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71-543: The university was founded in 1945, replacing the previous German University of Breslau . Following the territorial changes of Poland's borders , academics primarily from the Jan Kazimierz University of Lwów restored the university building, which had been heavily damaged in the 1945 Battle of Breslau . The oldest mention of a university in Wrocław comes from the foundation deed signed on 20 July 1505 for

142-402: A chemical veterinary institute, a veterinary institute, and a technological institute, was added to the university in 1881. In 1884, the university had 1,481 students in attendance, with a faculty numbering 131. The library in 1885 consisted of approximately 400,000 works, including about 2,400 incunabula, approximately 250 Aldines, and 2,840 manuscripts. These volumes came from the libraries of

213-478: A couple of papers in 1838 and 1839, he proved the first class number formula for quadratic forms (later refined by his student Kronecker). The formula, which Jacobi called a result "touching the utmost of human acumen", opened the way for similar results regarding more general number fields . Based on his research of the structure of the unit group of quadratic fields , he proved the Dirichlet unit theorem ,

284-479: A fundamental result in algebraic number theory . He first used the pigeonhole principle , a basic counting argument, in the proof of a theorem in diophantine approximation , later named after him Dirichlet's approximation theorem . He published important contributions to Fermat's Last Theorem , for which he proved the cases n  = 5 and n  = 14 , and to the biquadratic reciprocity law . The Dirichlet divisor problem , for which he found

355-623: A merchant. The young Dirichlet, who showed a strong interest in mathematics before age 12, persuaded his parents to allow him to continue his studies. In 1817 they sent him to the Gymnasium Bonn  [ de ] under the care of Peter Joseph Elvenich , a student his family knew. In 1820, Dirichlet moved to the Jesuit Gymnasium in Cologne , where his lessons with Georg Ohm helped widen his knowledge in mathematics. He left

426-668: A musician and perhaps been leader of a group. Next to Felix and Fanny, I could not aspire to any recognition. In 1832 she married Dirichlet, who was introduced to the Mendelssohn family by Alexander von Humboldt . In 1833 their first son, Walter, was born. She died in Göttingen in 1858. As soon as he came to Berlin, Dirichlet applied to lecture at the University of Berlin , and the Education Minister approved

497-573: A numerus clausus law that limited the number of Jews from non-German Eastern Europe (so called Ostjuden ) that could study in Germany to at most 900. The University of Breslau was allowed to take 100. As Germany turned to Nazism , the university became influenced by Nazi ideology . Polish students were beaten by NSDAP members just for speaking Polish. In 1939, all Polish students were expelled and an official university declaration stated, "We are deeply convinced that [another] Polish foot will never cross

568-458: A philological seminar, a seminar for German Philology, another seminar for Romanic and English philology, an historical seminar, a mathematical-physical one, a legal state seminar, and a scientific seminar. From 1842, the university also had a chair of Slavic Studies . The university had twelve different scientific institutes, six clinical centers, and three collections. An agricultural institute with ten teachers and forty-four students, comprising

639-471: A private tutor to teach his children German , the wage finally allowing Dirichlet to become independent from his parents' financial support. His first original research, comprising part of a proof of Fermat's Last Theorem for the case n  = 5 , brought him immediate fame, being the first advance in the theorem since Fermat 's own proof of the case n  = 4 and Euler 's proof for n  = 3 . Adrien-Marie Legendre , one of

710-501: A rigorous proof of convergence. The memoir pointed out Cauchy's mistake and introduced Dirichlet's test for the convergence of series. It also introduced the Dirichlet function as an example of a function that is not integrable (the definite integral was still a developing topic at the time) and, in the proof of the theorem for the Fourier series, introduced the Dirichlet kernel and the Dirichlet integral . Dirichlet also studied

781-637: A role. The first successful founding deed known as the Aurea bulla fundationis Universitatis Wratislaviensis was signed two centuries later, on 1 October 1702, by the Holy Roman Emperor Leopold I of the House of Austria, King of Hungary and Bohemia. The predecessor facilities, which existed since 1638, were converted into Jesuit school, and finally, upon instigation of the Jesuits and with

