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53-850: Pringsheim was born in Ohlau, Province of Silesia (now Oława , Poland). He came from an extremely wealthy Silesian merchant family with Jewish roots. He was the first-born child and only son of the Upper Silesian railway entrepreneur and coal mine owner Rudolf Pringsheim (1821–1901) and his wife Paula, née Deutschmann (1827–1909). He had a younger sister, Martha. Pringsheim attended the Maria Magdalena Gymnasium in Breslau, where he excelled in music and mathematics. Starting in 1868 he studied mathematics and physics in Berlin and at

106-583: A Neo-Renaissance villa at Arcisstrasse 12 designed by the Berlin architects Kayser & von Großheim with interior furnishings provided by Joh. Wachter and the court furniture manufacturer O. Fritsche of Munich. On major social nights the Munich elite was hosted here in what was known as the Pringsheim Palace. There he had the Romantic painter Hans Thoma , of similar political affiliation, decorate

159-521: A lectureship in the University of Bordeaux , where he proved his celebrated inequality on determinants , which led to the discovery of Hadamard matrices when equality holds. In 1896 he made two important contributions: he proved the prime number theorem , using complex function theory (also proved independently by Charles Jean de la Vallée-Poussin ); and he was awarded the Bordin Prize of

212-482: A power series with positive coefficients and radius of convergence equal to 1 has necessarily a singularity at the point 1. This theorem is used in analytic combinatorics and the Perron–Frobenius theory of positive operators on ordered vector spaces . Another theorem named after Pringsheim gives an analyticity criterion for a C function on a bounded interval, based on the behaviour of the radius of convergence of

265-514: A province of Nazi Germany before being divided back into Upper Silesia and Lower Silesia. Breslau (present-day Wrocław, Poland ) was the provincial capital. The territory on both sides of the Oder river formed the southeastern part of the Prussian kingdom. It comprised the bulk of the former Bohemian crown land of Upper and Lower Silesia as well as the adjacent County of Kladsko , which

318-533: A year after the war ended, the parts of Silesia remaining in Weimar Germany were re-organized into the two provinces of Lower Silesia ( Niederschlesien ) and Upper Silesia ( Oberschlesien , the former Regierungsbezirk Oppeln ). After three Silesian Uprisings and the 1921 Upper Silesia plebiscite , the East Upper Silesian part of the province around the industrial city of Katowice

371-488: A “German patriot” he subscribed to war loans which lost their nominal value after the war, which meant the loss of a major part of his capital. The disastrous inflation of 1923 and 1924 resulted in additional high losses. As a result, he had to sell part of his art collection, which probably included a mural by Hans Thoma . He commented, ironically, “I live from wall to mouth”. He also had to sell his marvellous mathematics library which contained many precious books dating back to

424-696: Is less well known. Pringsheim's house was forceably sold to the Nazi party. It was torn down and replaced by a party administration building. The files of all German Nazi party members were stored there until 1945. Today it houses the Institute of Art History of Munich University (LMU) and the offices of the Munich State Collection of Antiquities, among others entities. Pringsheim died on 25 June 1941 in Zürich. His wife then apparently burned all of

477-660: The Enzyklopädie der mathematischen Wissenschaften on the fundamentals of arithmetic and on number theory. He published papers in the Mathematische Annalen . As an officer of the Bayerische Akademie der Wissenschaften , he recorded the minutes of its scientific meetings. He also proved a significant part of the Abel–Dini–Pringsheim theorem , a convergence test for a series in which

530-484: The method of descent in the theory of partial differential equations , culminating in his seminal book on the subject, based on lectures given at Yale University in 1922. Later in his life he wrote on probability theory and mathematical education . Hadamard was elected to the French Academy of Sciences in 1916, in succession to Poincaré , whose complete works he helped edit. He became foreign member of

583-539: The "Sokół" Polish Gymnastic Society , shut down Polish newspapers and seized the funds of Polish banks from the pre-war German Province of Silesia. The arrested Poles were deported to concentration camps. Polish church services were abolished, with the last Polish service held in the Saint Martin church in Wrocław on 17 September 1939. Soon the border was extended eastwards when parts of Polish Silesia were annexed into

