Germans in the context of Theodor Escherich

The House of Schleswig-Holstein-Sonderburg-Glücksburg, also known by its short name as the House of Glücksburg, is the senior surviving branch of the German House of Oldenburg, one of Europe's oldest royal houses. Oldenburg house members have reigned at various times in Denmark, Norway, Sweden, Iceland, Greece, several northern German states, and Russia. It takes its name from the family seat in Glücksburg, a small town in Schleswig-Holstein, Germany.

Current monarch King Charles III and King Harald V, former monarch Queen Margrethe II and former consorts Queen Anne-Marie of Greece and Queen Sofia of Spain are patrilineal members of cadet branches of the House of Glücksburg.

The Germanic peoples were tribal groups who lived in Northern Europe during Classical antiquity and the Early Middle Ages. In modern scholarship, they typically include not only the Roman-era Germani who lived in both Germania and parts of the Roman Empire, but also all Germanic speaking peoples from this era, irrespective of where they lived, most notably the Goths. Another term, ancient Germans, is considered problematic by many scholars because it suggests identity with present-day Germans. Although the first Roman descriptions of Germani involved tribes west of the Rhine, their homeland of Germania was portrayed as stretching east of the Rhine, to southern Scandinavia and the Vistula in the east, and to the upper Danube in the south. Other Germanic speakers, such as the Bastarnae and Goths, lived further east in what is now Moldova and Ukraine. The term Germani is generally only used to refer to historical peoples from the 1st to 4th centuries CE.

Different academic disciplines have their own definitions of what makes someone or something "Germanic". Some scholars call for the term's total abandonment as a modern construct, since lumping "Germanic peoples" together implies a common group identity for which there is little evidence. Other scholars have defended the term's continued use and argue that a common Germanic language allows one to speak of "Germanic peoples", regardless of whether these ancient and medieval peoples saw themselves as having a common identity. Scholars generally agree that it is possible to refer to Germanic languages from about 500 BCE. Archaeologists usually associate the earliest clearly identifiable Germanic speaking peoples with the Jastorf culture of the Pre-Roman Iron Age in central and northern Germany and southern Denmark from the 6th to 1st centuries BCE. This culture existed around the same time that the First Germanic Consonant Shift is theorized to have occurred, leading to recognizably Germanic languages. Germanic languages expanded south, east, and west, coming into contact with Celtic, Iranic, Baltic, and Slavic peoples before they were noted by the Romans.

Sir Isaac Newton (/ˈnjuːtən/ ; 4 January [O.S. 25 December] 1643 – 31 March [O.S. 20 March] 1727) was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, author, and inventor. He was a key figure in the Scientific Revolution and the Enlightenment that followed. His book Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687, achieved the first great unification in physics and established classical mechanics. Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for formulating infinitesimal calculus, though he developed calculus years before Leibniz. Newton contributed to and refined the scientific method, and his work is considered the most influential in bringing forth modern science.

In the Principia, Newton formulated the laws of motion and universal gravitation that formed the dominant scientific viewpoint for centuries until it was superseded by the theory of relativity. He used his mathematical description of gravity to derive Kepler's laws of planetary motion, account for tides, the trajectories of comets, the precession of the equinoxes and other phenomena, eradicating doubt about the Solar System's heliocentricity. Newton solved the two-body problem and introduced the three-body problem. He demonstrated that the motion of objects on Earth and celestial bodies could be accounted for by the same principles. Newton's inference that the Earth is an oblate spheroid was later confirmed by the geodetic measurements of Alexis Clairaut, Charles Marie de La Condamine, and others, convincing most European scientists of the superiority of Newtonian mechanics over earlier systems. He was also the first to calculate the age of Earth by experiment, and described a precursor to the modern wind tunnel. Further, he was the first to provide a quantitative estimate of the solar mass.

French people (French: Les Français, lit. 'The French') are a nation primarily located in Western Europe that share a common French culture, history, and language, identified with the country of France.