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852-617: A royal pensioner, their friendship becoming even closer. In 1846, when the Heidelberg University tried to recruit Dirichlet, Jacobi provided von Humboldt the needed support to obtain a doubling of Dirichlet's pay at the university in order to keep him in Berlin; however, even then he was not paid a full professor wage and could not leave the Military Academy. Holding liberal views, Dirichlet and his family supported

923-477: A small community 5 km (3 miles) north east of Liège in Belgium , from which his surname "Lejeune Dirichlet" (" le jeune de Richelette ", French for "the youth from Richelette") was derived. Although his family was not wealthy and he was the youngest of seven children, his parents supported his education. They enrolled him in an elementary school and then private school in hope that he would later become

994-779: Is Lejeune Dirichlet, he is commonly referred to by his mononym Dirichlet , in particular for results named after him. Gustav Lejeune Dirichlet was born on 13 February 1805 in Düren , a town on the left bank of the Rhine which at the time was part of the First French Empire , reverting to Prussia after the Congress of Vienna in 1815. His father Johann Arnold Lejeune Dirichlet was the postmaster, merchant, and city councilor. His paternal grandfather had come to Düren from Richelette (or more likely Richelle  [ fr ] ),

1065-430: Is credited with introducing the modern concept of a function, as opposed to the older vague understanding of a function as an analytic formula. Imre Lakatos cites Hermann Hankel as the early origin of this attribution, but disputes the claim saying that "there is ample evidence that he had no idea of this concept [...] for instance when he discusses piecewise continuous functions, he says that at points of discontinuity,

1136-718: Is preserved in the department of physiology at the University of Göttingen, along with the brain of Gauss. The Academy in Berlin honored him with a formal memorial speech presented by Kummer in 1860, and later ordered the publication of his collected works edited by Kronecker and Lazarus Fuchs . Number theory was Dirichlet's main research interest, a field in which he found several deep results and in proving them introduced some fundamental tools, many of which were later named after him. In 1837, Dirichlet proved his theorem on arithmetic progressions using concepts from mathematical analysis to tackle an algebraic problem, thus creating

1207-541: The 1848 revolution ; he even guarded with a rifle the palace of the Prince of Prussia. After the revolution failed, the Military Academy closed temporarily, causing him a large loss of income. When it reopened, the environment became more hostile to him, as officers he was teaching were expected to be loyal to the constituted government. Some of the press who had not sided with the revolution pointed him out, as well as Jacobi and other liberal professors, as "the red contingent of

1278-591: The Generale litterarum Gymnasium in Wrocław by King Vladislaus II of Hungary ( Polish : Władysław II Jagiellończyk ) of the Polish Jagiellonian dynasty . However, the new academic institution requested by the town council was not built, because the King's deed was rejected by Pope Julius II for political reasons. Also, the numerous wars and opposition from the University of Kraków might have played

1349-580: The Königliche Universität zu Breslau – Universitas litterarum Vratislaviensis (in 1911 named the Schlesische Friedrich-Wilhelms-Universität zu Breslau , to honour the founder Frederick William III of Prussia ). At first, the conjoint academy had five faculties: philosophy, medicine, law, Protestant theology, and Catholic theology. Connected with the university were three theological seminars,

1420-683: The Potsdam Conference of August 1945 exactly as proposed by Stalin who already controlled the whole of East-Central Europe . Harry Truman remembered: I remember at Potsdam, we got to discussing a matter in eastern Poland, and it was remarked by the Prime Minister of Great Britain that the Pope would not be happy over the arrangement of that Catholic end of Poland. And the Generalissimo, the Prime Minister of Russia leaned on

1491-590: The Soviet occupation zone of Germany or the subsequent state of East Germany . The German population who had stayed at or had returned to their homes were forcibly expelled before these Recovered Territories (official term) were repopulated by Poles expelled from the eastern regions and those from central Poland. The borders of Poland resembled the borders of the German-Russian gains in World War 2, with

