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Gerhard Gentzen
Gerhard Karl Erich Gentzen (24 November 1909 – 4 August 1945) was a German mathematician and logician. He made major contributions to the foundations of mathematics, proof theory, especially on natural deduction and sequent calculus. He died of starvation in a Czech prison camp in Prague in 1945. Life and career Gentzen was a student of Paul Bernays at the University of Göttingen. Bernays was fired as "non-Aryan" in April 1933 and therefore Hermann Weyl formally acted as his supervisor. Gentzen joined the Sturmabteilung in November 1933, although he was by no means compelled to do so. Nevertheless, he kept in contact with Bernays until the beginning of the Second World War. In 1935, he corresponded with Abraham Fraenkel in Jerusalem and was implicated by the Nazi teachers' union as one who "keeps contacts to the Chosen People." In 1935 and 1936, Hermann Weyl, head of the Göttingen mathematics department in 1933 until his resignation under Nazi pressure, made strong efforts t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Greifswald
Greifswald (), officially the University and Hanseatic City of Greifswald (, Low German: ''Griepswoold'') is the fourth-largest city in the German state of Mecklenburg-Western Pomerania after Rostock, Schwerin and Neubrandenburg. In 2021 it surpassed Stralsund for the first time, and became the largest city in the Pomeranian part of the state. It sits on the River Ryck, at its mouth into the Danish Wiek, a sub-bay of the Bay of Greifswald, which is itself a sub-bay of the Bay of Pomerania of the Baltic Sea. It is the seat of the district of Vorpommern-Greifswald, Western Pomerania-Greifswald, and is located roughly in the middle between the two largest Pomeranian islands of Rügen and Usedom. The closest larger cities are Stralsund, Rostock, Szczecin and Schwerin. It lies west of the River Zarow, the historical cultural and linguistic boundary between West (west of the river) and Central Pomerania (east of the river). The city derives its name from the dukes of Pomerania, the Hous ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Logician
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to work." Premise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Nazi Party
The Nazi Party, officially the National Socialist German Workers' Party ( or NSDAP), was a far-right politics, far-right political party in Germany active between 1920 and 1945 that created and supported the ideology of Nazism. Its precursor, the German Workers' Party (; DAP), existed from 1919 to 1920. The Nazi Party emerged from the Extremism, extremist German nationalism, German nationalist ("Völkisch nationalism, ''Völkisch'' nationalist"), racism, racist, and populism, populist paramilitary culture, which fought against communism, communist uprisings in post–World War I Germany. The party was created to draw workers away from communism and into nationalism. Initially, Nazi political strategy focused on anti-big business, anti-bourgeoisie, and anti-capitalism, disingenuously using socialist rhetoric to gain the support of the lower middle class; it was later downplayed to gain the support of business leaders. By the 1930s, the party's main focus shifted to Antisemit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory). He adopted and defended Georg Cantor's set theory and transfinite numbers. In 1900, he presented a collection of problems that set a course for mathematical research of the 20th century. Hilbert and his students contributed to establishing rigor and developed important tools used in modern mathematical physics. He was a cofounder of proof theory and mathematical logic. Life Early life and education Hilbert, the first of two children and only son of O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Institute For Advanced Study
The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Einstein, J. Robert Oppenheimer, Emmy Noether, Hermann Weyl, John von Neumann, Michael Walzer, Clifford Geertz and Kurt Gödel, many of whom had emigrated from Europe to the United States. It was founded in 1930 by American educator Abraham Flexner, together with philanthropists Louis Bamberger and Caroline Bamberger Fuld. Despite collaborative ties and neighboring geographic location, the institute, being independent, has "no formal links" with Princeton University. The institute does not charge tuition or fees. Flexner's guiding principle in founding the institute was the pursuit of knowledge for its own sake.Jogalekar. The faculty have no classes to teach. There are no degree programs or experimental facilities at the institute. Research ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Chosen People
Throughout history, various groups of people have considered themselves to be the chosen people of a deity, for a particular purpose. The phenomenon of "chosen people" is well known among the Israelites and Jews, where the term () refers to the Israelites as being selected by Yahweh to worship only him and to fulfill the mission of proclaiming his truth throughout the world. Some claims of chosenness are based on parallel claims of Israelite ancestry, as is the case for the Christian Identity and Black Hebrew sects—both which claim themselves (and not Jews) to be the "true Israel". Others claim that the concept is spiritual, where individuals who genuinely believe in God are considered to be the "true" chosen people. This view is common among most Christian denominations, who historically believed that the church replaced Israel as the people of God. Anthropologists commonly regard claims of chosenness as a form of ethnocentrism. Judaism In Judaism, "chosenness" is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Abraham Fraenkel
