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Karl Weierstrass
Karl Theodor Wilhelm Weierstrass (; ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the " father of modern analysis". Despite leaving university without a degree, he studied mathematics and trained as a school teacher, eventually teaching mathematics, physics, botany and gymnastics. He later received an honorary doctorate and became professor of mathematics in Berlin. Among many other contributions, Weierstrass formalized the definition of the continuity of a function and complex analysis, proved the intermediate value theorem and the Bolzano–Weierstrass theorem, and used the latter to study the properties of continuous functions on closed bounded intervals. Biography Weierstrass was born into a Roman Catholic family in Ostenfelde, a village near Ennigerloh, in the Province of Westphalia. Karl Weierstrass was the son of Wilhelm Weierstrass and Theodora Vonderforst, the former of whom was a government official and both of whom were Cat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ennigerloh
Ennigerloh () is a town in the district of Warendorf, in North Rhine-Westphalia, Germany. It is situated approximately 25 km northeast of Hamm and 30 km southeast of Münster. The town, located in an agricultural area and with a well-preserved medieval quarter, became more industrial in the 20th century as several cement factories were installed. Some of these closed towards the end of the century. Furniture manufacturing was also a significant industry. Geography Subdivisions * Enniger * Westkirchen * Ostenfelde * Hoest Notable people * Alois Hanslian (born 1943), painter * Willy Hartner (1905–1981), professor, founded the Institute for the History of Natural Sciences in Frankfurt am Main * Karl Weierstrass Karl Theodor Wilhelm Weierstrass (; ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the " father of modern analysis". Despite leaving university without a degree, he studied mathematics and trained as a school t ... ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johannes Knoblauch
Johannes Knoblauch (27 August 1855, Halle (Saale) – 22 July 1915, Berlin) was a German mathematician. Biography Johannes Knoblauch, whose father was the physics professor Karl Hermann Knoblauch, studied law, mathematics and physics from 1872 in Halle, Heidelberg and Berlin. At the Friedrich Wilhelm University (later renamed the Humboldt University of Berlin) he studied from 1874 to 1878 and from 1880 to 1883 and received his ''Promotion'' (Ph.D.) in 1882 and his ''Habilitation'' in 1883. His doctoral dissertation "Ueber die Allgemeine Wellenfläche" was supervised by Karl Weierstrass. Knoblauch was a teacher for the academic year 1878–1879 at (his former school) the state ''Gymnasium'' in Halle and from 1879 to 1880 at Berlin's ''Gymnasium zum Grauen Kloster''. At the Friedrich Wilhelm University of Berlin, after his ''Habilitation'' in 1883 he was appointed Privatdozent. There in 1889 he was appointed professor extraordinarius and retained that academic post until his deat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weierstrass Function
In mathematics, the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function (mathematics), function that is continuous function, continuous everywhere but Differentiable function, differentiable nowhere. It is also an example of a fractal curve. The Weierstrass function has historically served the role of a pathological (mathematics), pathological function, being the first published example (1872) specifically concocted to challenge the notion that every continuous function is differentiable except on a set of isolated points. Weierstrass's demonstration that continuity did not imply almost-everywhere differentiability upended mathematics, overturning several proofs that relied on geometric intuition and vague definitions of smoothness. These types of functions were disliked by contemporaries: Charles Hermite, on finding that one class of function he was working on had such a property, described it as a "lamentable scourge". Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ludwig Stickelberger