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1562-481: The University of Göttingen decided to call Dirichlet as his successor. Given the difficulties faced in Berlin, he decided to accept the offer and immediately moved to Göttingen with his family. Kummer was called to assume his position as a professor of mathematics in Berlin. Dirichlet enjoyed his time in Göttingen, as the lighter teaching load allowed him more time for research and he came into close contact with

1633-644: The central limit theorem . The Dirichlet distribution and the Dirichlet process , based on the Dirichlet integral , are named after him. Dirichlet was elected as a member of several academies: In 1855 Dirichlet was awarded the civil class medal of the Pour le Mérite order at Alexander von Humboldt 's recommendation. The Dirichlet crater on the Moon and the 11665 Dirichlet asteroid are named after him. A complete bibliography of Dirichlet's published works, including translations thereof and lectures not contained in

1704-647: The former territory of Germany east of the Oder–Neisse line , consisting of the southern portion of East Prussia and most of Pomerania , Neumark (East Brandenburg), and German Silesia . Poland also received the town of Swinemünde (now Świnoujście ) on the island of Usedom and the city of Stettin (now Szczecin ) on the western bank of the Oder river in accordance with the Potsdam Agreement . Therefore, these transferred territories did not then form part of

1775-563: The Academy had also put Dirichlet in close contact with Fourier and Poisson , who raised his interest in theoretical physics , especially Fourier's analytic theory of heat . As General Foy died in November 1825 and he could not find any paying position in France, Dirichlet had to return to Prussia. Fourier and Poisson introduced him to Alexander von Humboldt , who had been called to join

1846-550: The Berlin Academy and, in 1842, obtained for him a full professor position at the University of Breslau. In 1840 Kummer married Ottilie Mendelssohn, a cousin of Rebecka's. In 1843, when Jacobi fell ill, Dirichlet traveled to Königsberg to help him, then obtained for him the assistance of King Friedrich Wilhelm IV 's personal physician. When the physician recommended that Jacobi spend some time in Italy, Dirichlet joined him on

1917-511: The German areas east of the rivers Oder and Neisse (see Recovered Territories ), pending a final peace conference with Germany. Since a peace conference never took place, the lands were effectively ceded by Germany. The population transfer of both Polish and Germans 1945–46 included many millions of people. The Polish territory in 1919–39 covered an area of 386,418 square kilometres (149,197 square miles). But from 1947, Poland's territory

1988-620: The Lwów Library, the Jan Kazimierz University and Ossoliński National Institute moved to the city. In mid-1948, over 60% of professors at the Wrocław University and Polytechnic were from Kresy , with academics from prewar Lwów playing a particularly important role in the newly established Polish institutions of higher learning. Stanisław Kulczyński from the University of Lwów was nominated the first president of

2059-617: The Military School. In 1832 Dirichlet became a member of the Prussian Academy of Sciences , the youngest member at only 27 years old. Dirichlet had a good reputation with students for the clarity of his explanations and enjoyed teaching, especially as his University lectures tended to be on the more advanced topics in which he was doing research: number theory (he was the first German professor to give lectures on number theory), analysis and mathematical physics . He advised

2130-1060: The Republic of Poland (1947–52). In 2015, nearly 80 years after the fact, the university restored academic degrees stripped from German Jews by the Nazis owing to German anti-Semitism. "Wroclaw University estimates that in total some 262 people suffered a similar fate." There are 10 faculties that provide 44 areas of study, in which the language medium is mostly in Polish, with only some in English. The University of Wrocław provides Bachelor, Master, and Doctoral level programmes. The degree certificates awarded by UWr are recognised globally. Honorary Doctorates [REDACTED] Media related to Wrocław University at Wikimedia Commons 51°6′49″N 17°2′0″E  /  51.11361°N 17.03333°E  / 51.11361; 17.03333 Territorial changes of Poland immediately after World War II At

