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Carl Friedrich Gauss

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120-494: Johann Carl Friedrich Gauss (German: Gauß [kaʁl ˈfʁiːdʁɪç ˈɡaʊs] ; Latin : Carolus Fridericus Gauss ; 30 April 1777 – 23 February 1855) was a German mathematician , astronomer , geodesist , and physicist who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and professor of astronomy from 1807 until his death in 1855. He

240-668: A Doctor of Philosophy in 1799, not in Göttingen, as is sometimes stated, but at the Duke of Brunswick's special request from the University of Helmstedt, the only state university of the duchy. Johann Friedrich Pfaff assessed his doctoral thesis, and Gauss got the degree in absentia without further oral examination. The Duke then granted him the cost of living as a private scholar in Brunswick. Gauss subsequently refused calls from

360-611: A couplet . Since 1600, the couplet has been featured as a part of the longer sonnet form, most notably in William Shakespeare 's sonnets. Sonnet 76 is an example. The two-line poetic form as a closed couplet was also used by William Blake in his poem " Auguries of Innocence ", and also by Byron in his poem Don Juan , by John Gay in his fables, and by Alexander Pope in his An Essay on Man . The first work of English literature penned in North America

480-487: A heliometer from Fraunhofer . The scientific activity of Gauss, besides pure mathematics, can be roughly divided into three periods: astronomy was the main focus in the first two decades of the 19th century, geodesy in the third decade, and physics, mainly magnetism, in the fourth decade. Gauss made no secret of his aversion to giving academic lectures. But from the start of his academic career at Göttingen, he continuously gave lectures until 1854. He often complained about

600-486: A basis for Gauss's research on their orbits, which he later published in his astronomical magnum opus Theoria motus corporum coelestium (1809). In November 1807, Gauss followed a call to the University of Göttingen , then an institution of the newly founded Kingdom of Westphalia under Jérôme Bonaparte , as full professor and director of the astronomical observatory , and kept the chair until his death in 1855. He

720-487: A considerable literary estate, too. Gauss referred to mathematics as "the queen of sciences" and arithmetics as "the queen of mathematics", and supposedly once espoused a belief in the necessity of immediately understanding Euler's identity as a benchmark pursuant to becoming a first-class mathematician. On certain occasions, Gauss claimed that the ideas of another scholar had already been in his possession previously. Thus his concept of priority as "the first to discover, not

840-486: A converted fortification tower, with usable, but partly out-of-date instruments. The construction of a new observatory had been approved by Prince-elector George III in principle since 1802, and the Westphalian government continued the planning, but Gauss could not move to his new place of work until September 1816. He got new up-to-date instruments, including two meridian circles from Repsold and Reichenbach , and

960-670: A critique of d'Alembert's work. He subsequently produced three other proofs, the last one in 1849 being generally rigorous. His attempts clarified the concept of complex numbers considerably along the way. In the preface to the Disquisitiones , Gauss dates the beginning of his work on number theory to 1795. By studying the works of previous mathematicians like Fermat, Euler, Lagrange, and Legendre, he realized that these scholars had already found much of what he had discovered by himself. The Disquisitiones Arithmeticae , written since 1798 and published in 1801, consolidated number theory as

1080-428: A curious feature of his working style that he carried out calculations with a high degree of precision much more than required, and prepared tables with more decimal places than ever requested for practical purposes. Very likely, this method gave him a lot of material which he used in finding theorems in number theory. Gauss refused to publish work that he did not consider complete and above criticism. This perfectionism

1200-470: A decade. Therese then took over the household and cared for Gauss for the rest of his life; after her father's death, she married actor Constantin Staufenau. Her sister Wilhelmina married the orientalist Heinrich Ewald . Gauss's mother Dorothea lived in his house from 1817 until she died in 1839. The eldest son Joseph, while still a schoolboy, helped his father as an assistant during the survey campaign in

1320-479: A discipline and covered both elementary and algebraic number theory . Therein he introduces the triple bar symbol ( ≡ ) for congruence and uses it for a clean presentation of modular arithmetic . It deals with the unique factorization theorem and primitive roots modulo n . In the main sections, Gauss presents the first two proofs of the law of quadratic reciprocity and develops the theories of binary and ternary quadratic forms . The Disquisitiones include

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1440-572: A doublesided page. A work isn't long if you can't take anything out of it, but you, Cosconius, write even a couplet too long. Poets known for their epigrams whose work has been lost include Cornificia . In early English literature the short couplet poem was dominated by the poetic epigram and proverb , especially in the translations of the Bible and the Greek and Roman poets . Two successive lines of verse that rhyme with each other are known as

1560-743: A few in German , Dutch , Norwegian , Danish and Swedish . Latin is still spoken in Vatican City, a city-state situated in Rome that is the seat of the Catholic Church . The works of several hundred ancient authors who wrote in Latin have survived in whole or in part, in substantial works or in fragments to be analyzed in philology . They are in part the subject matter of the field of classics . Their works were published in manuscript form before

1680-584: A geometrical problem that had occupied mathematicians since the Ancient Greeks , when he determined in 1796 which regular polygons can be constructed by compass and straightedge . This discovery ultimately led Gauss to choose mathematics instead of philology as a career. Gauss's mathematical diary, a collection of short remarks about his results from the years 1796 until 1814, shows that many ideas for his mathematical magnum opus Disquisitiones Arithmeticae (1801) date from this time. Gauss graduated as

1800-680: A habit in his later years, for example, the number of paths from his home to certain places in Göttingen, or the number of living days of persons; he congratulated Humboldt in December 1851 for having reached the same age as Isaac Newton at his death, calculated in days. Similar to his excellent knowledge of Latin he was also acquainted with modern languages. At the age of 62, he began to teach himself Russian , very likely to understand scientific writings from Russia, among them those of Lobachevsky on non-Euclidean geometry. Gauss read both classical and modern literature, and English and French works in

