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Arnold Scholz
Arnold Scholz (24 December 1904 in Berlin – 1 February 1942 in Flensburg) was a German mathematician who proved Scholz's reciprocity law and introduced the Scholz conjecture. Scholz participated in the Second Conference on the Epistemology of the Exact Sciences contributing the paper "On the Use of the Term Holism in Axiomatics" to the discussion on the foundation of mathematics Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathe .... Publications * References * * 1942 deaths 1904 births 20th-century German mathematicians {{Germany-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arnold Scholz
Arnold Scholz (24 December 1904 in Berlin – 1 February 1942 in Flensburg) was a German mathematician who proved Scholz's reciprocity law and introduced the Scholz conjecture. Scholz participated in the Second Conference on the Epistemology of the Exact Sciences contributing the paper "On the Use of the Term Holism in Axiomatics" to the discussion on the foundation of mathematics Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathe .... Publications * References * * 1942 deaths 1904 births 20th-century German mathematicians {{Germany-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin
Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constituent states, Berlin is surrounded by the State of Brandenburg and contiguous with Potsdam, Brandenburg's capital. Berlin's urban area, which has a population of around 4.5 million, is the second most populous urban area in Germany after the Ruhr. The Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Germany's third-largest metropolitan region after the Rhine-Ruhr and Rhine-Main regions. Berlin straddles the banks of the Spree, which flows into the Havel (a tributary of the Elbe) in the western borough of Spandau. Among the city's main topographical features are the many lakes in the western and southeastern boroughs formed by the Spree, Havel and Dahme, the largest of which is Lake Müggelsee. Due to its l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flensburg
Flensburg (; Danish, Low Saxon: ''Flensborg''; North Frisian: ''Flansborj''; South Jutlandic: ''Flensborre'') is an independent town (''kreisfreie Stadt'') in the north of the German state of Schleswig-Holstein. Flensburg is the centre of the region of Southern Schleswig. After Kiel and Lübeck, it is the third largest town in Schleswig-Holstein. The nearest larger towns are Kiel ( south) and Odense in Denmark ( northeast). Flensburg's city centre lies about from the Danish border. Known for In Germany, Flensburg is known for: * the Kraftfahrt-Bundesamt (roughly: National Driver and Vehicle Register) with its ''Verkehrssünderkartei'' (literally: "traffic sinner card file"), where details of traffic offences are stored * its beer '' Flensburger Pilsener'', also called "''Flens''" * the centre of the Danish national minority in Germany * the greeting Moin Moin * the large erotic mail-order companies ''Beate Uhse'' and ''Orion'' * its handball team SG Flensburg-Handewitt * th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scholz's Reciprocity Law
In mathematics, Scholz's reciprocity law is a reciprocity law for quadratic residue symbols of real quadratic number fields discovered by and rediscovered by . Statement Suppose that ''p'' and ''q'' are rational primes congruent to 1 mod 4 such that the Legendre symbol (''p''/''q'') is 1. Then the ideal (''p'') factorizes in the ring of integers of Q() as (''p'')=𝖕𝖕' and similarly (''q'')=𝖖𝖖' in the ring of integers of Q(). Write ε''p'' and ε''q'' for the fundamental units in these quadratic fields. Then Scholz's reciprocity law says that : ''p''/𝖖= ''q''/𝖕 where [] is the quadratic residue symbol in a quadratic number field. References * * *{{Citation , last1=Schönemann , first1=Theodor , title=Ueber die Congruenz x² + y² ≡ 1 (mod p) , url=http://resolver.sub.uni-goettingen.de/purl?GDZPPN002141868 , year=1839 , journal=Journal für die reine und angewandte Mathematik ''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics j ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scholz Conjecture
In mathematics, the Scholz conjecture is a conjecture on the length of certain addition chains. It is sometimes also called the Scholz–Brauer conjecture or the Brauer–Scholz conjecture, after Arnold Scholz who formulated it in 1937 and Alfred Brauer who studied it soon afterward and proved a weaker bound. Statement The conjecture states that :, where is the length of the shortest addition chain producing ''n''. Here, an addition chain is defined as a sequence of numbers, starting with 1, such that every number after the first can be expressed as a sum of two earlier numbers (which are allowed to both be equal). Its length is the number of sums needed to express all its numbers, which is one less than the length of the sequence of numbers (since there is no sum of previous numbers for the first number in the sequence, 1). Computing the length of the shortest addition chain that contains a given number can be done by dynamic programming for small numbers, but it is not known ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second Conference On The Epistemology Of The Exact Sciences
The Second Conference on the Epistemology of the Exact Sciences (german: 2. Tagung für Erkenntnislehre der exakten Wissenschaften in Königsberg) was held on 5–7 September 1930 in Königsberg, then located in East Prussia. It was at this conference that Kurt Gödel first presented his incompleteness theorems, though just "in an off-hand remark during a general discussion on the last day".Mancosu, Paolo "Between Vienna and Berlin: The immediate reception of Gödel's incompleteness theorems", History and Philosophy of Logic, 20, 1999, 33-45. The real first presentation took place in Vienna. The conference was organised by Kurt Reidemeister of the University of Königsberg. The presentations were grouped around two themes: firstly, the foundation of mathematics and secondly philosophical questions arising from Quantum mechanics. The conference was closely related to the journal ''Erkenntnis'' who published the associated papers and accounts of the discussion in ''Erkenntnis'' (1931), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foundation Of Mathematics
Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts (set, function, geometrical figure, number, etc.) and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics (formulas, theories and their models giving a meaning to formulas, definitions, proofs, algorithms, etc.) also called metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics. The search for foundations of mathematics is a central question of the philosophy of mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematische Nachrichten
''Mathematische Nachrichten'' (abbreviated ''Math. Nachr.''; English: ''Mathematical News'') is a mathematical journal published in 12 issues per year by Wiley-VCH GmbH. It should not be confused with the ''Internationale Mathematische Nachrichten'', an unrelated publication of the Austrian Mathematical Society. It was established in 1948 by East German mathematician Erhard Schmidt, who became its first editor-in-chief. At that time it was associated with the German Academy of Sciences at Berlin, and published by Akademie Verlag. After the fall of the Berlin Wall, Akademie Verlag was sold to VCH Verlagsgruppe Weinheim, which in turn was sold to John Wiley & Sons. According to the 2020 edition of Journal Citation Reports, the journal had an impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1942 Deaths
Year 194 ( CXCIV) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Septimius and Septimius (or, less frequently, year 947 ''Ab urbe condita''). The denomination 194 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Emperor Septimius Severus and Decimus Clodius Septimius Albinus Caesar become Roman Consuls. * Battle of Issus: Septimius Severus marches with his army (12 legions) to Cilicia, and defeats Pescennius Niger, Roman governor of Syria. Pescennius retreats to Antioch, and is executed by Severus' troops. * Septimius Severus besieges Byzantium (194–196); the city walls suffer extensive damage. Asia * Battle of Yan Province: Warlords Cao Cao and Lü Bu fight for control over Yan Province; the battle lasts for over 100 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1904 Births
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album ''63/19'' by Kool A.D. * ''Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album '' Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by Slipk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