2201-434: The University of Breslau. The probation was extended for three years until the position becoming definite in 1831. After Dirichlet's move to Berlin, Humboldt introduced him to the great salons held by the banker Abraham Mendelssohn Bartholdy and his family. Their house was a weekly gathering point for Berlin artists and scientists, including Abraham's children Felix and Fanny Mendelssohn , both outstanding musicians, and

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2272-557: The branch of analytic number theory . In proving the theorem, he introduced the Dirichlet characters and L-functions . In that article, he also noted the difference between the absolute and conditional convergence of series and its impact in what was later called the Riemann series theorem . In 1841, he generalized his arithmetic progressions theorem from integers to the ring of Gaussian integers Z [ i ] {\displaystyle \mathbb {Z} [i]} . In

2343-532: The chemical laboratory; the physiological plant; a mineralogical institute; an anatomical institute; clinical laboratories; a gallery (mostly from churches, monasteries, etc.) full of old German works; the museum of Silesian antiquities; and the state archives of Silesia. In the late 19th century, numerous internationally renowned and historically notable scholars lectured at the University of Breslau, Peter Gustav Lejeune Dirichlet , Ferdinand Cohn , and Gustav Kirchhoff among them. In 1817, Poles made up around 16% of

2414-496: The collection of the university library perished during the Soviet offensive in 1945, burned by soldiers on 10 May 1945, four days after the German garrison surrendered the city. Very quickly, some buildings were repaired, and a cadre of professors was built up, many coming from prewar Polish Jan Kazimierz University of Lwów and Stefan Batory University of Wilno. Following postwar border shifts , thousands of former employees of

2485-504: The court of King Friedrich Wilhelm III . Humboldt, planning to make Berlin a center of science and research, immediately offered his help to Dirichlet, sending letters in his favour to the Prussian government and to the Prussian Academy of Sciences . Humboldt also secured a recommendation letter from Gauss, who upon reading his memoir on Fermat's theorem wrote with an unusual amount of praise that "Dirichlet showed excellent talent". With

2556-475: The curriculum, raising the level of scientific education there. However, he gradually started feeling that his double teaching load, at the Military academy and at the university, was limiting the time available for his research. While in Berlin, Dirichlet kept in contact with other mathematicians. In 1829, during a trip, he met Carl Jacobi , at the time professor of mathematics at Königsberg University . Over

2627-761: The decisions made first by the Allies at the Tehran Conference of 1943 where the Soviet Union demanded the recognition of the line proposed by British Foreign Secretary Lord Curzon in 1920. The same Soviet stance was repeated by Joseph Stalin again at the Yalta Conference with Franklin D. Roosevelt and Winston Churchill in February 1945, but much more forcefully in the face of the looming German defeat. The new borders were ratified at

2698-520: The doctoral theses of several important German mathematicians, as Gotthold Eisenstein , Leopold Kronecker , Rudolf Lipschitz and Carl Wilhelm Borchardt , while being influential in the mathematical formation of many other scientists, including Elwin Bruno Christoffel , Wilhelm Weber , Eduard Heine , Ludwig von Seidel and Julius Weingarten . At the Military Academy, Dirichlet managed to introduce differential and integral calculus in

2769-627: The end of World War II , Poland underwent major changes to the location of its international border. In 1945, after the defeat of Nazi Germany , the Oder–Neisse line became its western border, resulting in gaining the Recovered Territories from Germany. The Curzon Line became its eastern border, resulting in the loss of the Eastern Borderlands to the Soviet Union . These decisions were in accordance with

2840-455: The exception of the city of Bialystok. This is called the Curzon line. The small area of Trans-Olza , which had been annexed by Poland in late 1938, was returned to Czechoslovakia on Stalin's orders. Peter Gustav Lejeune Dirichlet Johann Peter Gustav Lejeune Dirichlet ( / ˌ d ɪər ɪ ˈ k l eɪ / ; German: [ləˈʒœn diʁiˈkleː] ; 13 February 1805 – 5 May 1859)