Abraham Fraenkel (; 17 February, 1891 – 15 October, 1965) was a German-born Israeli mathematician. He was an early Zionist and the first Dean of Mathematics at the Hebrew University of Jerusalem. He is known for his contributions to axiomatic set theory, especially his additions to Ernst Zermelo's axioms, which resulted in the Zermelo–Fraenkel set theory. Biography Abraham Adolf Halevi Fraenkel studied mathematics at the Universities of Munich, Berlin, Marburg and Breslau. After graduating, he lectured at the University of Marburg from 1916, and was promoted to professor in 1922. In 1919, he married Wilhelmina Malka A. Prins (1892–1983). Due to the severe housing shortage in post-First World war Germany, for a few years the couple lived with fellow professor Kurt Hensel as subtenants. After leaving Marburg in 1928, Fraenkel taught at the University of Kiel for a year. He then made the choice of accepting a position at the Hebrew University of Jerusalem, which had b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Second World War
World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the world's countries participated, with many nations mobilising all resources in pursuit of total war. Tanks in World War II, Tanks and Air warfare of World War II, aircraft played major roles, enabling the strategic bombing of cities and delivery of the Atomic bombings of Hiroshima and Nagasaki, first and only nuclear weapons ever used in war. World War II is the List of wars by death toll, deadliest conflict in history, causing World War II casualties, the death of 70 to 85 million people, more than half of whom were civilians. Millions died in genocides, including the Holocaust, and by massacres, starvation, and disease. After the Allied victory, Allied-occupied Germany, Germany, Allied-occupied Austria, Austria, Occupation of Japan, Japan, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Sturmabteilung
The (; SA; or 'Storm Troopers') was the original paramilitary organisation under Adolf Hitler and the Nazi Party of Germany. It played a significant role in Adolf Hitler's rise to power, Hitler's rise to power in the 1920s and early 1930s. Its primary purposes were providing protection for Nazi rallies and assemblies, disrupting the meetings of opposing parties, fighting against the paramilitary units of the opposing parties, especially the ''Roter Frontkämpferbund'' of the Communist Party of Germany (KPD) and the ''Reichsbanner Schwarz-Rot-Gold'' of the Social Democratic Party of Germany (SPD), and intimidating Romani people, Romani, trade unionists, and especially Jews. The SA were colloquially called Brownshirts () because of the colour of their Uniforms and insignia of the Sturmabteilung, uniform's shirts, similar to Benito Mussolini's Blackshirts. The official uniform of the SA was a brown shirt with a brown tie. The color came about because a large shipment of Paul von ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Hermann Weyl
Hermann Klaus Hugo Weyl (; ; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is associated with the University of Göttingen tradition of mathematics, represented by Carl Friedrich Gauss, David Hilbert and Hermann Minkowski. His research has had major significance for theoretical physics as well as purely mathematical disciplines such as number theory. He was one of the most influential mathematicians of the twentieth century, and an important member of the Institute for Advanced Study during its early years. Weyl contributed to an exceptionally wide range of fields, including works on space, time, matter, philosophy, logic, symmetry and the history of mathematics. He was one of the first to conceive of combining general relativity with the laws of electromagnetism. Freeman Dyson wrote that Weyl alone bore comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Aryan
''Aryan'' (), or ''Arya'' (borrowed from Sanskrit ''ārya''), Oxford English Dictionary Online 2024, s.v. ''Aryan'' (adj. & n.); ''Arya'' (n.)''.'' is a term originating from the ethno-cultural self-designation of the Indo-Iranians. It stood in contrast to nearby outsiders, whom they designated as non-Aryan (). In ancient India, the term was used by the Indo-Aryan peoples of the Vedic period, both as an endonym and in reference to a region called ''Aryavarta'' (, ), where their culture emerged. Similarly, according to the Avesta, the Iranian peoples used the term to designate themselves as an ethnic group and to refer to a region called '' Airyanem Vaejah'' (, ), which was their mythical homeland. The word stem also forms the etymological source of place names like '' Alania'' () and ''Iran'' (). Although the stem may originate from the Proto-Indo-European language, it seems to have been used exclusively by the Indo-Iranian peoples, as there is no evidence of it having s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Sequent Calculus
In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology. Each conditional tautology is inferred from other conditional tautologies on earlier lines in a formal argument according to rules and procedures of inference, giving a better approximation to the natural style of deduction used by mathematicians than David Hilbert's earlier style of formal logic, in which every line was an unconditional tautology. More subtle distinctions may exist; for example, propositions may implicitly depend upon non-logical axioms. In that case, sequents signify conditional theorems of a first-order theory rather than conditional tautologies. Sequent calculus is one of several extant styles of proof calculus for expressing line-by-line logical arguments. * Hilbert style. Every line is an unconditional tautology (or theorem). * Gentzen s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