The French people, especially the native speakers of langues d'oïl from northern and central France, are primarily descended from Romans (or Gallo-Romans, western European Celtic and Italic peoples), Gauls (including the Belgae), as well as Germanic peoples such as the Franks, the Visigoths, the Suebi and the Burgundians who settled in Gaul from east of the Rhine after the fall of the Roman Empire, as well as various later waves of lower-level irregular migration that have continued to the present day. The Norsemen also settled in Normandy in the 10th century and contributed significantly to the ancestry of the Normans. Furthermore, regional ethnic minorities also exist within France that have distinct lineages, languages and cultures such as Bretons in Brittany, Occitans in Occitania, Basques in the French Basque Country, Catalans in northern Catalonia, Germans in Alsace, Corsicans in Corsica and Flemings in French Flanders.

Bratislava (German: Pressburg; Hungarian: Pozsony) is the capital and largest city of the Slovak Republic and the fourth largest of all cities on the river Danube. Officially, the population of the city is about 475,000; however, some sources estimate the daily number of people moving around the city based on mobile phone SIM cards is more than 570,000. Bratislava is in southwestern Slovakia at the foot of the Little Carpathians, occupying both banks of the Danube and the left bank of the River Morava. The city is situated on the border of three countries—Slovakia, Austria, and Hungary—and is the only national capital to have land borders with two other sovereign states. Its geographic position places it exceptionally close to the Austrian capital Vienna, making them the closest pair of capital cities in Europe at just 50 kilometres (31 mi) apart.

The city's history has been influenced by people of many nations and religions, including Austrians, Bulgarians, Croats, Czechs, Germans, Hungarians, Jews and Slovaks. It was the coronation site and legislative center and capital of the Kingdom of Hungary from 1536 to 1783; eleven Hungarian kings and eight queens were crowned in St Martin's Cathedral. Most Hungarian parliament assemblies were held here from the 17th century until the Hungarian Reform Era, and the city has been home to many Hungarian, German, and Slovak historical figures.

Silesians (Silesian: Ślōnzŏki or Ślůnzoki; Silesian German: Schläsinger or Schläsier; German: Schlesier pronounced [ˈʃleːzi̯ɐ] ; Polish: Ślązacy; Czech: Slezané) is both a linguistic as well as a geographical term for the inhabitants of Silesia, a historical region in Central Europe divided by the current national boundaries of Poland, Germany, and Czechia. Historically, the region of Silesia (Lower and Upper) has been inhabited by Polish (West Slavic Lechitic people), Czechs, and Germans. Therefore, the term Silesian can refer to anyone of these ethnic groups. However, in 1945, great demographic changes occurred in the region as a result of the Potsdam Agreement leaving most of the region ethnically Polish and/or Slavic Upper Silesian. The names of Silesia in different languages most likely share their etymology—Polish: Śląsk; German: Schlesien pronounced [ˈʃleːzi̯ən] ; Czech: Slezsko [ˈslɛsko]; Lower Silesian: Schläsing; Silesian: Ślōnsk [ɕlonsk]; Lower Sorbian: Šlazyńska [ˈʃlazɨnʲska]; Upper Sorbian: Šleska [ˈʃlɛska]; Latin, Spanish and English: Silesia; French: Silésie; Dutch: Silezië; Italian: Slesia; Slovak: Sliezsko; Kashubian: Sląsk. The names all relate to the name of a river (now Ślęza) and mountain (Mount Ślęża) in mid-southern Silesia, which served as a place of cult for pagans before Christianization.

Ślęża is listed as one of the numerous Pre-Indo-European topographic names in the region (see old European hydronymy). According to some Polonists, the name Ślęża [ˈɕlɛ̃ʐa] or Ślęż [ɕlɛ̃ʂ] is directly related to the Old Polish words ślęg [ɕlɛŋk] or śląg [ɕlɔŋk], which means dampness, moisture, or humidity. They disagree with the hypothesis of an origin for the name Śląsk [ɕlɔ̃sk] from the name of the Silings tribe, an etymology preferred by some German authors.

The high medieval Kingdom of Hungary was a regional power in central Europe. It came into existence in Central Europe when Stephen I, Grand Prince of the Hungarians, was crowned king in 1000 or 1001. He reinforced central authority and forced his subjects to accept Christianity. Although all written sources emphasize only the role played by German and Italian knights and clerics in the process, a significant part of the Hungarian vocabulary for agriculture and religion was taken from Slavic languages. Civil wars and pagan uprisings, along with attempts by the Holy Roman emperors to expand their authority over Hungary, jeopardized the new monarchy. The monarchy stabilized during the reigns of Ladislaus I (1077–1095) and Coloman (1095–1116). These rulers occupied Croatia and Dalmatia with the support of a part of the local population. Both realms retained their autonomous position. The successors of Ladislaus and Coloman—especially Béla II (1131–1141), Béla III (1176–1196), Andrew II (1205–1235), and Béla IV (1235–1270)—continued this policy of expansion towards the Balkan Peninsula and the lands east of the Carpathian Mountains, transforming their kingdom into one of the major powers of medieval Europe.

