Holy Roman Empire
The Holy Roman Empire was a multi-ethnic complex of territories in Western and Central Europe that developed during the Early Middle Ages and continued until its dissolution in 1806 during the Napoleonic Wars. The largest territory of the empire after 962 was the Kingdom of Germany, though it came to include the neighboring Kingdom of Bohemia, the Kingdom of Burgundy, the Kingdom of Italy, numerous other territories. On 25 December 800, Pope Leo III crowned the Frankish king Charlemagne as Emperor, reviving the title in Western Europe, more than three centuries after the fall of the earlier ancient Western Roman Empire in 476; the title continued in the Carolingian family until 888 and from 896 to 899, after which it was contested by the rulers of Italy in a series of civil wars until the death of the last Italian claimant, Berengar I, in 924. The title was revived again in 962 when Otto I was crowned emperor, fashioning himself as the successor of Charlemagne and beginning a continuous existence of the empire for over eight centuries.
Some historians refer to the coronation of Charlemagne as the origin of the empire, while others prefer the coronation of Otto I as its beginning. Scholars concur, however, in relating an evolution of the institutions and principles constituting the empire, describing a gradual assumption of the imperial title and role; the exact term "Holy Roman Empire" was not used until the 13th century, but the concept of translatio imperii, the notion that he—the sovereign ruler—held supreme power inherited from the ancient emperors of Rome, was fundamental to the prestige of the emperor. The office of Holy Roman Emperor was traditionally elective, although controlled by dynasties; the German prince-electors, the highest-ranking noblemen of the empire elected one of their peers as "King of the Romans", he would be crowned emperor by the Pope. The empire never achieved the extent of political unification as was formed to the west in France, evolving instead into a decentralized, limited elective monarchy composed of hundreds of sub-units: kingdoms, duchies, prince-bishoprics, Free Imperial Cities, other domains.
The power of the emperor was limited, while the various princes, lords and cities of the empire were vassals who owed the emperor their allegiance, they possessed an extent of privileges that gave them de facto independence within their territories. Emperor Francis II dissolved the empire on 6 August 1806 following the creation of the Confederation of the Rhine by emperor Napoleon I the month before. In various languages the Holy Roman Empire was known as: Latin: Sacrum Imperium Romanum, German: Heiliges Römisches Reich, Italian: Sacro Romano Impero, Czech: Svatá říše římská, Polish: Święte imperium rzymskie, Slovene: Sveto rimsko cesarstvo, Dutch: Heilige Roomse Rijk, French: Saint-Empire romain. Before 1157, the realm was referred to as the Roman Empire; the term sacrum in connection with the medieval Roman Empire was used beginning in 1157 under Frederick I Barbarossa: the term was added to reflect Frederick's ambition to dominate Italy and the Papacy. The form "Holy Roman Empire" is attested from 1254 onward.
In a decree following the 1512 Diet of Cologne, the name was changed to the Holy Roman Empire of the German Nation, a form first used in a document in 1474. The new title was adopted because the Empire had lost most of its Italian and Burgundian territories to the south and west by the late 15th century, but to emphasize the new importance of the German Imperial Estates in ruling the Empire due to the Imperial Reform. By the end of the 18th century, the term "Holy Roman Empire of the German Nation" had fallen out of official use. Besides, contradicting the traditional view concerning that designation, Hermann Weisert has stated in a study on imperial titulature that, despite the claim of many textbooks, the name "Holy Roman Empire of the German Nation" never had an official status and points out that documents were thirty times as to omit the national suffix as include it. This, or the shortened "Roman Empire of the German Nation", is used in Germany to refer to the Holy Roman Empire. In a famous assessment of the name, the political philosopher Voltaire remarked sardonically: "This body, called and which still calls itself the Holy Roman Empire was in no way holy, nor Roman, nor an empire."