1920-552: A heart attack in Göttingen; and was interred in the Albani Cemetery there. Heinrich Ewald , Gauss's son-in-law, and Wolfgang Sartorius von Waltershausen , Gauss's close friend and biographer, gave eulogies at his funeral. Gauss was a successful investor and accumulated considerable wealth with stocks and securities, finally a value of more than 150 thousand Thaler; after his death, about 18 thousand Thaler were found hidden in his rooms. The day after Gauss's death his brain

2040-550: A less educated person. Its content makes it clear how popular such poems were: Admiror, O paries, te non cecidisse ruinis qui tot scriptorum taedia sustineas. I'm astonished, wall, that you haven't collapsed into ruins, since you're holding up the weary verse of so many poets. However, in the literary world, epigrams were most often gifts to patrons or entertaining verse to be published, not inscriptions. Many Roman writers seem to have composed epigrams, including Domitius Marsus , whose collection Cicuta (now lost)

2160-562: A new Classical Latin arose, a conscious creation of the orators, poets, historians and other literate men, who wrote the great works of classical literature , which were taught in grammar and rhetoric schools. Today's instructional grammars trace their roots to such schools , which served as a sort of informal language academy dedicated to maintaining and perpetuating educated speech. Philological analysis of Archaic Latin works, such as those of Plautus , which contain fragments of everyday speech, gives evidence of an informal register of

2280-407: A power of 2 and any number of distinct Fermat primes . In the same section, he gives a result on the number of solutions of certain cubic polynomials with coefficients in finite fields , which amounts to counting integral points on an elliptic curve . An unfinished eighth chapter was found among left papers only after his death, consisting of work done during 1797–1799. One of Gauss's first results

2400-476: A remarkable unity in phonological forms and developments, bolstered by the stabilising influence of their common Christian (Roman Catholic) culture. It was not until the Muslim conquest of Spain in 711, cutting off communications between the major Romance regions, that the languages began to diverge seriously. The spoken Latin that would later become Romanian diverged somewhat more from the other varieties, as it

2520-495: A residual pressure to keep things concise , even when they were recited in Hellenistic times. Many of the characteristic types of literary epigram look back to inscriptional contexts, particularly funerary epigram, which in the Hellenistic era becomes a literary exercise. Many "sympotic" epigrams combine sympotic and funerary elements – they tell their readers (or listeners) to drink and live for today because life

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2640-699: A scandal in public, Eugen suddenly left Göttingen under dramatic circumstances in September 1830 and emigrated via Bremen to the United States. He wasted the little money he had taken to start, after which his father refused further financial support. The youngest son Wilhelm wanted to qualify for agricultural administration, but had difficulties getting an appropriate education, and eventually emigrated as well. Only Gauss's youngest daughter Therese accompanied him in his last years of life. Collecting numerical data on very different things, useful or useless, became

2760-709: A small number of Latin services held in the Anglican church. These include an annual service in Oxford, delivered with a Latin sermon; a relic from the period when Latin was the normal spoken language of the university. In the Western world, many organizations, governments and schools use Latin for their mottos due to its association with formality, tradition, and the roots of Western culture . Canada's motto A mari usque ad mare ("from sea to sea") and most provincial mottos are also in Latin. The Canadian Victoria Cross

2880-412: A strong calculus as the sole tasks of astronomy. At university, he was accompanied by a staff of other lecturers in his disciplines, who completed the educational program; these included the mathematician Thibaut with his lectures, the physicist Mayer , known for his textbooks, his successor Weber since 1831, and in the observatory Harding , who took the main part of lectures in practical astronomy. When

3000-471: A title for the couplet, as is shown in Sonnet VIII of the sequence. During the early 20th century, the rhymed epigram couplet form developed into a fixed verse image form, with an integral title as the third line. Adelaide Crapsey codified the couplet form into a two-line rhymed verse of ten syllables per line with her image couplet poem On Seeing Weather-Beaten Trees , first published in 1915. By

3120-442: A university chair in Göttingen, "because he was always involved in some polemic." Gauss's life was overshadowed by severe problems in his family. When his first wife Johanna suddenly died shortly after the birth of their third child, he revealed the grief in a last letter to his dead wife in the style of an ancient threnody , the most personal surviving document of Gauss. The situation worsened when tuberculosis ultimately destroyed

3240-411: Is Veritas ("truth"). Veritas was the goddess of truth, a daughter of Saturn, and the mother of Virtue. Switzerland has adopted the country's Latin short name Helvetia on coins and stamps, since there is no room to use all of the nation's four official languages . For a similar reason, it adopted the international vehicle and internet code CH , which stands for Confoederatio Helvetica ,

3360-716: Is a brief, interesting, memorable, sometimes surprising or satirical statement. The word derives from the Greek ἐπίγραμμα ( epígramma , "inscription", from ἐπιγράφειν [ epigráphein ], "to write on, to inscribe"). This literary device has been practiced for over two millennia. The presence of wit or sarcasm tends to distinguish non-poetic epigrams from aphorisms and adages , which typically do not show those qualities. The Greek tradition of epigrams began as poems inscribed on votive offerings at sanctuaries – including statues of athletes – and on funerary monuments, for example "Go tell it to

3480-420: Is a kind of written Latin used in the 3rd to 6th centuries. This began to diverge from Classical forms at a faster pace. It is characterised by greater use of prepositions, and word order that is closer to modern Romance languages, for example, while grammatically retaining more or less the same formal rules as Classical Latin. Ultimately, Latin diverged into a distinct written form, where the commonly spoken form