Rich in uncultivated lands, silver, gold, and salt deposits, Hungary became the preferred destination of mainly German, Italian, and French colonists. These immigrants were mostly peasants who settled in villages, but some were craftsmen and merchants, who established most of the cities of the Kingdom. Their arrival played a key role in the shaping of an urban lifestyle, habits, and culture in medieval Hungary. The location of the kingdom at the crossroads of international trade routes favored the coexistence of several cultures. Romanesque, Gothic, and Renaissance buildings and literary works written in Latin prove the predominantly Roman Catholic character of the culture; but Orthodox, and even non-Christian ethnic minority communities also existed. Latin was the language of legislation, administration and the judiciary, but "linguistic pluralism" contributed to the survival of many tongues, including a great variety of Slavic dialects.

Gottfried Wilhelm Leibniz (or Leibnitz; 1 July 1646 [O.S. 21 June] – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Isaac Newton, with the creation of calculus in addition to many other branches of mathematics, such as binary arithmetic and statistics. Leibniz has been called the "last universal genius" due to his vast expertise across fields, which became a rarity after his lifetime with the coming of the Industrial Revolution and the spread of specialized labour. He is a prominent figure in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history, philology, games, music, and other studies. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science.

Leibniz contributed to the field of library science, developing a cataloguing system (at the Herzog August Library in Wolfenbüttel, Germany) that came to serve as a model for many of Europe's largest libraries. His contributions to a wide range of subjects were scattered in various learned journals, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primarily in Latin, French and German.

The House of Hanover (German: Haus Hannover German pronunciation: [haʊ̯s haˈnoːfɐ]) is a German royal house with roots tracing back to the 17th century. Its members, known as Hanoverians, ruled Hanover, Great Britain, Ireland, and the British Empire at various times during the 17th to 20th centuries. Originating as a cadet branch of the House of Welf (also "Guelf" or "Guelph") in 1635, also known then as the House of Brunswick-Lüneburg, the Hanoverians ascended to prominence with Hanover's elevation to an Electorate of the Holy Roman Empire in 1692. In 1714 George I, prince-elector of Hanover and a descendant of King James VI and I, assumed the throne of Great Britain and Ireland, marking the beginning of Hanoverian rule over the British Empire. At the end of this line, Queen Victoria's death in 1901, the throne of the United Kingdom passed to her eldest son Edward VII, a member of the House of Saxe-Coburg and Gotha, through his father Albert, Prince Consort. The last reigning members of the House of Hanover lost the Duchy of Brunswick in 1918 when Germany became a republic and abolished royalty and nobility.

The formal name of the house was the "House of Brunswick-Lüneburg, Hanover line". The senior line of Brunswick-Lüneburg, which ruled Brunswick-Wolfenbüttel, became extinct in 1884. The House of Hanover is now the only surviving branch of the House of Welf, which is the senior branch of the House of Este. The current head of the House of Hanover is Ernst August, Prince of Hanover.

The House of Oldenburg is a German dynasty whose members rule or have ruled in Denmark, Iceland, Greece, Norway, Russia, Sweden, the United Kingdom, Livonia, Schleswig, Holstein, and Oldenburg. The current kings of Norway and the United Kingdom are patrilineal descendants of the Glücksburg branch of this house.

The dynasty rose to prominence when Count Christian I of Oldenburg was elected King of Denmark in 1448, of Norway in 1450 and of Sweden in 1457. Denmark's current monarch, King Frederik X, belongs to the Glücksburg branch of the House of Oldenburg through his mother, Queen Margrethe II.