As Roman power in Gaul declined during the 5th century, local Germanic tribes assumed control. In the late 5th and early 6th centuries, the Merovingians, under Clovis I and his successors, consolidated Frankish tribes and extended hegemony over others to gain control of northern Gaul and the middle Rhine river valley region. By the middle of the 8th century, the Merovingians had been reduced to figureheads, the Carolingians, led by Charles Martel, had become the de facto rulers. In 751, Martel's son Pepin became King of the Franks, gained the sanction of the Pope; the Carolingians would maintain a close alliance with the Papacy. In 768, Pepin's son Charlemagne became King of the Franks and began an extensive expansion of the realm, he incorporated the territories of present-day France, northern Italy, beyond, linking the Frankish kingdom with Papal lands. In 797, the Eastern Roman Emperor Constantine VI was removed from the throne by his mother Irene who declared herself Empress; as the Church regarded a male Roman Emperor as the head of Christendom, Pope
Germany the Federal Republic of Germany, is a country in Central and Western Europe, lying between the Baltic and North Seas to the north, the Alps to the south. It borders Denmark to the north and the Czech Republic to the east and Switzerland to the south, France to the southwest, Luxembourg and the Netherlands to the west. Germany includes 16 constituent states, covers an area of 357,386 square kilometres, has a temperate seasonal climate. With 83 million inhabitants, it is the second most populous state of Europe after Russia, the most populous state lying in Europe, as well as the most populous member state of the European Union. Germany is a decentralized country, its capital and largest metropolis is Berlin, while Frankfurt serves as its financial capital and has the country's busiest airport. Germany's largest urban area is the Ruhr, with its main centres of Essen; the country's other major cities are Hamburg, Cologne, Stuttgart, Düsseldorf, Dresden, Bremen and Nuremberg. Various Germanic tribes have inhabited the northern parts of modern Germany since classical antiquity.
A region named Germania was documented before 100 AD. During the Migration Period, the Germanic tribes expanded southward. Beginning in the 10th century, German territories formed a central part of the Holy Roman Empire. During the 16th century, northern German regions became the centre of the Protestant Reformation. After the collapse of the Holy Roman Empire, the German Confederation was formed in 1815; the German revolutions of 1848–49 resulted in the Frankfurt Parliament establishing major democratic rights. In 1871, Germany became a nation state when most of the German states unified into the Prussian-dominated German Empire. After World War I and the revolution of 1918–19, the Empire was replaced by the parliamentary Weimar Republic; the Nazi seizure of power in 1933 led to the establishment of a dictatorship, the annexation of Austria, World War II, the Holocaust. After the end of World War II in Europe and a period of Allied occupation, Austria was re-established as an independent country and two new German states were founded: West Germany, formed from the American and French occupation zones, East Germany, formed from the Soviet occupation zone.
Following the Revolutions of 1989 that ended communist rule in Central and Eastern Europe, the country was reunified on 3 October 1990. Today, the sovereign state of Germany is a federal parliamentary republic led by a chancellor, it is a great power with a strong economy. As a global leader in several industrial and technological sectors, it is both the world's third-largest exporter and importer of goods; as a developed country with a high standard of living, it upholds a social security and universal health care system, environmental protection, a tuition-free university education. The Federal Republic of Germany was a founding member of the European Economic Community in 1957 and the European Union in 1993, it is part of the Schengen Area and became a co-founder of the Eurozone in 1999. Germany is a member of the United Nations, NATO, the G7, the G20, the OECD. Known for its rich cultural history, Germany has been continuously the home of influential and successful artists, musicians, film people, entrepreneurs, scientists and inventors.