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636-935: The Duchy of Warsaw and was made up of former parts of the Prussian and Austrian partitions . Congress Poland was in a personal union with the Russian Empire until 1867 when it was formally integrated as the Vistula Land . In the east lay the Austrian share, the Lesser Polish Kingdom of Galicia and Lodomeria with the Free City of Kraków until 1846, and in the south the remaining Bohemian crown lands of Austrian Silesia , Moravia and Bohemia proper. The incorporated Upper Lusatian strip of land in

689-458: The French Academy of Sciences for his work on geodesics in the differential geometry of surfaces and dynamical systems . In the same year he was appointed Professor of Astronomy and Rational Mechanics in Bordeaux. His foundational work on geometry and symbolic dynamics continued in 1898 with the study of geodesics on surfaces of negative curvature . For his cumulative work, he was awarded

742-740: The Prix Poncelet in 1898. After the Dreyfus affair , which involved him personally because his second cousin Lucie was the wife of Dreyfus, Hadamard became politically active and a staunch supporter of Jewish causes though he professed to be an atheist in his religion. In 1897 he moved back to Paris, holding positions in the Sorbonne and the Collège de France , where he was appointed Professor of Mechanics in 1909. In addition to this post, he

795-788: The Royal Netherlands Academy of Arts and Sciences in 1920. He was elected a foreign member of the Academy of Sciences of the USSR in 1929. He visited the Soviet Union in 1930 and 1934 and China in 1936 at the invitation of Soviet and Chinese mathematicians. Hadamard stayed in France at the beginning of the Second World War and escaped to southern France in 1940. The Vichy government permitted him to leave for

848-612: The Upper Silesian Coal Basin , there was considerable industrialization and urbanization in Upper Silesia and many people from neighbouring Posen and Congress Poland immigrated at that time. In 1871, Silesia became part of the German Empire as a province of Prussia following the unification of Germany . The Upper Silesian Industrial Region was the second largest industrial agglomeration of

901-633: The École Normale Supérieure , having placed first in the entrance examinations both there and at the École Polytechnique . His teachers included Tannery , Hermite , Darboux , Appell , Goursat , and Picard . He obtained his doctorate in 1892 and in the same year was awarded the Grand Prix des Sciences Mathématiques for his essay on the Riemann zeta function . In 1892 Hadamard married Louise-Anna Trénel, also of Jewish descent, with whom he had three sons and two daughters. The following year he took up

954-561: The Berlin actress Gertrude Hedwig Anna Dohm (1855–1942), whose mother was the Berlin advocate of women's rights Hedwig Dohm (1831–1919). They had five children: Erik (1879–1909), Peter (born 1881), Heinz (born 1882) and twins born in 1883, Klaus and Katharina, known as Katia . His first-born son, Erik, was exiled to Argentina because of his dissolute life and gambling debts and died there at an early age. His sons Peter and Klaus followed him in pursuing academic careers, obtaining professorships in physics and musical composition. One musician in

1007-889: The German Empire after the Ruhr area. Over decades the mainly Catholic Upper Silesian citizens in majority voted for the German Centre Party , while the Lower Silesian constituencies were dominated by the Free-minded Party and the Social Democrats . Ethnic tensions rose on the eve of World War I , with politicians like Wojciech Korfanty separating from the Centre Party and giving utterance to distinct Polish interests. In 1919,

1060-764: The Lutheran Church not to staff bilingual German-Sorbian parishes with new Sorbian preachers, and the Bund Deutscher Osten demanded a ban on Sorbian church masses, but only a limit of two such masses per month was imposed. There were instances of expulsions of Sorbian pastors. During the German invasion of Poland , which started World War II in September 1939, Gestapo carried out mass arrests of Polish activists, teachers, journalists, entrepreneurs, library directors and chairmen of local branches of

1113-491: The Mathematical Field , Hadamard uses the results of introspection to study mathematical thought processes, and tries to report and interpret observations, personal or gathered from other scholars engaged in the work of invention. In sharp contrast to authors who identify language and cognition , he describes his own mathematical thinking as largely wordless, often accompanied by mental images that represent

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1166-650: The Museum Boijmans Van Beuningen Foundation to restitute to them seven pieces of Italian maiolica that the museum had acquired by the collector J.N. Bastert. Research into paintings and other objects is ongoing. More than 400 artworks are registered with the German Lost Art Foundation in its Lostart database. Province of Silesia The Province of Silesia ( German : Provinz Schlesien ; Polish : Prowincja Śląska ; Silesian : Prowincyjŏ Ślōnskŏ )