Ludwig Stickelberger (18 May 1850 – 11 April 1936) was a Swiss mathematician who made important contributions to linear algebra (theory of elementary divisors) and algebraic number theory (Stickelberger relation in the theory of cyclotomic fields). Short biography Stickelberger was born in Buch in the canton of Schaffhausen into a family of a pastor. He graduated from a gymnasium in 1867 and studied next in the University of Heidelberg. In 1874 he received a doctorate in Berlin under the direction of Karl Weierstrass for his work on the transformation of quadratic forms to a diagonal form. In the same year, he obtained his Habilitation from Polytechnicum in Zurich (now ETH Zurich). In 1879 he became an extraordinary professor in the Albert Ludwigs University of Freiburg. From 1896 to 1919 he worked there as a full professor, and from 1919 until his return to Basel in 1924 he held the title of a distinguished professor ("ordentlicher Honorarprofessor"). He was married in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermann Schwarz
Karl Hermann Amandus Schwarz (; 25 January 1843 – 30 November 1921) was a German mathematician, known for his work in complex analysis. Life Schwarz was born in Hermsdorf, Silesia (now Sobieszów, Poland). In 1868 he married Marie Kummer, who was the daughter to the mathematician Ernst Eduard Kummer and Ottilie née Mendelssohn (a daughter of Nathan Mendelssohn's and granddaughter of Moses Mendelssohn). Schwarz and Kummer had six children, including his daughter Emily Schwarz. Schwarz originally studied chemistry in Berlin but Ernst Eduard Kummer and Karl Theodor Wilhelm Weierstrass persuaded him to change to mathematics. He received his Ph.D. from the Universität Berlin in 1864 and was advised by Kummer and Weierstrass. Between 1867 and 1869 he worked at the University of Halle, then at the Swiss Federal Polytechnic. From 1875 he worked at Göttingen University, dealing with the subjects of complex analysis, differential geometry and the calculus of variations. H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedrich Schottky
Friedrich Hermann Schottky (24 July 1851 – 12 August 1935) was a German mathematician who worked on elliptic, abelian, and theta functions and introduced Schottky groups and Schottky's theorem. Biography Friedrich Hermann Schottky was born in Breslau, Germany (now Wrocław, Poland). His father, Dr. Hermann Friedrich Schottky, was an English teacher and his mother, Louise Winkler, was a florist. He attended from 1860 to 1870, where his classmates included , , and Eberhard Gothein.From 1870 to 1874 he attended the University of Breslau. In 1875 Schottky received his doctorate, studying under Karl Weierstrass and Hermann von Helmholtz at Friedrich Wilhelm University of Berlin. Schottky was a lecturer at the University of Breslau from 1878 to 1882, a professor at the University of Zurich from 1882 to 1892, and a professor at Philipps University of Marburg from 1892 to 1902. In 1902, through his friendship with Ferdinand Georg Frobenius, Schottky was able to obtain a p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arthur Schoenflies
Arthur Moritz Schoenflies (; 17 April 1853 – 27 May 1928), sometimes written as Schönflies, was a German mathematician, known for his contributions to the application of group theory to crystallography, and for work in topology. Schoenflies was born in Landsberg an der Warthe (modern Gorzów, Poland). Arthur Schoenflies married Emma Levin (1868–1939) in 1896. He studied under Ernst Kummer and Karl Weierstrass, and was influenced by Felix Klein. The Schoenflies problem is to prove that an (n - 1)-sphere in Euclidean ''n''-space bounds a topological ball, however embedded. This question is much more subtle than it initially appears. He studied at the University of Berlin from 1870 to 1875. He obtained a doctorate in 1877, and in 1878 he was a teacher at a school in Berlin. In 1880, he went to Colmar to teach. Schoenflies was a frequent contributor to Klein's ''Encyclopedia of Mathematical Sciences'': In 1898 he wrote on set theory, in 1902 on kinematics, and on project ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Runge
