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89-457: Jacobi was born of Ashkenazi Jewish parentage in Potsdam on 10 December 1804. He was the second of four children of a banker, Simon Jacobi. His elder brother, Moritz , would also become known later as an engineer and physicist. He was initially home schooled by his uncle Lehman, who instructed him in the classical languages and elements of mathematics. In 1816, the twelve-year-old Jacobi went to

178-467: A breakdown from overwork in 1843. He then visited Italy for a few months to regain his health. On his return he moved to Berlin, where he lived as a royal pensioner, apart from a very brief interim, until his death. During the Revolution of 1848 Jacobi was politically involved and unsuccessfully presented his parliamentary candidature on behalf of a Liberal club. This led, after the suppression of

267-794: A brief period of stability and unity in Francia . This created opportunities for Jewish merchants to settle again north of the Alps. Charlemagne granted the Jews freedoms similar to those once enjoyed under the Roman Empire . In addition, Jews from southern Italy, fleeing religious persecution, began to move into Central Europe. Returning to Frankish lands, many Jewish merchants took up occupations in finance and commerce, including money lending, or usury . (Church legislation banned Christians from lending money in exchange for interest.) From Charlemagne's time to

356-512: A cultural reorientation. Under the influence of the Haskalah and the struggle for emancipation, as well as the intellectual and cultural ferment in urban centres, some gradually abandoned Yiddish in favor of German and developed new forms of Jewish religious life and cultural identity . Throughout the centuries, Ashkenazim made significant contributions to Europe's philosophy , scholarship, literature , art , music , and science . As

445-649: A figure of one million Jews living in Egypt. Brian McGing rejects Baron's figures entirely, arguing that we have no clue as to the size of the Jewish demographic in the ancient world. Sometimes the scholars who accepted the high number of Jews in Rome had explained it by Jews having been active in proselytising . The idea of ancient Jews trying to convert Gentiles to Judaism is nowadays rejected by several scholars. The Romans did not distinguish between Jews inside and outside of

534-466: A genus g {\displaystyle g} algebraic curve, obtained by quotienting C g {\displaystyle {\mathbf {C} }^{g}} by the lattice of periods is referred to as the Jacobian variety . This method of inversion, and its subsequent extension by Weierstrass and Riemann to arbitrary algebraic curves, may be seen as a higher genus generalization of

623-651: A number of push and pull factors . More Jews moved into these communities as a result of wars, persecution, unrest, and for opportunities in trade and commerce. Jews migrated to southern Europe from the Middle East voluntarily for opportunities in trade and commerce. Following Alexander the Great 's conquests, Jews migrated to Greek settlements in the Eastern Mediterranean, spurred on by economic opportunities. Jewish economic migration to southern Europe

712-494: A proportion of the world Jewish population , Ashkenazim were estimated to be 3% in the 11th century, rising to 92% in 1930 near the population's peak. The Ashkenazi population was significantly diminished by the Holocaust carried out by Nazi Germany during World War II which killed some six million Jews, affecting almost every European Jewish family. In 1933, prior to World War II, the estimated worldwide Jewish population

801-512: A result of Judeo-Latin language contact with various High German vernaculars in the medieval period. It is a Germanic language written in Hebrew letters, and heavily influenced by Hebrew and Aramaic , with some elements of Romance and later Slavic languages . Historical records show evidence of Jewish communities north of the Alps and Pyrenees as early as the 8th and 9th centuries. By

890-546: A very different lifestyle to that of their neighbours; all of these tendencies increased with every outbreak of antisemitism . In parts of Eastern Europe, before the arrival of the Ashkenazi Jews from Central Europe, some non-Ashkenazi Jews were present who spoke Leshon Knaan and held various other Non-Ashkenazi traditions and customs. In 1966, the historian Cecil Roth questioned the inclusion of all Yiddish speaking Jews as Ashkenazim in descent, suggesting that upon

979-546: A very high toll of life and enslavement. The First Jewish-Roman War (66–73 CE) resulted in the destruction of Jerusalem and the Second Temple . Two generations later, the Bar Kokhba Revolt (132–136 CE) erupted. Judea's countryside was devastated, and many were killed, displaced or sold into slavery. Jerusalem was rebuilt as a Roman colony under the name of Aelia Capitolina , and the province of Judea

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1068-594: Is also believed to have occurred during the Roman period. In 63 BCE, the Siege of Jerusalem saw the Roman Republic conquer Judea, and thousands of Jewish prisoners of war were brought to Rome as slaves. After gaining their freedom, they settled permanently in Rome as traders. It is likely that there was an additional influx of Jewish slaves taken to southern Europe by Roman forces after the capture of Jerusalem by