1219-747: The Prussian King Frederick the Great had all conquered from the Austrian Habsburg monarchy under Empress Maria Theresa in the 18th century Silesian Wars . It included the northeastern part of Upper Lusatia around Görlitz and Lauban ( Lubań ), ceded to Prussia by the Kingdom of Saxony according to the resolutions of the Congress of Vienna in 1815. The province bordered on the Prussian heartland of Brandenburg (including

1272-524: The Prussian forces had conquered almost all of the Habsburg crown land in Silesia. According to the peace treaties of Breslau and Berlin , only some smaller parts in the extreme southeast, like the Duchy of Cieszyn as well as the southern parts of the duchies of Troppau and Nysa , remained possessions of the Habsburg monarchy as Austrian Silesia . Attempts by Maria Theresa to regain the crown land in

1325-606: The Prussian territories were reorganized upon the Congress of Vienna , the province of Silesia was created out of the territories acquired by Prussia in the Silesian Wars, as well as those Upper Lusatian territories which King Frederick Augustus I of Saxony had to relinquish due to his indecisive attitude in the Napoleonic Wars . As the lands had been part of the Holy Roman Empire until 1806, Silesia

1378-592: The Ruprecht Karl University in Heidelberg . In 1872 he was awarded a doctorate in mathematics, studying under Leo Königsberger . In 1875, he moved from Berlin, where his parents lived, to Munich to earn his habilitation . Two years later he became a lecturer at Ludwig Maximilian University in Munich. In 1886 Pringsheim was appointed associate professor of mathematics there, and in 1901 full professor. He retired as emeritus professor in 1922. He

1431-727: The Second Silesian War (1744–1745) failed and she ultimately had to relinquish her claims over Silesia by the Treaty of Dresden . The Third Silesian War (1756–1763), a theatre of the Seven Years' War , once again confirmed Prussian control over most of Silesia, and due to its predominantly Protestant population especially in Lower Silesia, it became one of the most loyal territories of the House of Hohenzollern . When

1484-551: The Silesian inhabitants were German –speaking, while a majority of the population to the east of the Oder river spoke Polish , including Silesian and Lach dialects . The indigenous Polish and Sorbian population was subjected to Germanisation policies. Sorbian-language Lutheran preparations for Confirmation were prohibited with the ban lifted only after World War I. Because of the extended iron ore and black coal deposits of

1537-480: The Taylor expansion around a point of the interval. However, Pringsheim's original proof had a flaw (related to uniform convergence ), and a correct proof was provided by Ralph P. Boas . Pringsheim and Ivan Śleszyński , working separately, proved what is now called the Śleszyński–Pringsheim theorem on convergence of certain continued fractions . Besides his research in analysis, Pringsheim also wrote articles for

1590-878: The United States in 1941 and he obtained a visiting position at Columbia University in New York. He moved to London in 1944 and returned to France when the war ended in 1945. Hadamard was awarded an honorary doctorate ( LL.D. ) by Yale University in October 1901, during celebrations for the bicentenary of the university. He was awarded the CNRS Gold medal for his lifetime achievements in 1956. He died in Paris in 1963, aged ninety-seven. Hadamard's students included Maurice Fréchet , Paul Lévy , Szolem Mandelbrojt , and André Weil . In his book Psychology of Invention in

1643-521: The character Samuel Spoelman. In mathematical analysis , Pringsheim studied real and complex functions , following the power-series -approach of the Weierstrass school. Pringsheim published numerous works on the subject of complex analysis , with a focus on the summability theory of infinite series and the boundary behavior of analytic functions. One of Pringsheim's theorems, according to Hadamard earlier proved by E. Borel , states that

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1696-422: The entire solution to a problem. He surveyed 100 of the leading physicists of the day (approximately 1900), asking them how they did their work. Hadamard described the experiences of the mathematicians/theoretical physicists Carl Friedrich Gauss , Hermann von Helmholtz , Henri Poincaré and others as viewing entire solutions with "sudden spontaneousness". Hadamard described the process as having four steps of

1749-489: The family was enough, so his third son, Heinz, became an archaeologist with a doctorate in that field, but soon changed course, becoming a successful conductor and critic in Berlin and Munich. His daughter Katia was the first female in Munich to earn the qualifications for university admission and was one of the first active women students at Munich University. She later became the wife of the author and Nobel Prize winner Thomas Mann . In 1889 Pringsheim and his family moved into