Carl David Tolmé Runge (; 30 August 1856 – 3 January 1927) was a German mathematician, physicist, and spectroscopist. He was co-developer and co-eponym of the Runge–Kutta method (), in the field of what is today known as numerical analysis. Life and work Runge spent the first few years of his life in Havana, where his father Julius Runge was the Danish consul. His mother was Fanny Schwartz Tolmé. The family later moved to Bremen, where his father died early (in 1864). In 1880, he received his Ph.D. in mathematics at Berlin, where he studied under Karl Weierstrass. In 1886, he became a professor at the Technische Hochschule Hannover in Hanover, Germany. His interests included mathematics, spectroscopy, geodesy, and astrophysics. In addition to pure mathematics, he did experimental work studying spectral lines of various elements (together with Heinrich Kayser), and was very interested in the application of this work to astronomical spectroscopy. In 1904, on the ini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adolf Piltz
Adolf Piltz (8 December 1855 – 1940) was a German mathematician who contributed to number theory. Piltz was arguably the first to formulate a generalized Riemann hypothesis, in 1884.Davenport, p. 124. Notes References *Harold Davenport, Davenport, Harold. ''Multiplicative number theory''. Third edition. Revised and with a preface by Hugh L. Montgomery. Graduate Texts in Mathematics, 74. Springer-Verlag, New York, 2000. xiv+177 pp. . Further reading * External links * 1855 births 1940 deaths 19th-century German mathematicians Humboldt University of Berlin alumni 20th-century German mathematicians Mathematicians from the German Empire {{Germany-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eugen Netto
Eugen Otto Erwin Netto (30 June 1848 – 13 May 1919) was a German mathematician. He was born in Halle and died in Giessen. Netto's theorem, on the dimension-preserving properties of continuous bijections, is named for Netto. Netto published this theorem in 1878, in response to Georg Cantor's proof of the existence of discontinuous bijections between the unit interval and unit square In mathematics, a unit square is a square whose sides have length . Often, ''the'' unit square refers specifically to the square in the Cartesian plane with corners at the four points ), , , and . Cartesian coordinates In a Cartesian coordinat .... His proof was not fully rigorous, but its errors were later repaired. Works''Substitutionentheorie und ihre Anwendung auf die Algebra.''Teubner 1882.''Theory of Substitutions and Its Applications to Algebra.''Ann Arbor, Mich. 1892.''Die Determinanten.''Teubner, 1910. *''Die Determinanten.'' Teubner, 2nd edition 1925.''Lehrbuch der Combinatorik. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hans Von Mangoldt
Hans Carl Friedrich von Mangoldt ( 1854 in Weimar– 1925 in Danzig) was a German mathematician who contributed to the solution of the prime number theorem. Biography Mangoldt completed his Doctorate of Philosophy (Ph.D) in 1878 at the University of Berlin, where his supervisors were Ernst Kummer and Karl Weierstrass. He contributed to the solution of the prime number theorem by providing rigorous proofs of two statements in Bernhard Riemann's seminal paper "On the Number of Primes Less Than a Given Magnitude". Riemann himself had only given partial proofs of these statements. Mangoldt worked as professor at the RWTH Aachen and was succeeded by Otto Blumenthal. See also * Prime-counting function * Cartan–Hadamard theorem * Riemann–von Mangoldt formula * Von Mangoldt function In mathematics, the von Mangoldt function is an arithmetic function named after German mathematician Hans von Mangoldt. It is an example of an important arithmetic function that is neither mu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathias Lerch
Mathias Lerch or Matyáš Lerch (; 20 February 1860, Milínov – 3 August 1922, Sušice) was a Czech mathematician who published about 250 papers, largely on mathematical analysis and number theory. He studied in Prague (Czech Technical University) and Berlin; subsequently held teaching positions at the University of Fribourg in Switzerland, the Brno University of Technology in Brno, and finally at then newly founded (1920) Masaryk University in Brno where he became its first mathematics professor. In 1900, he was awarded the Grand Prize of the French Academy of Sciences for his number-theoretic work. The Lerch zeta function is named after him, as is the Appell–Lerch sum. His doctoral students include Michel Plancherel and Otakar Borůvka Otakar Borůvka (10 May 1899 – 22 July 1995) was a Czech mathematician. He is best known for his work in graph theory.. Education and career Borůvka was born in Uherský Ostroh, a town in Moravia, Austria-Hungary (today in the Cze ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