The Brothers Grimm (German: die Brüder Grimm or die Gebrüder Grimm), Jacob (1785–1863) and Wilhelm (1786–1859), were German academics who together collected and published folklore. The brothers are among the best-known storytellers of folktales, popularizing stories such as "Cinderella" ("Aschenputtel"), "The Frog Prince" ("Der Froschkönig"), "Hansel and Gretel" ("Hänsel und Gretel"), "Town Musicians of Bremen" ("Die Bremer Stadtmusikanten"), "Little Red Riding Hood" ("Rotkäppchen"), "Rapunzel", "Rumpelstiltskin" ("Rumpelstilzchen"), "Sleeping Beauty" ("Dornröschen"), and "Snow White" ("Schneewittchen"). Their first collection of folktales, Children's and Household Tales (Kinder- und Hausmärchen), was first published in 1812.

The Brothers Grimm spent their formative years in the town of Hanau in the Landgraviate of Hesse-Kassel. Their father's death in 1796 (when Jacob was 11 and Wilhelm 10) caused great poverty for the family and greatly affected the brothers throughout their lives. Both brothers attended Marburg University, where they developed a curiosity about German folklore, which grew into a lifelong dedication to collecting German folktales.

The Sack of Rome, then part of the Papal States, followed the capture of Rome on 6 May 1527 by the mutinous troops of Charles V, Holy Roman Emperor, during the War of the League of Cognac. Charles V only intended to threaten military action to make Pope Clement VII come to his terms. However, most of the Imperial army (14,000 Germans, including Lutherans, 6,000 Spaniards and some Italians) were largely unpaid. Despite being ordered not to storm Rome, they broke into the scarcely defended city and began looting, killing, and holding citizens for ransom without any restraint. Clement VII took refuge in Castel Sant'Angelo after the Swiss Guard were annihilated in a delaying rear guard action; he remained there until a ransom was paid to the pillagers.

Benvenuto Cellini, eyewitness to the events, described the sack in his works. It was not until February 1528 that the spread of a plague and the approach of the League forces under Marshal of France Odet de Foix forced the army to withdraw towards Naples from the city. Rome's population had dropped from 55,000 to 10,000 due to the atrocities, famine, an outbreak of plague, and flight from the city. The subsequent loss of the League army during the Siege of Naples secured a victory in the War of the League of Cognac for Charles V. The Emperor denied responsibility for the sack and came to terms again with Clement VII. On the other hand, the Sack of Rome further exacerbated religious hatred and antagonism between Catholics and Lutherans.

Luxembourgers (/ˈlʌksəmbɜːrɡərz/ LUK-səm-bur-gərz; Luxembourgish: Lëtzebuerger [ˈlətsəbu̯əjɐ] ) are an ethnic group native to their nation state of Luxembourg, where they make up around half of the population. They share the culture of Luxembourg and speak Luxembourgish, a West Germanic language.

Luxembourgers were, much like Austrians and some aspects of the Swiss historically considered to be a regional sub-group of ethnic Germans and viewed themselves as such until the collapse of the German Confederation. Luxembourg became independent, while remaining in personal union with the Netherlands, after the signing of the Treaty of London in 1839. The personal union proved short-lived as it was bilaterally and amicably dissolved in 1890.

In mathematics, Hilbert's program, formulated by German mathematician David Hilbert in the early 1920s, was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathematics were found to suffer from paradoxes and inconsistencies. As a solution, Hilbert proposed to ground all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent. Hilbert proposed that the consistency of more complicated systems, such as real analysis, could be proven in terms of simpler systems. Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic.

Gödel's incompleteness theorems, published in 1931, showed that Hilbert's program was unattainable for key areas of mathematics. In his first theorem, Gödel showed that any consistent system with a computable set of axioms which is capable of expressing arithmetic can never be complete: it is possible to construct a statement that can be shown to be true, but that cannot be derived from the formal rules of the system. In his second theorem, he showed that such a system could not prove its own consistency, so it certainly cannot be used to prove the consistency of anything stronger with certainty. This refuted Hilbert's assumption that a finitistic system could be used to prove the consistency of itself, and therefore could not prove everything else.

Henry Oldenburg (also Henry Oldenbourg) FRS (c. 1618 as Heinrich Oldenburg – 5 September 1677) was a German theologian, diplomat, and natural philosopher, known as one of the creators of modern scientific peer review. He was one of the foremost intelligencers of 17th-century Europe, with a network of correspondents to rival those of Fabri de Peiresc, Marin Mersenne, and Ismaël Boulliau. At the foundation of the Royal Society in London, he took on the task of foreign correspondence, as the first Secretary.