1802-471: The field of music. His association with Wagner was so intense that Pringsheim supported Wagner financially to a significant extent, and also backed the Bayreuth music festival. In gratitude, he received a certificate designating him as a patron, which guaranteed him a seat at certain performances. In her memoirs about this acquaintance with Wagner, his granddaughter, Erika Mann , wrote that Prof. Pringsheim

1855-654: The last minute, he and his wife were able to leave for Zürich , Switzerland on 31 October 1939 after suffering further grave humiliations. During Kristallnacht , in November 1938, the SS seized Pringsheim's maiolica collection from his home in Munich. His world famous collection of majolica was sold in a forced sale by the Nazis at Sotheby's in London in 1939 in exchange for permission to emigrate..The fate of his goldsmith collection

1908-654: The music room. Besides mathematics, ever since his youth Pringsheim was also intensively occupied with music, and adapted various compositions of Richard Wagner for the piano. Later he became interested in the theory and history of art, building up important collections of majolica earthenware and silver. His was the largest and most important private collection of majolica in Germany consisting of 440 pieces. He also collected enamels, stained-glass panels, tapestries, and paintings by Franz von Lenbach . In his novel Royal Highness , Thomas Mann portrayed his father-in-law as

1961-655: The newly acquired lands of Lower Lusatia ) in the northwest, and on the Grand Duchy of Posen ( Province of Posen from 1848) in the north, i.e. the Greater Polish lands that before the 18th century Partitions of Poland had belonged to the Polish–Lithuanian Commonwealth . In the northeast, Upper Silesia bordered on Congress Poland , i.e. the Kingdom of Poland which had been reconstituted from

2014-401: The nth term is divided by the nth partial sum. Pringsheim had a deep, early interest in music and was especially fascinated by the works of Richard Wagner . He corresponded with Wagner personally, and he took Wagner's letters with him when he went into exile to Switzerland. His musical inclinations led to the publication of several arrangements of Wagner's work, and he also wrote on subjects in

2067-446: The personal effects which had been brought to Switzerland, including the letters from Richard Wagner . She died one year later. Pringheim's heirs have requested that artworks looted by the Nazis and sold in forced sales be returned to the family. According to Christie's some of the works were restituted in 1953. However, other sources specify that there was a financial settlement with the German government. In 2008 Pringheim's heirs asked

2120-427: The province intensified in 1938–1939 with expulsions of Polish activists, distributors of Polish press, priests, craftsmen, farmers, students etc., attacks on Polish cultural centers, banks, enterprises, schools, churches and houses, seizure of Polish libraries, confiscations of Polish press, arrests and deportations of Polish activists to concentration camps and even assassinations. In 1938, Nazi authorities forced

2173-916: The province of Silesia was divided again by reverting into Upper Silesia and Lower Silesia. In the Prussian census of 1890, the province of Silesia had a population of 4,224,458, of which 3,105,843 (73.52%) spoke German , 973,596 (23.05%) spoke Polish , 68,781 (1.63%) spoke Czech , 26,257 (0.62%) spoke Sorbian and 48,045 (1.14%) identified as bilingual. Regierungsbezirk Liegnitz - 1,047,405 (96.41% German, 2.51% Sorbian, 0.53% Polish, 0.11% Czech, 0.38% bilingual). Regierungsbezirk Breslau - 1,599,322 (95.63% German, 3.08% Polish, 0.59% Czech, 0.64% bilingual). Regierungsbezirk Oppeln - 1,577,731 (58.23% Polish, 35.91% German, 3.69% Czech, 2.14% bilingual). Regierungsbezirk Breslau Regierungsbezirk Liegnitz Regierungsbezirk Oppeln Hadamard Jacques Salomon Hadamard ForMemRS ( French: [adamaʁ] ; 8 December 1865 – 17 October 1963)

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2226-577: The province. In the annexed pre-war Polish part the occupiers conducted the genocidal Intelligenzaktion campaign and expulsions of Poles . The Germans also established the Gross-Rosen concentration camp and multiple prisoner-of-war camps with numerous forced labour subcamps in the region, including Stalag VIII-A , Stalag VIII-B , Stalag VIII-C , Stalag VIII-E , Oflag VIII-A, Oflag VIII-B, Oflag VIII-C, Oflag VIII-F , for Polish POWs and civilians, and French , Belgian, Dutch and later also other Allied POWs. On 27 January 1941, during World War II,