Germany has a large number of World Heritage sites and is among the top tourism destinations in the world. The English word Germany derives from the Latin Germania, which came into use after Julius Caesar adopted it for the peoples east of the Rhine; the German term Deutschland diutisciu land is derived from deutsch, descended from Old High German diutisc "popular" used to distinguish the language of the common people from Latin and its Romance descendants. This in turn descends from Proto-Germanic *þiudiskaz "popular", derived from *þeudō, descended from Proto-Indo-European *tewtéh₂- "people", from which the word Teutons originates; the discovery of the Mauer 1 mandible shows that ancient humans were present in Germany at least 600,000 years ago. The oldest complete hunting weapons found anywhere in the world were discovered in a coal mine in Schöningen between 1994 and 1998 where eight 380,000-year-old wooden javelins of 1.82 to 2.25 m length were unearthed. The Neander Valley was the location where the first non-modern human fossil was discovered.
The Neanderthal 1 fossils are known to be 40,000 years old. Evidence of modern humans dated, has been found in caves in the Swabian Jura near Ulm; the finds included 42,000-year-old bird bone and mammoth ivory flutes which are the oldest musical instruments found, the 40,000-year-old Ice Age Lion Man, the oldest uncontested figurative art discovered, the 35,000-year-old Venus of Hohle Fels, the oldest uncontested human figurative art discovered. The Nebra sky disk is a bronze artefact created during the European Bronze Age attributed to a site near Nebra, Saxony-Anhalt, it is part of UNESCO's Memory of the World Programme. The Germanic tribes are thought to date from the Pre-Roman Iron Age. From southern Scandinavia and north Germany, they expanded south and west from the 1st century BC, coming into contact with the Celtic tribes of Gaul as well
Konrad Hermann Joseph Adenauer was a German statesman who served as the first Chancellor of the Federal Republic of Germany from 1949 to 1963. He was co-founder and first leader of the Christian Democratic Union, a Christian Democratic party that under his leadership became one of the most influential parties in the country. In the early years of the Federal Republic he switched focus from denazification to recovery and led his country from the ruins of World War II to becoming a productive and prosperous nation that forged close relations with France, the United Kingdom and the United States. During his years in power, West Germany achieved democracy, international respect and economic prosperity. Adenauer belied his age by his uncanny political instinct, he displayed a strong dedication to a broad vision of market-based liberal democracy and anti-communism. A shrewd politician, Adenauer was committed to a Western-oriented foreign policy and restoring the position of West Germany on the world stage.
He worked to restore the West German economy from the destruction of World War II to a central position in Europe, presiding over the German Economic Miracle together with his Minister of Economics, Ludwig Erhard. He was a driving force behind West Germany becoming the first German state to re-establish a national military in 1955, he came to terms with France. Adenauer opposed rival East Germany and made his nation a member of NATO and a firm ally of the United States. Adenauer, Chancellor until age 87, was dubbed "Der Alte". British politician and historian Roy Jenkins says he was "the oldest statesman to function in elected office." He remains the oldest head of government for a major country. A devout Roman Catholic and member of the Catholic Centre Party, he was a leading politician in the Weimar Republic, serving as Mayor of Cologne and as president of the Prussian State Council. Konrad Adenauer was born as the third of five children of Johann Konrad Adenauer and his wife Helene in Cologne, Rhenish Prussia, on 5 January 1876.
His siblings were August, Johannes and Elisabeth, who died shortly after birth in c. 1880. One of the formative influences of Adenauer's youth was the Kulturkampf, an experience that as related to him by his parents left him with a lifelong dislike for "Prussianism", led him like many other Catholic Rhinelanders of the 19th century to resent the Rhineland's inclusion in Prussia. In 1894, he completed his Abitur and began studying law and politics at the universities of Freiburg and Bonn. In 1896, at the age of 20, he was conscripted into the German army, but did not pass the physical exam due to chronic respiratory problems he had experienced since childhood, he was a member of several Roman Catholic students' associations under the K. St. V. Arminia Bonn in Bonn, he graduated in 1900, afterwards worked as a lawyer at the court in Cologne. As a devout Catholic, he joined the Centre Party in 1906 and was elected to Cologne's city council in the same year. In 1909, he became Vice-Mayor of Cologne, an industrial metropolis with a population of 635,000 in 1914.