3600-640: Is a reversal of the original phrase Non terrae plus ultra ("No land further beyond", "No further!"). According to legend , this phrase was inscribed as a warning on the Pillars of Hercules , the rocks on both sides of the Strait of Gibraltar and the western end of the known, Mediterranean world. Charles adopted the motto following the discovery of the New World by Columbus, and it also has metaphorical suggestions of taking risks and striving for excellence. In

3720-607: Is considered to be the master of the Latin epigram. His technique relies heavily on the satirical poem with a joke in the last line, thus drawing him closer to the modern idea of epigram as a genre. Here he defines his genre against a (probably fictional) critic (in the latter half of 2.77): Disce quod ignoras: Marsi doctique Pedonis saepe duplex unum pagina tractat opus. Non sunt longa quibus nihil est quod demere possis, sed tu, Cosconi, disticha longa facis. Learn what you don't know: one work of (Domitius) Marsus or learned Pedo often stretches out over

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3840-660: Is highly fusional , with classes of inflections for case , number , person , gender , tense , mood , voice , and aspect . The Latin alphabet is directly derived from the Etruscan and Greek alphabets . Latin remains the official language of the Holy See and the Roman Rite of the Catholic Church at the Vatican City . The church continues to adapt concepts from modern languages to Ecclesiastical Latin of

3960-689: Is modelled after the British Victoria Cross which has the inscription "For Valour". Because Canada is officially bilingual, the Canadian medal has replaced the English inscription with the Latin Pro Valore . Spain's motto Plus ultra , meaning "even further", or figuratively "Further!", is also Latin in origin. It is taken from the personal motto of Charles V , Holy Roman Emperor and King of Spain (as Charles I), and

4080-436: Is short. Generally, any theme found in classical elegies could be and were adapted for later literary epigrams. Hellenistic epigrams are also thought of as having a "point" – that is, the poem ends in a punchline or satirical twist. By no means do all Greek epigrams behave this way; many are simply descriptive, but Meleager of Gadara and Philippus of Thessalonica , the first comprehensive anthologists, preferred

4200-1011: Is taught at many high schools, especially in Europe and the Americas. It is most common in British public schools and grammar schools, the Italian liceo classico and liceo scientifico , the German Humanistisches Gymnasium and the Dutch gymnasium . Occasionally, some media outlets, targeting enthusiasts, broadcast in Latin. Notable examples include Radio Bremen in Germany, YLE radio in Finland (the Nuntii Latini broadcast from 1989 until it

4320-427: Is widely considered one of the greatest mathematicians ever. While studying at the University of Göttingen , he propounded several mathematical theorems . Gauss completed his masterpieces Disquisitiones Arithmeticae and Theoria motus corporum coelestium as a private scholar. He gave the second and third complete proofs of the fundamental theorem of algebra , made contributions to number theory , and developed

4440-543: The Corpus Inscriptionum Latinarum (CIL). Authors and publishers vary, but the format is about the same: volumes detailing inscriptions with a critical apparatus stating the provenance and relevant information. The reading and interpretation of these inscriptions is the subject matter of the field of epigraphy . About 270,000 inscriptions are known. The Latin influence in English has been significant at all stages of its insular development. In

4560-512: The Gauss composition law for binary quadratic forms, as well as the enumeration of the number of representations of an integer as the sum of three squares. As an almost immediate corollary of his theorem on three squares , he proves the triangular case of the Fermat polygonal number theorem for n = 3. From several analytic results on class numbers that Gauss gives without proof towards the end of

4680-884: The Hellenistic period through the Imperial period and Late Antiquity into the compiler's own Byzantine era – a thousand years of short elegiac texts on every topic under the sun. The Anthology includes one book of Christian epigrams as well as one book of erotic and amorous homosexual epigrams called the Μοῦσα Παιδικἠ ( Mousa Paidike , "The Boyish Muse"). Roman epigrams owe much to their Greek predecessors and contemporaries. Roman epigrams, however, were often more satirical than Greek ones, and at times used obscene language for effect. Latin epigrams could be composed as inscriptions or graffiti , such as this one from Pompeii , which exists in several versions and seems from its inexact meter to have been composed by

4800-528: The Holy See , the primary language of its public journal , the Acta Apostolicae Sedis , and the working language of the Roman Rota . Vatican City is also home to the world's only automatic teller machine that gives instructions in Latin. In the pontifical universities postgraduate courses of Canon law are taught in Latin, and papers are written in the same language. There are

4920-502: The Late Latin period, language changes reflecting spoken (non-classical) norms tend to be found in greater quantities in texts. As it was free to develop on its own, there is no reason to suppose that the speech was uniform either diachronically or geographically. On the contrary, Romanised European populations developed their own dialects of the language, which eventually led to the differentiation of Romance languages . Late Latin

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5040-607: The Middle Ages as a working and literary language from the 9th century to the Renaissance , which then developed a classicizing form, called Renaissance Latin . This was the basis for Neo-Latin which evolved during the early modern period . In these periods Latin was used productively and generally taught to be written and spoken, at least until the late seventeenth century, when spoken skills began to erode. It then became increasingly taught only to be read. Latin grammar

5160-574: The Middle Ages , borrowing from Latin occurred from ecclesiastical usage established by Saint Augustine of Canterbury in the 6th century or indirectly after the Norman Conquest , through the Anglo-Norman language . From the 16th to the 18th centuries, English writers cobbled together huge numbers of new words from Latin and Greek words, dubbed " inkhorn terms ", as if they had spilled from a pot of ink. Many of these words were used once by

5280-535: The Russian Academy of Sciences in St. Peterburg and Landshut University . Later, the Duke promised him the foundation of an observatory in Brunswick in 1804. Architect Peter Joseph Krahe made preliminary designs, but one of Napoleon's wars cancelled those plans: the Duke was killed in the battle of Jena in 1806. The duchy was abolished in the following year, and Gauss's financial support stopped. When Gauss