2279-436: The sixteenth century. The auction catalogue is still preserved in the Bayerische Staatsbibliothek . When the Nazis came to power in 1933, Pringsheim was persecuted because of his Jewish origins. In 1933, the Nazis seized the Pringsheim Palace. In 1934, he refused to take a loyalty oath to Hitler's Nazi government. The Pringheim's passports were canceled by the Nazi authorities in early 1937. Primarily because of his age (he

2332-424: The west touched the remaining territory of the Saxon kingdom and in the furthest west the Prussian Province of Saxony . The coronation of Maria Theresa as queen regnant of the Kingdom of Bohemia immediately triggered an invasion of the region of Silesia by King Frederick the Great of Prussia , thereby starting the War of the Austrian Succession (1740–1748). By the end of the First Silesian War in 1742,

2385-431: Was a province of Prussia from 1815 to 1919. The Silesia region was part of the Prussian realm since 1742 and established as an official province in 1815, then became part of the German Empire in 1871. In 1919, as part of the Free State of Prussia within Weimar Germany , Silesia was divided into the provinces of Upper Silesia and Lower Silesia . Silesia was reunified briefly from 1 April 1938 to 27 January 1941 as

2438-412: Was a French mathematician who made major contributions in number theory , complex analysis , differential geometry , and partial differential equations . The son of a teacher, Amédée Hadamard, of Jewish descent, and Claire Marie Jeanne Picard, Hadamard was born in Versailles, France and attended the Lycée Charlemagne and Lycée Louis-le-Grand , where his father taught. In 1884 Hadamard entered

2491-399: Was among the western Prussian provinces that lay within the borders of the German Confederation . In 1815, after the Napoleonic wars, Prussian Silesia was formally reorganized into the province of Silesia. The character of the province's eastern third, Upper Silesia, had been much lesser shaped by the medieval German Ostsiedlung . According to the census of 1905, about three-quarters of

2544-403: Was appointed to chairs of analysis at the École Polytechnique in 1912 and at the École Centrale in 1920, succeeding Jordan and Appell. In Paris Hadamard concentrated his interests on the problems of mathematical physics, in particular partial differential equations , the calculus of variations and the foundations of functional analysis . He introduced the idea of well-posed problem and

2597-487: Was elected a member of the Bavarian Academy of Sciences in 1898, a position he held until 1938, and was a corresponding member of the Göttingen Academy of Sciences. He was also awarded membership in the Leopoldina , Germany's oldest academy of natural sciences. Pringsheim considered himself to be a German citizen who no longer followed the "Mosaic belief" (meaning conservative or orthodox Judaism ). He repeatedly declined to have himself baptized. In 1878 Pringsheim married

2650-488: Was even once involved in a duel because someone had insulted Wagner. His family's fortune left Pringsheim a wealthy man. He also had a sizeable monthly income as a full professor at the university. After the death of the family patriarch in 1913 he had at his disposal assets amounting to 13 million marks and an annual income of 800,000 marks, which is today equivalent to 10.5 million euro and 646,000 euro, respectively. Pringsheim's financial decline began with World War I . As

2703-399: Was in his mid-80s) he did not want to go abroad, as did most of his family, and remained in Germany. One of many antisemitic pieces of Nazi legislation, the Namensänderungsverordnung  [ de ] which came into effect 1 January 1938, forced him to legally change his name into Alfred Israel Pringsheim at age 87. At first, he was not allowed to leave the country. Winifred Wagner

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2756-403: Was not able to help the elderly Wagner devotee in this respect. Through the intervention of the then-rector of Munich University ( LMU ), his former neighbor Karl Haushofer , who was a friend of Rudolf Hess , and the professor of mathematics Oskar Perron , one of Alfred Pringsheim's former students, as well as through the initiative of a courageous member of the SS who arranged for passports at

2809-418: Was transferred to the Second Polish Republic and incorporated into the Silesian Voivodeship in 1922. In 1920 the Hlučín Region was ceded to Czechoslovakia according to the Treaty of Versailles . ( Niederschlesiens Ostmark ) On 1 April 1938 the province of Silesia was re-established by Nazi Germany by uniting the existing Upper Silesia and Lower Silesia provinces. Nazi German persecution of Poles in

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