2911-524: The first boundary-value problem , for the Laplace equation , proving the uniqueness of the solution; this type of problem in the theory of partial differential equations was later named the Dirichlet problem after him. A function satisfying a partial differential equation subject to the Dirichlet boundary conditions must have fixed values on the boundary. In the proof he notably used the principle that

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2982-574: The first results by introducing the Dirichlet hyperbola method , is still an unsolved problem in number theory despite later contributions by other mathematicians. Inspired by the work of his mentor in Paris, Dirichlet published in 1829 a famous memoir giving the conditions , showing for which functions the convergence of the Fourier series holds. Before Dirichlet's solution, not only Fourier, but also Poisson and Cauchy had tried unsuccessfully to find

3053-516: The former universities of Frankfurt and Breslau and from disestablished monasteries, and also included the oriental collections of the Bibliotheca Habichtiana and the academic Leseinstitut . In addition, the university owned an observatory; a five-hectare botanical garden ; a botanical museum and a zoological garden founded in 1862 by a joint-stock company; a natural history museum ; zoological, chemical, and physical collections;

3124-628: The function has two values". Dirichlet also worked in mathematical physics , lecturing and publishing research in potential theory (including the Dirichlet problem and Dirichlet principle mentioned above), the theory of heat and hydrodynamics . He improved on Lagrange 's work on conservative systems by showing that the condition for equilibrium is that the potential energy is minimal. Dirichlet also lectured on probability theory and least squares , introducing some original methods and results, in particular for limit theorems and an improvement of Laplace's method of approximation related to

3195-470: The gymnasium a year later with only a certificate, as his inability to speak fluent Latin prevented him from earning the Abitur . Dirichlet again persuaded his parents to provide further financial support for his studies in mathematics, against their wish for a career in law. As Germany provided little opportunity to study higher mathematics at the time, with only Gauss at the University of Göttingen who

3266-616: The names Rebecka Henriette Mendelssohn Bartholdy. She became a part of the notable salon of her parents, Abraham Mendelssohn and his wife Lea, having social contacts with the important musicians, artists and scientists in a highly creative period of German intellectual life. In 1829 she sang a small role in the premiere, given at the Mendelssohn house, of Felix's Singspiel Die Heimkehr aus der Fremde . She later wrote: My older brother and sister stole my reputation as an artist. In any other family I would have been highly regarded as

3337-454: The new generation of researchers, especially Richard Dedekind and Bernhard Riemann . After moving to Göttingen he was able to obtain a small annual stipend for Riemann to retain him in the teaching staff there. Dedekind, Riemann, Moritz Cantor and Alfred Enneper , although they had all already earned their PhDs, attended Dirichlet's classes to study with him. Dedekind, who felt that there were gaps in his mathematics education, considered that

3408-437: The occasion to study with Dirichlet made him "a new human being". He later edited and published Dirichlet's lectures and other results in number theory under the title Vorlesungen über Zahlentheorie ( Lectures on Number Theory ). In the summer of 1858, during a trip to Montreux , Dirichlet suffered a heart attack. On 5 May 1859, he died in Göttingen, several months after the death of his wife Rebecka. Dirichlet's brain

3479-574: The painter Wilhelm Hensel (Fanny's husband). Dirichlet showed great interest in Abraham's daughter Rebecka, whom he married in 1832. Rebecka Henriette Lejeune Dirichlet (née Rebecka Mendelssohn; 11 April 1811 – 1 December 1858) was a granddaughter of Moses Mendelssohn and the youngest sister of Felix Mendelssohn and Fanny Mendelssohn . Rebecka was born in Hamburg . In 1816 her parents arranged for her to be baptised at which point she took

3550-725: The problem by awarding him an honorary doctorate in February 1827. Also, the Minister of Education granted him a dispensation for the Latin disputation required for the Habilitation . Dirichlet earned the Habilitation and lectured in the 1827–28 year as a Privatdozent at Breslau . While in Breslau, Dirichlet continued his number-theoretic research, publishing important contributions to the biquadratic reciprocity law which at