5400-407: The common language of international communication , science, scholarship and academia in Europe until well into the early 19th century, by which time modern languages had supplanted it in common academic and political usage. Late Latin is the literary language from the 3rd century AD onward. No longer spoken as a native language, Medieval Latin was used across Western and Catholic Europe during

5520-546: The popularization of scientific matters. His only attempts at popularization were his works on the date of Easter (1800/1802) and the essay Erdmagnetismus und Magnetometer of 1836. Gauss published his papers and books exclusively in Latin or German . He wrote Latin in a classical style but used some customary modifications set by contemporary mathematicians. In his inaugural lecture at Göttingen University from 1808, Gauss claimed reliable observations and results attained only by

5640-574: The British Crown. The motto is featured on all presently minted coinage and has been featured in most coinage throughout the nation's history. Several states of the United States have Latin mottos , such as: Many military organizations today have Latin mottos, such as: Some law governing bodies in the Philippines have Latin mottos, such as: Some colleges and universities have adopted Latin mottos, for example Harvard University 's motto

5760-495: The Duke granted him the resources for studies of mathematics, sciences, and classical languages at the University of Göttingen until 1798. His professor in mathematics was Abraham Gotthelf Kästner , whom Gauss called "the leading mathematician among poets, and the leading poet among mathematicians" because of his epigrams . Astronomy was taught by Karl Felix Seyffer , with whom Gauss stayed in correspondence after graduation; Olbers and Gauss mocked him in their correspondence. On

5880-491: The French language. Gauss was "in front of the new development" with documented research since 1799, his wealth of new ideas, and his rigour of demonstration. Whereas previous mathematicians like Leonhard Euler let the readers take part in their reasoning for new ideas, including certain erroneous deviations from the correct path, Gauss however introduced a new style of direct and complete explanation that did not attempt to show

6000-703: The Germanic and Slavic nations. It became useful for international communication between the member states of the Holy Roman Empire and its allies. Without the institutions of the Roman Empire that had supported its uniformity, Medieval Latin was much more liberal in its linguistic cohesion: for example, in classical Latin sum and eram are used as auxiliary verbs in the perfect and pluperfect passive, which are compound tenses. Medieval Latin might use fui and fueram instead. Furthermore,

6120-599: The Grinch Stole Christmas! , The Cat in the Hat , and a book of fairy tales, " fabulae mirabiles ", are intended to garner popular interest in the language. Additional resources include phrasebooks and resources for rendering everyday phrases and concepts into Latin, such as Meissner's Latin Phrasebook . Some inscriptions have been published in an internationally agreed, monumental, multivolume series,

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6240-507: The Kingdom of Hanover together with an arc measurement project from 1820 to 1844; he was one of the founders of geophysics and formulated the fundamental principles of magnetism . Fruits of his practical work were the inventions of the heliotrope in 1821, a magnetometer in 1833 and – alongside Wilhelm Eduard Weber – the first electromagnetic telegraph in 1833. Gauss was the first to discover and study non-Euclidean geometry , coining

6360-630: The Latin language. Contemporary Latin is more often studied to be read rather than spoken or actively used. Latin has greatly influenced the English language , along with a large number of others, and historically contributed many words to the English lexicon , particularly after the Christianization of the Anglo-Saxons and the Norman Conquest . Latin and Ancient Greek roots are heavily used in English vocabulary in theology ,

6480-456: The Spartans, passersby..." . These original epigrams did the same job as a short prose text might have done, but in verse . Epigram became a literary genre in the Hellenistic period , probably developing out of scholarly collections of inscriptional epigrams. Though modern epigrams are usually thought of as very short, Greek literary epigram was not always as short as later examples, and

6600-467: The United States the unofficial national motto until 1956 was E pluribus unum meaning "Out of many, one". The motto continues to be featured on the Great Seal . It also appears on the flags and seals of both houses of congress and the flags of the states of Michigan, North Dakota, New York, and Wisconsin. The motto's 13 letters symbolically represent the original Thirteen Colonies which revolted from

6720-504: The University of Kentucky, the University of Oxford and also Princeton University. There are many websites and forums maintained in Latin by enthusiasts. The Latin Misplaced Pages has more than 130,000 articles. Italian , French , Portuguese , Spanish , Romanian , Catalan , Romansh , Sardinian and other Romance languages are direct descendants of Latin. There are also many Latin borrowings in English and Albanian , as well as

6840-472: The act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again. The posthumous papers, his scientific diary , and short glosses in his own textbooks show that he worked to a great extent in an empirical way. He was a lifelong busy and enthusiastic calculator, who made his calculations with extraordinary rapidity, mostly without precise controlling, but checked

6960-427: The author and then forgotten, but some useful ones survived, such as 'imbibe' and 'extrapolate'. Many of the most common polysyllabic English words are of Latin origin through the medium of Old French . Romance words make respectively 59%, 20% and 14% of English, German and Dutch vocabularies. Those figures can rise dramatically when only non-compound and non-derived words are included. Epigram An epigram

7080-535: The beginning of the Renaissance . Petrarch for example saw Latin as a literary version of the spoken language. Medieval Latin is the written Latin in use during that portion of the post-classical period when no corresponding Latin vernacular existed, that is from around 700 to 1500 AD. The spoken language had developed into the various Romance languages; however, in the educated and official world, Latin continued without its natural spoken base. Moreover, this Latin spread into lands that had never spoken Latin, such as

7200-425: The benefit of those who do not understand Latin. There are also songs written with Latin lyrics . The libretto for the opera-oratorio Oedipus rex by Igor Stravinsky is in Latin. Parts of Carl Orff 's Carmina Burana are written in Latin. Enya has recorded several tracks with Latin lyrics. The continued instruction of Latin is seen by some as a highly valuable component of a liberal arts education. Latin