Avoiding the extreme political movements that attracted so many of his generation, Adenauer was committed to bourgeois decency, order, Christian morals and values, was dedicated to rooting out disorder, inefficiency and political immorality. From 1917 to 1933, he became a member of the Prussian House of Lords. Adenauer headed Cologne during World War I, working with the army to maximize the city's role as a rear base of supply and transportation for the Western Front, he paid special attention to the civilian food supply, enabling the residents to avoid the worst of the severe shortages that beset most German cities during 1918–19. In the face of the collapse of the old regime and the threat of revolution and widespread disorder in late 1918, Adenauer maintained control in Cologne using his good working relationship with the Social Democrats. In a speech on 1 February 1919 Adenauer called for the dissolution of Prussia, for the Prussian Rhineland to become a new autonomous Land in the Reich.
Adenauer claimed. Both the Reich and Prussian governments were against Adenauer's plans for breaking up Prussia; when the terms of the Treaty of Versailles were presented to Germany in June 1919, Adenauer again suggested to Berlin his plan for an autonomous Rhineland state and again his plans were rejected by the Reich government. He was mayor during the postwar British occupation, he established a good working relationship with the British military authorities, using them to neutralize the workers' and soldiers' council that had become an alternative base of power for the city's left wing. During the Weimar Republic, he was president of the Prussian State Council from 1921–33, the representation of the provinces of Prussia in its legislation. Since 1906, a major debate within the Zentrum concerned the question of whether the Zentrum should "leave the tower" or "stay in the tower". Adenauer was one of the leading advocates of "leaving the tower", which led to a dramatic clash between him and Cardinal Michael von Faulhaber at the 1922 Katholikentag, where the Cardinal publicly admonished Adenauer
Cologne is the largest city of Germany's most populous federal state of North Rhine-Westphalia, its 1 million+ inhabitants make it the fourth most populous city in Germany after Berlin and Munich. The largest city on the Rhine, it is the most populous city both of the Rhine-Ruhr Metropolitan Region, Germany's largest and one of Europe's major metropolitan areas, of the Rhineland. Centred on the left bank of the Rhine, Cologne is about 45 kilometres southeast of North Rhine-Westphalia's capital of Düsseldorf and 25 kilometres northwest of Bonn, it is the largest city in the Central Ripuarian dialect areas. The city's famous Cologne Cathedral is the seat of the Catholic Archbishop of Cologne. There are many institutions of higher education in the city, most notably the University of Cologne, one of Europe's oldest and largest universities, the Technical University of Cologne, Germany's largest university of applied sciences, the German Sport University Cologne, Germany's only sport university.
Cologne Bonn Airport lies in the southeast of the city. The main airport for the Rhine-Ruhr region is Düsseldorf Airport. Cologne was founded and established in Ubii territory in the 1st century AD as the Roman Colonia Claudia Ara Agrippinensium, the first word of, the origin of its name. An alternative Latin name of the settlement is Augusta Ubiorum, after the Ubii. "Cologne", the French version of the city's name, has become standard in English as well. The city functioned as the capital of the Roman province of Germania Inferior and as the headquarters of the Roman military in the region until occupied by the Franks in 462. During the Middle Ages it flourished on one of the most important major trade routes between east and west in Europe. Cologne was one of the leading members of the Hanseatic League and one of the largest cities north of the Alps in medieval and Renaissance times. Prior to World War II the city had undergone several occupations by the French and by the British. Cologne was one of the most bombed cities in Germany during World War II, with the Royal Air Force dropping 34,711 long tons of bombs on the city.