3621-472: The referees, soon completed the proof for this case; Dirichlet completed his own proof a short time after Legendre, and a few years later produced a full proof for the case n  = 14 . In June 1825 he was accepted to lecture on his partial proof for the case n  = 5 at the French Academy of Sciences , an exceptional feat for a 20-year-old student with no degree. His lecture at

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3692-506: The solution is the function that minimizes the so-called Dirichlet energy . Riemann later named this approach the Dirichlet principle , although he knew it had also been used by Gauss and by Lord Kelvin . While trying to gauge the range of functions for which convergence of the Fourier series can be shown, Dirichlet defines a function by the property that "to any x there corresponds a single finite y ", but then restricts his attention to piecewise continuous functions. Based on this, he

3763-422: The staff". In 1849 Dirichlet participated, together with his friend Jacobi, in the jubilee of Gauss's doctorate. Despite Dirichlet's expertise and the honours he received, and even though, by 1851, he had finally completed all formal requirements for a full professor, the issue of raising his pay at the university still dragged on and he was still unable to leave the Military Academy. In 1855, upon Gauss's death,

3834-481: The student body. At the end of the 19th century around 10% of the students were Polish and 16% were Jewish . This situation reflected the multi ethnic and international character of the university. Both minorities, as well as the German students, established their own student organisations, called Burschenschaften . Polish student organisations included Concordia, Polonia, and a branch of the Sokol association. Many of

3905-640: The students came from other areas of partitioned Poland. The Jewish students unions were the Viadrina (founded 1886) and the Student Union (1899). Teutonia , a German Burschenschaft founded in 1817, was actually one of the oldest student fraternities in Germany, founded only two years after the Urburschenschaft . The Polish fraternities were all eventually disbanded by the German professor Felix Dahn , and in 1913 Prussian authorities established

3976-469: The support of Humboldt and Gauss, Dirichlet was offered a teaching position at the University of Breslau . However, as he had not passed a doctoral dissertation, he submitted his memoir on the Fermat theorem as a thesis to the University of Bonn . Again his lack of fluency in Latin rendered him unable to hold the required public disputation of his thesis; after much discussion, the university decided to bypass

4047-552: The support of the Silesian Oberamtsrat (Second Secretary) Johannes Adrian von Plencken, donated as a university in 1702 by Emperor Leopold I as a School of Philosophy and Catholic Theology with the designated name Leopoldina . On 15 November 1702, the university opened. Johannes Adrian von Plencken also became chancellor of the university. As a Catholic institute in Protestant Breslau, the new university

4118-537: The table, and he pulled his mustache like that, and looked over to Mr. Churchill and said: Mr. Churchill, Mr. Prime Minister, how many divisions did you say the Pope had? Large territories of Polish Second Republic were ceded to the Soviet Union by the Moscow-backed Polish government, and today form part of Lithuania , Belarus and Ukraine . Poland was instead given the Free State of Danzig and

4189-635: The territories ceded to the Soviet Union. The prewar eastern Polish territories of Kresy , which the Red Army had overrun during the Nazi-Soviet invasion of Poland in 1939 (excluding the Białystok region) were permanently ceded to the USSR by the new Polish communist government, and most of their Polish inhabitants expelled . As a result of the Potsdam Agreement to which Poland's government-in-exile

4260-478: The threshold of this German university". In that same year, German scholars from the university worked on a scholarly thesis of historical justification for a "plan of mass deportation in Eastern territories"; among the people involved was Walter Kuhn , a specialist of Ostforschung . Other projects during World War II involved creating evidence to justify German annexation of Polish territories, and presenting Kraków and Lublin as German cities. In January 2015,

4331-421: The time was a focal point of Gauss's research. Alexander von Humboldt took advantage of these new results, which had also drawn enthusiastic praise from Friedrich Bessel , to arrange for him the desired transfer to Berlin. Given Dirichlet's young age (he was 23 years old at the time), Humboldt was able to get him only a trial position at the Prussian Military Academy in Berlin while remaining nominally employed by