7320-634: The best-paid professors of the university. When Gauss was asked for help by his colleague and friend Friedrich Wilhelm Bessel in 1810, who was in trouble at Königsberg University because of his lack of an academic title, Gauss provided a doctorate honoris causa for Bessel from the Philosophy Faculty of Göttingen in March 1811. Gauss gave another recommendation for an honorary degree for Sophie Germain but only shortly before her death, so she never received it. He also gave successful support to

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7440-515: The birth of Louis, who himself died a few months later. Gauss chose the first names of his children in honour of Giuseppe Piazzi , Wilhelm Olbers, and Karl Ludwig Harding, the discoverers of the first asteroids. On 4 August 1810, Gauss married Wilhelmine (Minna) Waldeck, a friend of his first wife, with whom he had three more children: Eugen (later Eugene) (1811–1896), Wilhelm (later William) (1813–1879), and Therese (1816–1864). Minna Gauss died on 12 September 1831 after being seriously ill for more than

7560-695: The burdens of teaching, feeling that it was a waste of his time. On the other hand, he occasionally described some students as talented. Most of his lectures dealt with astronomy, geodesy, and applied mathematics , and only three lectures on subjects of pure mathematics. Some of Gauss's students went on to become renowned mathematicians, physicists, and astronomers: Moritz Cantor , Dedekind , Dirksen , Encke , Gould , Heine , Klinkerfues , Kupffer , Listing , Möbius , Nicolai , Riemann , Ritter , Schering , Scherk , Schumacher , von Staudt , Stern , Ursin ; as geoscientists Sartorius von Waltershausen , and Wappäus . Gauss did not write any textbook and disliked

7680-430: The comic playwrights Plautus and Terence and the author Petronius . While often called a "dead language", Latin did not undergo language death . By the 6th to 9th centuries, natural language change eventually resulted in Latin as a vernacular language evolving into distinct Romance languages in the large areas where it had come to be natively spoken. However, even after the fall of Western Rome , Latin remained

7800-494: The contemporary school of Naturphilosophie . Gauss had an "aristocratic and through and through conservative nature", with little respect for people's intelligence and morals, following the motto " mundus vult decipi ". He disliked Napoleon and his system, and all kinds of violence and revolution caused horror to him. Thus he condemned the methods of the Revolutions of 1848 , though he agreed with some of their aims, such as

7920-465: The country's full Latin name. Some film and television in ancient settings, such as Sebastiane , The Passion of the Christ and Barbarians (2020 TV series) , have been made with dialogue in Latin. Occasionally, Latin dialogue is used because of its association with religion or philosophy, in such film/television series as The Exorcist and Lost (" Jughead "). Subtitles are usually shown for

8040-503: The decline in written Latin output. Despite having no native speakers, Latin is still used for a variety of purposes in the contemporary world. The largest organisation that retains Latin in official and quasi-official contexts is the Catholic Church . The Catholic Church required that Mass be carried out in Latin until the Second Vatican Council of 1962–1965 , which permitted the use of the vernacular . Latin remains

8160-568: The development of European culture, religion and science. The vast majority of written Latin belongs to this period, but its full extent is unknown. The Renaissance reinforced the position of Latin as a spoken and written language by the scholarship by the Renaissance humanists . Petrarch and others began to change their usage of Latin as they explored the texts of the Classical Latin world. Skills of textual criticism evolved to create much more accurate versions of extant texts through

8280-439: The divide between "epigram" and " elegy " is sometimes indistinct (they share a characteristic metre , elegiac couplets ). In the classical period , the clear distinction between them was that epigrams were inscribed and meant to be read, while elegies were recited and meant to be heard. Some elegies could be quite short, but only public epigrams were longer than ten lines. All the same, the origin of epigram in inscription exerted

8400-413: The earliest extant Latin literary works, such as the comedies of Plautus and Terence . The Latin alphabet was devised from the Etruscan alphabet . The writing later changed from what was initially either a right-to-left or a boustrophedon script to what ultimately became a strictly left-to-right script. During the late republic and into the first years of the empire, from about 75 BC to AD 200,

8520-445: The fifteenth and sixteenth centuries, and some important texts were rediscovered. Comprehensive versions of authors' works were published by Isaac Casaubon , Joseph Scaliger and others. Nevertheless, despite the careful work of Petrarch, Politian and others, first the demand for manuscripts, and then the rush to bring works into print, led to the circulation of inaccurate copies for several centuries following. Neo-Latin literature

8640-413: The fifth section, it appears that Gauss already knew the class number formula in 1801. In the last section, Gauss gives proof for the constructibility of a regular heptadecagon (17-sided polygon) with straightedge and compass by reducing this geometrical problem to an algebraic one. He shows that a regular polygon is constructible if the number of its sides is either a power of 2 or the product of

8760-666: The first investigations, due to mislabelling, with that of the physician Conrad Heinrich Fuchs , who died in Göttingen a few months after Gauss. A further investigation showed no remarkable anomalies in the brains of both persons. Thus, all investigations on Gauss's brain until 1998, except the first ones of Rudolf and Hermann Wagner, actually refer to the brain of Fuchs. Gauss married Johanna Osthoff on 9 October 1805 in St. Catherine's church in Brunswick. They had two sons and one daughter: Joseph (1806–1873), Wilhelmina (1808–1840), and Louis (1809–1810). Johanna died on 11 October 1809, one month after

8880-439: The first to publish" differed from that of his scientific contemporaries. In contrast to his perfectionism in presenting mathematical ideas, he was criticized for a negligent way of quoting. He justified himself with a very special view of correct quoting: if he gave references, then only in a quite complete way, with respect to the previous authors of importance, which no one should ignore; but quoting in this way needed knowledge of