1157-667: The Saquliba or Slavic territories , and such usage covered also the lands of tribes neighboring the Slavs, and Eastern and Central Europe. In modern times, Samuel Krauss identified the Biblical "Ashkenaz" with Khazaria . Sometime in the Early Medieval period, the Jews of central and eastern Europe came to be called by this term. Conforming to the custom of designating areas of Jewish settlement with biblical names, Spain

1246-541: The Berlin Academy . Ashkenazi Jew Ashkenazi Jews ( / ˌ ɑː ʃ k ə ˈ n ɑː z i , ˌ æ ʃ -/ A(H)SH -kə- NAH -zee ; also known as Ashkenazic Jews or Ashkenazim ) constitute a Jewish diaspora population that emerged in the Holy Roman Empire around the end of the first millennium CE . They traditionally speak Yiddish , a language that originated in

1335-770: The Cimmerians . The Biblical Ashkenaz is usually derived from Assyrian Aškūza ( cuneiform Aškuzai/Iškuzai ), a people who expelled the Cimmerians from the Armenian area of the Upper Euphrates ; the name Aškūza is identified with the Scythians . The intrusive n in the Biblical name is likely due to a scribal error confusing a vav ו ‎ with a nun נ ‎ . In Jeremiah 51:27, Ashkenaz figures as one of three kingdoms in

1424-733: The Crusaders as Ashkenazim. Given the close links between the Jewish communities of France and Germany following the Carolingian unification , the term Ashkenazi came to refer to the Jews of both medieval Germany and France. Like other Jewish ethnic groups , the Ashkenazi originate from the Israelites and Hebrews of historical Israel and Judah . Ashkenazi Jews share a significant amount of ancestry with other Jewish populations and derive their ancestry mostly from populations in

1513-691: The Hamilton–Jacobi theory . It was in algebraic development that Jacobi's particular power mainly lay, and he made important contributions of this kind in many areas of mathematics, as shown by his long list of papers in Crelle's Journal and elsewhere from 1826 onwards. He is said to have told his students that when looking for a research topic, one should 'Invert, always invert' (German original: "man muss immer umkehren" ), reflecting his belief that inverting known results can open up new fields for research, for example inverting elliptic integrals and focusing on

1602-478: The Holocaust . The answer to why there was so little assimilation of Jews in central and eastern Europe for so long would seem to lie in part in the probability that the alien surroundings in central and eastern Europe were not conducive, though there was some assimilation. Furthermore, Jews lived almost exclusively in shtetls , maintained a strong system of education for males, heeded rabbinic leadership, and had

1691-631: The Isthmus of Corinth in Greece. Jewish slaves and their children eventually gained their freedom and joined local free Jewish communities. Many Jews were denied full Roman citizenship until Emperor Caracalla granted all free peoples this privilege in 212 CE. Jews were required to pay a poll tax until the reign of Emperor Julian in 363 CE. In the late Roman Empire, Jews were free to form networks of cultural and religious ties and enter into various local occupations. However, after Christianity became

1780-631: The Jacobi integral (1836) for a sidereal coordinate system . His theory of the last multiplier is treated in Vorlesungen über Dynamik , edited by Alfred Clebsch (1866). He left many manuscripts, portions of which have been published at intervals in Crelle's Journal. His other works include Commentatio de transformatione integralis duplicis indefiniti in formam simpliciorem (1832), Canon arithmeticus (1839), and Opuscula mathematica (1846–1857). His Gesammelte Werke (1881–1891) were published by

1869-675: The Minhag of Ashkenaz and Poland. According to 16th-century mystic Rabbi Elijah of Chelm , Ashkenazi Jews lived in Jerusalem during the 11th century. The story is told that a German-speaking Jew saved the life of a young German man surnamed Dolberger. So when the knights of the First Crusade came to siege Jerusalem, one of Dolberger's family members who was among them rescued Jews in Palestine and carried them back to Worms to repay

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1958-512: The Plücker relations for Grassmannians . Students of vector fields , Lie theory , Hamiltonian mechanics and operator algebras often encounter the Jacobi identity , the analog of associativity for the Lie bracket operation. Planetary theory and other particular dynamical problems likewise occupied his attention from time to time. While contributing to celestial mechanics , he introduced

2047-561: The Republican Party , while Conservative, Reform, and non denominational ones tend to support the Democratic Party. Religious Jews have minhagim , customs, in addition to halakha , or religious law, and different interpretations of the law. Different groups of religious Jews in different geographic areas historically adopted different customs and interpretations. On certain issues, Orthodox Jews are required to follow