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4402-501: The transfer and in 1831 assigned him to the faculty of philosophy . The faculty required him to undertake a renewed habilitation qualification, and although Dirichlet wrote a Habilitationsschrift as needed, he postponed giving the mandatory lecture in Latin for another 20 years, until 1851. As he had not completed this formal requirement, he remained attached to the faculty with less than full rights, including restricted emoluments, forcing him to keep in parallel his teaching position at

4473-408: The trip together with his family. They were accompanied to Italy by Ludwig Schläfli , who came as a translator; as he was strongly interested in mathematics, both Dirichlet and Jacobi lectured to him during the trip, and he later became an important mathematician himself. The Dirichlet family extended their stay in Italy to 1845, their daughter Flora being born there. In 1844, Jacobi moved to Berlin as

4544-513: The two Polish universities in Wrocław, while Edward Sucharda from the Lwów Polytechnic became the vice-president. The University of Wrocław was refounded as a Polish state university by the decree of the State National Council issued on 24 August 1945. The first lecture was given on 15 November 1945, by Ludwik Hirszfeld . Between 1952 and 1989 the university was named Bolesław Bierut University of Wrocław (Polish: Uniwersytet Wrocławski im. Bolesława Bieruta ) after Bolesław Bierut , President of

4615-428: The university restored 262 PhD degrees stripped during the Nazi period from Jews and other scholars seen as hostile to the Nazis. After the Siege of Breslau , the Red Army took the city in May 1945. Breslau, now known as Wrocław, became part of the Republic of Poland . The first Polish team of academics arrived in Wrocław in late May 1945 and took custody of the university buildings, which were 70% destroyed. Parts of

4686-440: The years they kept meeting and corresponding on research matters, in time becoming close friends. In 1839, during a visit to Paris, Dirichlet met Joseph Liouville , the two mathematicians becoming friends, keeping in contact and even visiting each other with the families a few years later. In 1839, Jacobi sent Dirichlet a paper by Ernst Kummer , at the time a schoolteacher. Realizing Kummer's potential, they helped him get elected in

4757-424: Was a German mathematician . In number theory , he proved special cases of Fermat's last theorem and created analytic number theory . In analysis , he advanced the theory of Fourier series and was one of the first to give the modern formal definition of a function . In mathematical physics, he studied potential theory , boundary-value problems , and heat diffusion , and hydrodynamics . Although his surname

4828-495: Was an important instrument of the Counter-Reformation in Silesia. After Silesia passed to Prussia , the university lost its ideological character, but remained a religious institution for the education of Catholic clergy in Prussia. After the defeat of Prussia by Napoleon and the subsequent reorganisation of the Prussian state, the academy was merged on 3 August 1811 with the Protestant Viadrina University , previously located in Frankfurt (Oder) , and re-established in Breslau as

4899-447: Was nominally a professor of astronomy and anyway disliked teaching, Dirichlet decided to go to Paris in May 1822. There he attended classes at the Collège de France and at the University of Paris , learning mathematics from Hachette among others, while undertaking private study of Gauss's Disquisitiones Arithmeticae , a book he kept close for his entire life. In 1823 he was recommended to General Maximilien Foy , who hired him as

4970-412: Was not invited, Poland lost 179,000 square kilometres (69,000 square miles) (45%) of prewar territories in the east, including over 12 million citizens of whom 4.3 million were Polish-speakers. Today, these territories are part of sovereign Belarus , Ukraine , and Lithuania . In turn, postwar Poland was assigned considerably smaller territories to the west including the prewar Free City of Danzig and

5041-418: Was reduced to 312,679 square kilometres (120,726 square miles), so the country lost 73,739 square kilometres (28,471 square miles) of land. This difference amounts almost to the size of the Czech Republic , although Poland ended up with a much longer coastline on the Baltic Sea compared to its 1939 borders. In addition, the infrastructure in the former eastern territories of Germany was more developed than in

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