9000-577: The genre, aligning it with the indigenous Roman tradition of "satura", hexameter satire , as practised by (among others) his contemporary Juvenal . Greek epigram was actually much more diverse, as the Milan Papyrus now indicates. A major source for Greek literary epigram is the Greek Anthology , a compilation from the 10th century AD based on older collections, including those of Meleager and Philippus. It contains epigrams ranging from

9120-523: The health of his second wife Minna over 13 years; both his daughters later suffered from the same disease. Gauss himself gave only slight hints of his distress: in a letter to Bessel dated December 1831 he described himself as "the victim of the worst domestic sufferings". By reason of his wife's illness, both younger sons were educated for some years in Celle , far from Göttingen. The military career of his elder son Joseph ended after more than two decades with

9240-546: The history of Latin, and the kind of informal Latin that had begun to move away from the written language significantly in the post-Imperial period, that led ultimately to the Romance languages . During the Classical period, informal language was rarely written, so philologists have been left with only individual words and phrases cited by classical authors, inscriptions such as Curse tablets and those found as graffiti . In

9360-456: The history of science and more time than he wished to spend. Soon after Gauss's death, his friend Sartorius published the first biography (1856), written in a rather enthusiastic style. Sartorius saw him as a serene and forward-striving man with childlike modesty, but also of "iron character" with an unshakeable strength of mind. Apart from his closer circle, others regarded him as reserved and unapproachable "like an Olympian sitting enthroned on

9480-462: The idea of a unified Germany. As far as the political system is concerned, he had a low estimation of the constitutional system; he criticized parliamentarians of his time for a lack of knowledge and logical errors. Some Gauss biographers have speculated on his religious beliefs. He sometimes said "God arithmetizes" and "I succeeded – not on account of my hard efforts, but by the grace of the Lord." Gauss

9600-703: The invention of printing and are now published in carefully annotated printed editions, such as the Loeb Classical Library , published by Harvard University Press , or the Oxford Classical Texts , published by Oxford University Press . Latin translations of modern literature such as: The Hobbit , Treasure Island , Robinson Crusoe , Paddington Bear , Winnie the Pooh , The Adventures of Tintin , Asterix , Harry Potter , Le Petit Prince , Max and Moritz , How

9720-704: The language of the Roman Rite . The Tridentine Mass (also known as the Extraordinary Form or Traditional Latin Mass) is celebrated in Latin. Although the Mass of Paul VI (also known as the Ordinary Form or the Novus Ordo) is usually celebrated in the local vernacular language, it can be and often is said in Latin, in part or in whole, especially at multilingual gatherings. It is the official language of

9840-405: The language, Vulgar Latin (termed sermo vulgi , "the speech of the masses", by Cicero ). Some linguists, particularly in the nineteenth century, believed this to be a separate language, existing more or less in parallel with the literary or educated Latin, but this is now widely dismissed. The term 'Vulgar Latin' remains difficult to define, referring both to informal speech at any time within

9960-597: The mathematician Gotthold Eisenstein in Berlin. Gauss was loyal to the House of Hanover . After King William IV died in 1837, the new Hanoverian King Ernest Augustus annulled the 1833 constitution. Seven professors, later known as the " Göttingen Seven ", protested against this, among them his friend and collaborator Wilhelm Weber and Gauss's son-in-law Heinrich Ewald. All of them were dismissed, and three of them were expelled, but Ewald and Weber could stay in Göttingen. Gauss

10080-431: The meanings of many words were changed and new words were introduced, often under influence from the vernacular. Identifiable individual styles of classically incorrect Latin prevail. Renaissance Latin, 1300 to 1500, and the classicised Latin that followed through to the present are often grouped together as Neo-Latin , or New Latin, which have in recent decades become a focus of renewed study , given their importance for

10200-586: The observatory was completed, Gauss took his living accommodation in the western wing of the new observatory and Harding in the eastern one. They had once been on friendly terms, but over time they became alienated, possibly – as some biographers presume – because Gauss had wished the equal-ranked Harding to be no more than his assistant or observer. Gauss used the new meridian circles nearly exclusively, and kept them away from Harding, except for some very seldom joint observations. Brendel subdivides Gauss's astronomic activity chronologically into seven periods, of which

10320-406: The original languages. His favorite English author was Walter Scott , his favorite German Jean Paul . Gauss liked singing and went to concerts. He was a busy newspaper reader; in his last years, he used to visit an academic press salon of the university every noon. Gauss did not care much for philosophy, and mocked the "splitting hairs of the so-called metaphysicians", by which he meant proponents of

10440-413: The other hand, he thought highly of Georg Christoph Lichtenberg , his teacher of physics, and of Christian Gottlob Heyne , whose lectures in classics Gauss attended with pleasure. Fellow students of this time were Johann Friedrich Benzenberg , Farkas Bolyai , and Heinrich Wilhelm Brandes . He was likely a self-taught student in mathematics since he independently rediscovered several theorems. He solved

10560-473: The problem by accepting offers from Berlin in 1810 and 1825 to become a full member of the Prussian Academy without burdening lecturing duties, as well as from Leipzig University in 1810 and from Vienna University in 1842, perhaps because of the family's difficult situation. Gauss's salary was raised from 1000 Reichsthaler in 1810 to 2400 Reichsthaler in 1824, and in his later years he was one of

10680-435: The prolific American poet Emily Dickinson . Her poem No. 1534 is a typical example of her eleven poetic epigrams. The novelist George Eliot also included couplets throughout her writings. Her best example is in her sequenced sonnet poem entitled Brother and Sister in which each of the eleven sequenced sonnet ends with a couplet. In her sonnets, the preceding lead-in-line, to the couplet ending of each, could be thought of as

10800-588: The railroad system in the US for some months. Eugen left Göttingen in September 1830 and emigrated to the United States, where he joined the army for five years. He then worked for the American Fur Company in the Midwest. Later, he moved to Missouri and became a successful businessman. Wilhelm married a niece of the astronomer Bessel ; he then moved to Missouri, started as a farmer and became wealthy in