The bombing reduced the population by 95% due to evacuation, destroyed the entire city. With the intention of restoring as many historic buildings as possible, the successful postwar rebuilding has resulted in a mixed and unique cityscape. Cologne is a major cultural centre for the Rhineland. Exhibitions range from local ancient Roman archeological sites to contemporary graphics and sculpture; the Cologne Trade Fair hosts a number of trade shows such as Art Cologne, imm Cologne and the Photokina. The first urban settlement on the grounds of modern-day Cologne was Oppidum Ubiorum, founded in 38 BC by the Ubii, a Cisrhenian Germanic tribe. In 50 AD, the Romans founded Colonia Claudia Ara Agrippinensium on the river Rhine and the city became the provincial capital of Germania Inferior in 85 AD. Considerable Roman remains can be found in present-day Cologne near the wharf area, where a 1,900-year-old Roman boat was discovered in late 2007. From 260 to 271 Cologne was the capital of the Gallic Empire under Postumus and Victorinus.
In 310 under emperor Constantine I a bridge was built over the Rhine at Cologne. Roman imperial governors resided in the city and it became one of the most important trade and production centres in the Roman Empire north of the Alps. Cologne is shown on the 4th century Peutinger Map. Maternus, elected as bishop in 313, was the first known bishop of Cologne; the city was the capital of a Roman province until it was occupied by the Ripuarian Franks in 462. Parts of the original Roman sewers are preserved underneath the city, with the new sewerage system having opened in 1890. Early medieval Cologne was part of Austrasia within the Frankish Empire. In 716, Charles Martel commanded an army for the first time and suffered the only defeat of his life when Chilperic II, King of Neustria, invaded Austrasia and the city fell to him in the Battle of Cologne. Charles fled to the Eifel mountains, rallied supporters, took the city back that same year after defeating Chilperic in the Battle of Amblève. Cologne had been the seat of a bishop since the Roman period.
In 843, Cologne became a city within the Treaty of Verdun-created East Francia. In 953, the archbishops of Cologne first gained noteworthy secular power, when bishop Bruno was appointed as duke by his brother Otto I, King of Germany. In order to weaken the secular nobility, who threatened his power, Otto endowed Bruno and his successors on the bishop's see with the prerogatives of secular princes, thus establishing the Electorate of Cologne, formed by the temporal possessions of the archbishopric and included in the end a strip of territory along the left Bank of the Rhine east of Jülich, as well as the Duchy of Westphalia on the other side of the Rhine, beyond Berg and Mark. By the end of the 12th century, the Archbishop of Cologne was one of the seven electors of the Holy Roman Emperor. Besides being prince elector, he was Arch-chancellor of Italy as well, technically from 1238 and permanently from 1263 until 1803. Following the Battle of Worringen in 1288, Cologne gained its independence from the archbishops and became a Free City.
Archbishop Sigfried II von Westerburg was forced to reside in Bonn. The archbishop preserv
Prussia was a prominent German state that originated in 1525 with a duchy centred on the region of Prussia on the southeast coast of the Baltic Sea. It was de facto dissolved by an emergency decree transferring powers of the Prussian government to German Chancellor Franz von Papen in 1932 and de jure by an Allied decree in 1947. For centuries, the House of Hohenzollern ruled Prussia expanding its size by way of an unusually well-organised and effective army. Prussia, with its capital in Königsberg and from 1701 in Berlin, decisively shaped the history of Germany. In 1871, German states united to create the German Empire under Prussian leadership. In November 1918, the monarchies were abolished and the nobility lost its political power during the German Revolution of 1918–19; the Kingdom of Prussia was thus abolished in favour of a republic—the Free State of Prussia, a state of Germany from 1918 until 1933. From 1933, Prussia lost its independence as a result of the Prussian coup, when the Nazi regime was establishing its Gleichschaltung laws in pursuit of a unitary state.
