff, a charter of privilege was bestowed upon the society of masters and scholars by the Bishop of St Andrews, Henry Wardlaw, on 28 February 1411. Wardlaw then successfully petitioned the Avignon Pope Benedict XIII to grant the university status by issuing a series of papal bulls. King James I of Scotland confirmed the charter of the university in 1432, subsequent kings supported the university with King James V confirming privileges of the university in 1532. A college of theology and arts called St Johns College was founded in 1418 by Robert of Montrose, St Salvators College was established in 1450, by Bishop James Kennedy. St Leonards College was founded in 1511 by Archbishop Alexander Stewart, St Johns College was refounded by Cardinal James Beaton under the name St Marys College in 1538 for the study of divinity and law. Some university buildings that date from this period are still in use today, such as St Salvators Chapel, St Leonards College Chapel, at this time, the majority of the teaching was of a religious nature and was conducted by clerics associated with the cathedral. During the 17th and 18th centuries, the university had mixed fortunes and was beset by civil. He described it as pining in decay and struggling for life, in the second half of the 19th century, pressure was building upon universities to open up higher education to women. In 1876, the University Senate decided to allow women to receive an education at St Andrews at a roughly equal to the Master of Arts degree that men were able to take at the time. The scheme came to be known as the L. L. A and it required women to pass five subjects at an ordinary level and one at honours level and entitled them to hold a degree from the university. In 1889 the Universities Act made it possible to admit women to St Andrews. Agnes Forbes Blackadder became the first woman to graduate from St Andrews on the level as men in October 1894
University of St Andrews
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College Hall, within the 16th century St Mary's College building
University of St Andrews
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University of St Andrews
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University of St Andrews
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St Salvator's Chapel in 1843
University of St Andrews
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The "Gateway" building, built in 2000 and now used for the university's management department