10920-436: The rank of a poorly paid first lieutenant , although he had acquired a considerable knowledge of geodesy. He needed financial support from his father even after he was married. The second son Eugen shared a good measure of his father's talent in computation and languages, but had a vivacious and sometimes rebellious character. He wanted to study philology, whereas Gauss wanted him to become a lawyer. Having run up debts and caused

11040-433: The reader the author's train of thought. Gauss was the first to restore that rigor of demonstration which we admire in the ancients and which had been forced unduly into the background by the exclusive interest of the preceding period in new developments. But for himself, he propagated a quite different ideal, given in a letter to Farkas Bolyai as follows: It is not knowledge, but the act of learning, not possession but

11160-462: The results by masterly estimation. Nevertheless, his calculations were not always free from mistakes. He coped with the enormous workload by using skillful tools. Gauss used a lot of mathematical tables , examined their exactness, and constructed new tables on various matters for personal use. He developed new tools for effective calculation, for example the Gaussian elimination . It has been taken as

11280-421: The sciences , medicine , and law . A number of phases of the language have been recognized, each distinguished by subtle differences in vocabulary, usage, spelling, and syntax. There are no hard and fast rules of classification; different scholars emphasize different features. As a result, the list has variants, as well as alternative names. In addition to the historical phases, Ecclesiastical Latin refers to

11400-555: The shoe business in St. Louis in later years. Eugene and William have numerous descendants in America, but the Gauss descendants left in Germany all derive from Joseph, as the daughters had no children. In the first two decades of the 19th century, Gauss was the only important mathematician in Germany, comparable to the leading French ones; his Disquisitiones Arithmeticae was the first mathematical book from Germany to be translated into

11520-476: The short and witty epigram. Since their collections helped form knowledge of the genre in Rome and then later throughout Europe, Epigram came to be associated with 'point', especially because the European epigram tradition takes the Latin poet Martial as its principal model; he copied and adapted Greek models (particularly the contemporary poets Lucillius and Nicarchus ) selectively and in the process redefined

11640-641: The styles used by the writers of the Roman Catholic Church from late antiquity onward, as well as by Protestant scholars. The earliest known form of Latin is Old Latin, also called Archaic or Early Latin, which was spoken from the Roman Kingdom , traditionally founded in 753 BC, through the later part of the Roman Republic , up to 75 BC, i.e. before the age of Classical Latin . It is attested both in inscriptions and in some of

11760-577: The summer of 1821. After a short time at university, in 1824 Joseph joined the Hanoverian army and assisted in surveying again in 1829. In the 1830s he was responsible for the enlargement of the survey network to the western parts of the kingdom. With his geodetical qualifications, he left the service and engaged in the construction of the railway network as director of the Royal Hanoverian State Railways . In 1836 he studied

11880-419: The summit of science". His close contemporaries agreed that Gauss was a man of difficult character. He often refused to accept compliments. His visitors were occasionally irritated by his grumpy behaviour, but a short time later his mood could change, and he would become a charming, open-minded host. Gauss abominated polemic natures; together with his colleague Hausmann he opposed to a call for Justus Liebig on

12000-473: The term as well. He further developed a fast Fourier transform some 160 years before John Tukey and James Cooley . Gauss refused to publish incomplete work and left several works to be edited posthumously . He believed that the act of learning, not possession of knowledge, provided the greatest enjoyment. Gauss confessed to disliking teaching, but some of his students became influential mathematicians, such as Richard Dedekind and Bernhard Riemann . Gauss

12120-417: The theories of binary and ternary quadratic forms. Gauss was instrumental in the identification of Ceres as a dwarf planet. His work on the motion of planetoids disturbed by large planets led to the introduction of the Gaussian gravitational constant and the method of least squares , which he had discovered before Adrien-Marie Legendre published it. Gauss was in charge of the extensive geodetic survey of

12240-422: The written form of Latin was increasingly standardized into a fixed form, the spoken forms began to diverge more greatly. Currently, the five most widely spoken Romance languages by number of native speakers are Spanish , Portuguese , French , Italian , and Romanian . Despite dialectal variation, which is found in any widespread language, the languages of Spain, France, Portugal, and Italy have retained

12360-417: The years since 1820 are taken as a "period of lower astronomical activity". The new, well-equipped observatory did not work as effectively as other ones; Gauss's astronomical research had the character of a one-man enterprise without a long-time observation program, and the university established a place for an assistant only after Harding died in 1834. Nevertheless, Gauss twice refused the opportunity to solve

12480-412: Was Robert Hayman 's Quodlibets, Lately Come Over from New Britaniola, Old Newfoundland , which is a collection of over 300 epigrams, many of which do not conform to the two-line rule or trend. While the collection was written between 1618 and 1628 in what is now Harbour Grace, Newfoundland, it was published shortly after his return to Britain. In Victorian times the epigram couplet was often used by

12600-790: Was a member of the Lutheran church , like most of the population in northern Germany. It seems that he did not believe all dogmas or understand the Holy Bible quite literally. Sartorius mentioned Gauss's religious tolerance , and estimated his "insatiable thirst for truth" and his sense of justice as motivated by religious convictions. In his doctoral thesis from 1799, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root . Mathematicians including Jean le Rond d'Alembert had produced false proofs before him, and Gauss's dissertation contains

12720-730: Was also used as a convenient medium for translations of important works first written in a vernacular, such as those of Descartes . Latin education underwent a process of reform to classicise written and spoken Latin. Schooling remained largely Latin medium until approximately 1700. Until the end of the 17th century, the majority of books and almost all diplomatic documents were written in Latin. Afterwards, most diplomatic documents were written in French (a Romance language ) and later native or other languages. Education methods gradually shifted towards written Latin, and eventually concentrating solely on reading skills. The decline of Latin education took several centuries and proceeded much more slowly than