With the end of the Nazi regime, in 1945, the division of Germany into allied-occupation zones and the separation of its territories east of the Oder–Neisse line, which were incorporated into Poland and the Soviet Union, the State of Prussia ceased to exist de facto. Prussia existed de jure until its formal abolition by the Allied Control Council Enactment No. 46 of 25 February 1947. The name Prussia derives from the Old Prussians. In 1308, the Teutonic Knights conquered the region of Pomerelia with Gdańsk, their monastic state was Germanised through immigration from central and western Germany, and, in the south, it was Polonised by settlers from Masovia. The Second Peace of Thorn split Prussia into the western Royal Prussia, a province of Poland, the eastern part, from 1525 called the Duchy of Prussia, a fief of the Crown of Poland up to 1657; the union of Brandenburg and the Duchy of Prussia in 1618 led to the proclamation of the Kingdom of Prussia in 1701. Prussia entered the ranks of the great powers shortly after becoming a kingdom, exercised most influence in the 18th and 19th centuries.
During the 18th century it had a major say in many international affairs under the reign of Frederick the Great. During the 19th century, Chancellor Otto von Bismarck united the German principalities into a "Lesser Germany", which excluded the Austrian Empire. At the Congress of Vienna, which redrew the map of Europe following Napoleon's defeat, Prussia acquired rich new territories, including the coal-rich Ruhr; the country grew in influence economically and politically, became the core of the North German Confederation in 1867, of the German Empire in 1871. The Kingdom of Prussia was now so large and so dominant in the new Germany that Junkers and other Prussian élites identified more and more as Germans and less as Prussians; the Kingdom ended in 1918 along with other German monarchies that collapsed as a result of the German Revolution. In the Weimar Republic, the Free State of Prussia lost nearly all of its legal and political importance following the 1932 coup led by Franz von Papen. Subsequently, it was dismantled into Nazi German Gaue in 1935.
Some Prussian ministries were kept and Hermann Göring remained in his role as Minister President of Prussia until the end of World War II. Former eastern territories of Germany that made up a significant part of Prussia lost the majority of their German population after 1945 as the People's Republic of Poland and the Soviet Union both absorbed these territories and had most of its German inhabitants expelled by 1950. Prussia, deemed a bearer of militarism and reaction by the Allies, was abolished by an Allied declaration in 1947; the international status of the former eastern territories of Germany was disputed until the Treaty on the Final Settlement with Respect to Germany in 1990, while its return to Germany remains a topic among far right politicians, the Federation of Expellees and various political revisionists. The term Prussian has been used outside Germany, to emphasise professionalism, aggressiveness and conservatism of the Junker class of landed aristocrats in the East who dominated first Prussia and the German Empire.
The main coat of arms of Prussia, as well as the flag of Prussia, depicted a black eagle on a white background. The black and white national colours were used by the Teutonic Knights and by the Hohenzollern dynasty; the Teutonic Order wore a white coat embroidered with a black cross with gold insert and black imperial eagle. The combination of the black and white colours with the white and red Hanseatic colours of the free cities Bremen, Hamburg and Lübeck, as well as of Brandenburg, resulted in the black-white-red commercial flag of the North German Confederation, which became the flag of the German Empire in 1871. Suum cuique, the motto of the Order of the Black Eagle created by King Frederick I in 1701, was associated with the whole of Prussia; the Iron Cross, a military decoration created by King Frederick William III in 1813, was commonly associated with the country. The region populated by Baltic Old Prussians who were Christianised, became a favoured location for immigration by Germans, as well as Poles and Lithuanians along the border regions.
Before its abolition, the territory of the Kingdom of Prussia included the provinces of West Prussia.
Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to
Charles University, known as Charles University in Prague or as the University of Prague, is the oldest and largest university in the Czech Republic. Founded in 1348, it was the first university in Central Europe, it is one of the oldest universities in Europe in continuous operation and ranks in the upper 1.5 percent of the world’s best universities. Today, the university consists of 17 faculties located in Hradec Králové and Pilsen, its academic publishing house is Karolinum Press. The university operates several museums and two botanical gardens, its seal shows its protector Emperor Charles IV, with his coats of arms as King of the Romans and King of Bohemia, kneeling in front of St. Wenceslas, the patron saint of Bohemia, it is surrounded by Sigillum Universitatis Scolarium Studii Pragensis. The establishment of a medieval university in Prague was inspired by Holy Roman Emperor Charles IV, he asked Pope Clement VI, to do so. On 26 January 1347 the pope issued the bull establishing a university in Prague, modeled on the University of Paris, with the full number of faculties, including theological.
On 7 April 1348 Charles, the king of Bohemia, gave to the established university privileges and immunities from the secular power in a Golden Bull and on 14 January 1349 he repeated that as the King of the Romans. Most Czech sources since the 19th century—encyclopedias, general histories, materials of the University itself—prefer to give 1348 as the year of the founding of the university, rather than 1347 or 1349; this was caused by an anticlerical shift in the 19th century, shared by both Germans. The university was opened in 1349; the university was sectioned into parts called nations: the Bohemian, Bavarian and Saxon. The Bohemian natio included Bohemians, southern Slavs, Hungarians. Ethnically Czech students made 16–20% of all students. Archbishop Arnošt of Pardubice took an active part in the foundation by obliging the clergy to contribute and became a chancellor of the university; the first graduate was promoted in 1359. The lectures were held in the colleges, of which the oldest was named for the king the Carolinum, established in 1366.
In 1372 the Faculty of Law became an independent university. In 1402 Jerome of Prague in Oxford copied out the Trialogus of John Wycliffe; the dean of the philosophical faculty, Jan Hus, translated Trialogus into the Czech language. In 1403 the university forbade its members to follow the teachings of Wycliffe, but his doctrine continued to gain in popularity. In the Western Schism, the Bohemian natio took the side of king Wenceslaus and supported the Council of Pisa; the other nationes of the university declared their support for the side of Pope Gregory XII, thus the vote was 1:3 against the Bohemians. Hus and other Bohemians, took advantage of Wenceslaus' opposition to Gregory. By the Decree of Kutná Hora on 18 January 1409, the king subverted the university constitution by granting the Bohemian masters three votes. Only a single vote was left for all other three nationes combined, compared to one vote per each natio before; the result of this coup was the emigration of foreign professors and students, founding the University of Leipzig in May 1409.
Before that, in 1408, the university had about 200 doctors and magisters, 500 bachelors, 30,000 students. In the autumn of 1409, Hus was elected rector of the now Czech-dominated rump university. Thus, the Prague university lost the largest part of its students and faculty. From on the university declined to a regional institution with a low status. Soon, in 1419, the faculties of theology and law disappeared, only the faculty of arts remained in existence; the faculty of arts became a centre of the Hussite movement, the chief doctrinal authority of the Utraquists. No degrees were given in the years 1417–30. Emperor Sigismund, son of Charles IV, took what was left into his personal property and some progress was made; the emperor Ferdinand I called the Jesuits to Prague and in 1562 they opened an academy—the Clementinum. From 1541 till 1558 the Czech humanist Mattheus Collinus was a professor of Greek language; some progress was made again. In 1609 the obligatory celibacy of the professors was abolished.
In 1616 the Jesuit Academy became a university. Jesuits were expelled 1618–1621 during the early stages of the Thirty Years' War, started in Prague by anti-Catholic and anti-Imperial Bohemians. By 1622 the Jesuits had a predominant influence over the emperor. An Imperial decree of 19 September 1622 gave the Jesuits supreme control over the entire school system of Bohemia and Silesia; the last four professors at the Carolinum resigned and all of the Carolinum and nine colleges went to the Jesuits. The right of handing out degrees, of holding chancellorships and of appointing the secular professors was granted to the Jesuits. Cardinal Ernst Adalbert von Harrach opposed union of the university with another institution and the withdrawal of the archepiscopal right to the chanc