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Hans Heilbronn
Hans Arnold Heilbronn (8 October 1908 – 28 April 1975) was a mathematician. Education He was born into a German-Jewish family. He was a student at the universities of Berlin, Freiburg and Göttingen, where he met Edmund Landau, who supervised his doctorate. In his thesis, he improved a result of Hoheisel on the size of prime gaps. Life Heilbronn fled Germany for Britain in 1933 due to the rise of Nazism. He arrived in Cambridge, then found accommodation in Manchester and eventually was offered a position at Bristol University, where he stayed for about one and a half years. There he proved that the class number of the number field \mathbb(\sqrt) tends to plus infinity as d does, as well as, in collaboration with Edward Linfoot, that there are at most ten quadratic number fields of the form \mathbb(\sqrt), d a natural number, with class number 1. On invitation of Louis Mordell he moved back to Manchester in 1934, but left again only one year later, accepting the Bevan Fe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin
Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population within city limits, highest population within its city limits of any city in the European Union. The city is also one of the states of Germany, being the List of German states by area, third smallest state in the country by area. Berlin is surrounded by the state of Brandenburg, and Brandenburg's capital Potsdam is nearby. The urban area of Berlin has a population of over 4.6 million and is therefore the most populous urban area in Germany. The Berlin/Brandenburg Metropolitan Region, Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Germany's second-largest metropolitan region after the Rhine-Ruhr region, as well as the List of EU metropolitan areas by GDP, fifth-biggest metropolitan region by GDP in the European Union. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jewish
Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of History of ancient Israel and Judah, ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, religion, and community are highly interrelated, as Judaism is their ethnic religion, though it is not practiced by all ethnic Jews. Despite this, religious Jews regard Gerim, converts to Judaism as members of the Jewish nation, pursuant to the Conversion to Judaism, long-standing conversion process. The Israelites emerged from the pre-existing Canaanite peoples to establish Kingdom of Israel (Samaria), Israel and Kingdom of Judah, Judah in the Southern Levant during the Iron Age.John Day (Old Testament scholar), John Day (2005), ''In Search of Pre-Exilic Israel'', Bloomsbury Publishing, pp. 47.5 [48] 'In this sense, the emergence of ancient Israel is viewed not as the cause of the demise of Canaanite culture but as its upshot'. Originally, J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trinity College, Cambridge
Trinity College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any college at Oxford or Cambridge. Trinity has some of the most distinctive architecture in Cambridge with its Trinity Great Court, Great Court said to be the largest enclosed courtyard in Europe. Academically, Trinity performs exceptionally as measured by the Tompkins Table (the annual unofficial league table of Cambridge colleges), coming top from 2011 to 2017, and regaining the position in 2024. Members of Trinity have been awarded 34 Nobel Prizes out of the 121 received by members of the University of Cambridge (more than any other Oxford or Cambridge college). Members of the college have received four Fields Medals, one Turing Award and one Abel Prize. Trinity alumni include Francis Bacon, six British Prime Minister of the United Kingdo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Louis Mordell
Louis Joel Mordell (28 January 1888 – 12 March 1972) was an American-born British mathematician, known for his research in number theory. He was born in Philadelphia, United States, in a Jewish family of Lithuanian extraction. Education Mordell was educated at the University of Cambridge where he completed the Cambridge Mathematical Tripos as a student of St John's College, Cambridge, starting in 1906 after successfully passing the scholarship examination. He graduated as third wrangler in 1909. Research After graduating Mordell began independent research into particular diophantine equations: the question of integer points on the cubic curve, and special case of what is now called a Thue equation, the Mordell equation :''y''2 = ''x''3 + ''k''. He took an appointment at Birkbeck College, London in 1913. During World War I he was involved in war work, but also produced one of his major results, proving in 1917 the multiplicative property of Srinivasa Ramanujan's tau-fun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward Linfoot
Edward Hubert Linfoot FRAS (8 June 1905 – 14 October 1982) was a British mathematician, primarily known for his work on optics, but also noted for his work in pure mathematics. Early life and career Edward Linfoot was born in Sheffield, England, in 1905. He was the eldest child of George Edward Linfoot, a violinist and mathematician, and George's wife Laura, née Clayton. After attending King Edward VII School he won a scholarship to Balliol College at the University of Oxford. During his time at Oxford he met the number theorist G. H. Hardy, and after graduating in 1926, Linfoot completed a D.Phil under the supervision of Hardy with a thesis entitled ''Applications of the Theory of Functions of a Complex Variable''. After brief stints at the University of Göttingen, Princeton University, and Balliol College, Linfoot took a job in 1932 as assistant lecturer, and later lecturer, at the University of Bristol. During the 1930s Linfoot's interests slowly made the tran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Field
In mathematics, an algebraic number field (or simply number field) is an extension field K of the field of rational numbers such that the field extension K / \mathbb has finite degree (and hence is an algebraic field extension). Thus K is a field that contains \mathbb and has finite dimension when considered as a vector space over The study of algebraic number fields, that is, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory. This study reveals hidden structures behind the rational numbers, by using algebraic methods. Definition Prerequisites The notion of algebraic number field relies on the concept of a field. A field consists of a set of elements together with two operations, namely addition, and multiplication, and some distributivity assumptions. These operations make the field into an abelian group under addition, and they make the nonzero elements of the field into another abelian group under multiplication ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Class Number (number Theory)