12840-569: Was born on 30 April 1777 in Brunswick in the Duchy of Brunswick-Wolfenbüttel (now in the German state of Lower Saxony ). His family was of relatively low social status. His father Gebhard Dietrich Gauss (1744–1808) worked variously as a butcher, bricklayer, gardener, and treasurer of a death-benefit fund. Gauss characterized his father as honourable and respected, but rough and dominating at home. He

12960-472: Was calculating asteroid orbits in the first years of the century, he established contact with the astronomical community of Bremen and Lilienthal , especially Wilhelm Olbers , Karl Ludwig Harding , and Friedrich Wilhelm Bessel , as part of the informal group of astronomers known as the Celestial police . One of their aims was the discovery of further planets. They assembled data on asteroids and comets as

13080-698: Was deeply affected by this quarrel but saw no possibility to help them. Gauss took part in academic administration: three times he was elected as dean of the Faculty of Philosophy. Being entrusted with the widow's pension fund of the university, he dealt with actuarial science and wrote a report on the strategy for stabilizing the benefits. He was appointed director of the Royal Academy of Sciences in Göttingen for nine years. Gauss remained mentally active into his old age, even while suffering from gout and general unhappiness. On 23 February 1855, he died of

13200-572: Was experienced in writing and calculating, whereas his second wife Dorothea, Carl Friedrich's mother, was nearly illiterate. He had one elder brother from his father's first marriage. Gauss was a child prodigy in mathematics. When the elementary teachers noticed his intellectual abilities, they brought him to the attention of the Duke of Brunswick who sent him to the local Collegium Carolinum , which he attended from 1792 to 1795 with Eberhard August Wilhelm von Zimmermann as one of his teachers. Thereafter

13320-491: Was extensive and prolific, but less well known or understood today. Works covered poetry, prose stories and early novels, occasional pieces and collections of letters, to name a few. Famous and well regarded writers included Petrarch, Erasmus, Salutati , Celtis , George Buchanan and Thomas More . Non fiction works were long produced in many subjects, including the sciences, law, philosophy, historiography and theology. Famous examples include Isaac Newton 's Principia . Latin

13440-516: Was in keeping with the motto of his personal seal Pauca sed Matura ("Few, but Ripe"). Many colleagues encouraged him to publicize new ideas and sometimes rebuked him if he hesitated too long, in their opinion. Gauss defended himself, claiming that the initial discovery of ideas was easy, but preparing a presentable elaboration was a demanding matter for him, for either lack of time or "serenity of mind". Nevertheless, he published many short communications of urgent content in various journals, but left

13560-503: Was largely separated from the unifying influences in the western part of the Empire. Spoken Latin began to diverge into distinct languages by the 9th century at the latest, when the earliest extant Romance writings begin to appear. They were, throughout the period, confined to everyday speech, as Medieval Latin was used for writing. For many Italians using Latin, though, there was no complete separation between Italian and Latin, even into

13680-500: Was named after the poisonous plant Cicuta for its biting wit, and Lucan , more famous for his epic Pharsalia . Authors whose epigrams survive include Catullus , who wrote both invectives and love epigrams – his poem 85 is one of the latter. Odi et amo. Quare id faciam fortasse requiris. Nescio, sed fieri sentio, et excrucior. I hate and I love. Maybe you'd like to know why I do? I don't know, but I feel it happening, and I am tormented. Martial , however,

13800-732: Was originally spoken by the Latins in Latium (now known as Lazio ), the lower Tiber area around Rome , Italy. Through the expansion of the Roman Republic it became the dominant language in the Italian Peninsula and subsequently throughout the Roman Empire . By the late Roman Republic , Old Latin had evolved into standardized Classical Latin . Vulgar Latin refers to the less prestigious colloquial registers , attested in inscriptions and some literary works such as those of

13920-529: Was perceived as a separate language, for instance early French or Italian dialects, that could be transcribed differently. It took some time for these to be viewed as wholly different from Latin however. After the Western Roman Empire fell in 476 and Germanic kingdoms took its place, the Germanic people adopted Latin as a language more suitable for legal and other, more formal uses. While

14040-509: Was removed, preserved, and studied by Rudolf Wagner , who found its mass to be slightly above average, at 1,492 grams (3.29 lb). Wagner's son Hermann , a geographer, estimated the cerebral area to be 219,588 square millimetres (340.362 sq in) in his doctoral thesis. In 2013, a neurobiologist at the Max Planck Institute for Biophysical Chemistry in Göttingen discovered that Gauss's brain had been mixed up soon after

14160-482: Was shut down in June 2019), and Vatican Radio & Television, all of which broadcast news segments and other material in Latin. A variety of organisations, as well as informal Latin 'circuli' ('circles'), have been founded in more recent times to support the use of spoken Latin. Moreover, a number of university classics departments have begun incorporating communicative pedagogies in their Latin courses. These include

14280-486: Was soon confronted with the demand for two thousand francs from the Westphalian government as a war contribution, which he could not afford to pay. Both Olbers and Laplace wanted to help him with the payment, but Gauss refused their assistance. Finally, an anonymous person from Frankfurt , later discovered to be Prince-primate Dalberg , paid the sum. Gauss took on the directorate of the 60-year-old observatory, founded in 1748 by Prince-elector George II and built on

14400-534: Was the empirically found conjecture of 1792 – the later called prime number theorem – giving an estimation of the number of prime numbers by using the integral logarithm . Latin language Latin ( lingua Latina , pronounced [ˈlɪŋɡʷa ɫaˈtiːna] , or Latinum [ɫaˈtiːnʊ̃] ) is a classical language belonging to the Italic branch of the Indo-European languages . Latin

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