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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. Neill Clift has announced an example showing that the bound of the conjecture is not always tight. 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 chai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conjecture
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them. Resolution of conjectures Proof Formal mathematics is based on ''provable'' truth. In mathematics, any number of cases supporting a universally quantified conjecture, no matter how large, is insufficient for establishing the conjecture's veracity, since a single counterexample could immediately bring down the conjecture. Mathematical journals sometimes publish the minor results of research teams having extended the search for a counterexample farther than previously done. For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1.2 × 101 ... [...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 working in algebraic number theory who proved Scholz's reciprocity law and introduced the Scholz conjecture. Biography Life Scholz was the son of Reinhold Scholz, an executive at the Prussian Military Research Office. He attended the Kaiserin Auguste Gymnasium in Charlottenburg. From 1923 to 1928, he studied Mathematics, Philosophy and Musicology at the Universität Berlin. In 1928, Scholz wrote his dissertation, supervised by Issai Schur and titled ''Über die Bildung algebraischer Zahlkörper mit auflösbarer Galoisscher Gruppe'' ("On the creation of algebraic number fields with solvable Galois Groups"). In 1927, Scholz spent a semester in Vienna, where he studied under Philipp Furtwängler. After his promotion, he became a lecture assistant in Berlin in 1928, a Privatdozent in Freiburg im Breisgau in 1930, and a lecturer at the University of Kiel from 1935-1940. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfred Brauer
Alfred Theodor Brauer (April 9, 1894 – December 23, 1985) was a German-American mathematician who did work in number theory. He was born in Charlottenburg, and studied at the Humboldt University of Berlin, 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 Hitler's rise to power.Bergmann, Birgit; Epple, Moritz; and Ungar, Ruti''Transcending Tradition: Jewish Mathematicians in German Speaking Academic Culture'' p. 54. Springer, 2012. . Accessed February 25, 2013. "Schur's disciple Alfred Brauer was the last Jewish mathematician who managed to complete his habilitation and become Privatdozent at the University of Berlin before the Nazi regime began." In 1935 he lost his position and in 1938 he tried to leave Germany, but was not able to until the following year. He initially worked in Northeastern United States, the Northeast, but in 1942 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