In mathematics, the ideal class group (or class group) of an algebraic number field K is the quotient group J_K/P_K where J_K is the group of fractional ideals of the ring of integers of K, and P_K is its subgroup of principal ideals. The class group is a measure of the extent to which unique factorization fails in the ring of integers of K. The order of the group, which is finite, is called the class number of K. The theory extends to Dedekind domains and their fields of fractions, for which the multiplicative properties are intimately tied to the structure of the class group. For example, the class group of a Dedekind domain is trivial if and only if the ring is a unique factorization domain. History and origin of the ideal class group Ideal class groups (or, rather, what were effectively ideal class groups) were studied some time before the idea of an ideal was formulated. These groups appeared in the theory of quadratic forms: in the case of binary integral quadratic f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bristol University
The University of Bristol is a public research university in Bristol, England. It received its royal charter in 1909, although it can trace its roots to a Merchant Venturers' school founded in 1595 and University College, Bristol, which had been in existence since 1876. Bristol Medical School, founded in 1833, was merged with the University College in 1893, and later became the university's school of medicine. The university is organised into six academic faculties composed of multiple schools and departments running over 200 undergraduate courses, largely in the Tyndalls Park area of the city. It had a total income of £1.06 billion in 2023–24, of which £294.1 million was from research grants and contracts, with an expenditure of £768.7 million. It is the largest independent employer in Bristol. Current academics include 23 fellows of the Academy of Medical Sciences, 13 fellows of the British Academy, 43 fellows of the Academy of Social Sciences, 13 fellows of the Roy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manchester
Manchester () is a city and the metropolitan borough of Greater Manchester, England. It had an estimated population of in . Greater Manchester is the third-most populous metropolitan area in the United Kingdom, with a population of 2.92 million, and the largest in Northern England. It borders the Cheshire Plain to the south, the Pennines to the north and east, and the neighbouring city of Salford to the west. The city borders the boroughs of Trafford, Metropolitan Borough of Stockport, Stockport, Tameside, Metropolitan Borough of Oldham, Oldham, Metropolitan Borough of Rochdale, Rochdale, Metropolitan Borough of Bury, Bury and City of Salford, Salford. The history of Manchester began with the civilian settlement associated with the Roman fort (''castra'') of Mamucium, ''Mamucium'' or ''Mancunium'', established on a sandstone bluff near the confluence of the rivers River Medlock, Medlock and River Irwell, Irwell. Throughout the Middle Ages, Manchester remained a ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge
Cambridge ( ) is a List of cities in the United Kingdom, city and non-metropolitan district in the county of Cambridgeshire, England. It is the county town of Cambridgeshire and is located on the River Cam, north of London. As of the 2021 United Kingdom census, the population of the City of Cambridge was 145,700; the population of the wider built-up area (which extends outside the city council area) was 181,137. (2021 census) There is archaeological evidence of settlement in the area as early as the Bronze Age, and Cambridge became an important trading centre during the Roman Britain, Roman and Viking eras. The first Town charter#Municipal charters, town charters were granted in the 12th century, although modern city status was not officially conferred until 1951. The city is well known as the home of the University of Cambridge, which was founded in 1209 and consistently ranks among the best universities in the world. The buildings of the university include King's College Chap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nazism
Nazism (), formally named National Socialism (NS; , ), is the far-right totalitarian socio-political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Germany. During Hitler's rise to power, it was frequently referred to as Hitler Fascism () and Hitlerism (). The term " neo-Nazism" is applied to other far-right groups with similar ideology, which formed after World War II, and after Nazi Germany collapsed. Nazism is a form of fascism, with disdain for liberal democracy and the parliamentary system. Its beliefs include support for dictatorship, fervent antisemitism, anti-communism, anti-Slavism, anti-Romani sentiment, scientific racism, white supremacy, Nordicism, social Darwinism, homophobia, ableism, and the use of eugenics. The ultranationalism of the Nazis originated in pan-Germanism and the ethno-nationalist '' Völkisch'' movement which had been a prominent aspect of German ultranationalism since the late 19th centu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Gap
A prime gap is the difference between two successive prime numbers. The ''n''-th prime gap, denoted ''g''''n'' or ''g''(''p''''n'') is the difference between the (''n'' + 1)-st and the ''n''-th prime numbers, i.e., :g_n = p_ - p_n. We have ''g''1 = 1, ''g''2 = ''g''3 = 2, and ''g''4 = 4. The sequence (''g''''n'') of prime gaps has been extensively studied; however, many questions and conjectures remain unanswered. The first 60 prime gaps are: :1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 14, 4, 6, 2, 10, 2, 6, 6, 4, 6, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4, 6, 2, 10, 6, 6, 6, 2, 6, 4, 2, ... . By the definition of ''g''''n'' every prime can be written as :p_ = 2 + \sum_^n g_i. Simple observations The first, smallest, and only odd prime gap is the gap of size 1 between 2, the only even prime number, and 3, the first odd prime. All other prime gaps are even. There is only one pair of consecutive gaps having length 2: the gap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