2136-865: The SHuM cities of Speyer, Worms, and Mainz. The cluster of cities contain the earliest Jewish settlements north of the Alps, and played a major role in the formation of Ashkenazi Jewish religious tradition, along with Troyes and Sens in France. Nonetheless, Jewish life in Germany persisted, while some Ashkenazi Jews joined Sephardic Jewry in Spain. Expulsions from England (1290), France (1394), and parts of Germany (15th century), gradually pushed Ashkenazi Jewry eastward, to Poland (10th century), Lithuania (10th century), and Russia (12th century). Over this period of several hundred years, some have suggested, Jewish economic activity

2225-701: The Statute of Kalisz of 1264. By the 15th century, the Ashkenazi Jewish communities in Poland were the largest Jewish communities of the Diaspora. This area, which eventually fell under the domination of Russia, Austria , and Prussia (Germany) following the Partitions of Poland , and was later largely regained by reborn Poland in the interbellum , would remain the main center of Ashkenazi Jewry until

2314-596: The partial derivative ∂ notation of Legendre , which was to become standard. He was one of the first to introduce and study the symmetric polynomials that are now known as Schur polynomials , giving the so-called bialternant formula for these, which is a special case of the Weyl character formula , and deriving the Jacobi–Trudi identities . He also discovered the Desnanot–Jacobi formula for determinants , which underlie

2403-471: The 11th century, Hai Gaon refers to questions that had been addressed to him from Ashkenaz, by which he undoubtedly means Germany. Rashi in the latter half of the 11th century refers to both the language of Ashkenaz and the country of Ashkenaz. During the 12th century, the word appears quite frequently. In the Mahzor Vitry , the kingdom of Ashkenaz is referred to chiefly in regard to the ritual of

2492-477: The 11th century, Jewish settlers moving from southern European and Middle Eastern centers (such as Babylonian Jews and Persian Jews ) and Maghrebi Jewish traders from North Africa who had contacts with their Ashkenazi brethren and had visited each other from time to time in each's domain appear to have begun to settle in the north, especially along the Rhine, often in response to new economic opportunities and at

2581-539: The 9th century, and largely migrated towards northern and eastern Europe during the late Middle Ages due to persecution . Hebrew was primarily used as a literary and sacred language until its 20th-century revival as a common language in Israel. Ashkenazim adapted their traditions to Europe and underwent a transformation in their interpretation of Judaism. In the late 18th and 19th centuries, Jews who remained in or returned to historical German lands experienced

2670-529: The Hellenized parts of the Roman Empire. The excavations suggest they first lived in isolated enclaves attached to Roman legion camps and intermarried with other similar oriental families within the military orders of the region. Raphael Patai states that later Roman writers remarked that they differed little in either customs, manner of writing, or names from the people among whom they dwelt; and it

2759-567: The Holocaust. These included 3 million of 3.3 million Polish Jews (91%); 900,000 of 1.5 million in Ukraine (60%); and 50–90% of the Jews of other Slavic nations, Germany, Hungary, and the Baltic states, and over 25% of the Jews in France. Sephardi communities suffered similar devastation in a few countries, including Greece, the Netherlands and the former Yugoslavia. As the large majority of

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2848-482: The Middle East, Southern Europe and Eastern Europe. Other than their origins in ancient Israel, the question of how Ashkenazi Jews came to exist as a distinct community is unknown, and has given rise to several theories. Beginning in the fourth century BCE, Jewish colonies sprang up in southern Europe, including the Aegean Islands, Greece, and Italy. Jews left ancient Israel for a number of causes, including

2937-568: The Potsdam Gymnasium , where students were taught all the standard subjects: classical languages, history, philology, mathematics, sciences, etc. As a result of the good education he had received from his uncle, as well as his own remarkable abilities, after less than half a year Jacobi was moved to the senior year despite his young age. However, as the University would not accept students younger than 16 years old, he had to remain in

3026-741: The Responsa of Isaac ben Sheshet (numbers 193, 268, 270). In the Midrash compilation, Genesis Rabbah , Rabbi Berechiah mentions Ashkenaz, Riphath, and Togarmah as German tribes or as German lands. It may correspond to a Greek word that may have existed in the Greek dialect of the Jews in Syria Palaestina , or the text is corrupted from "Germanica". This view of Berechiah is based on the Talmud (Yoma 10a; Jerusalem Talmud Megillah 71b), where Gomer,

3115-660: The Theory of Elliptic Functions ) is a treatise on elliptic functions by German mathematician Carl Gustav Jacob Jacobi . The book was first published in 1829, and has been reprinted in volume 1 of his collected works and on several later occasions. The book introduces Jacobi elliptic functions and the Jacobi triple product identity . One of the most exciting moments of my life was when, after computing several of these series, I went down to our mathematical library and found some of them in Jacobi's "Fundamenta nova theoriae..."[3], with

3204-746: The United States after the war. Following the Holocaust, some sources place Ashkenazim today as making up approximately 83%–85% of Jews worldwide, while Sergio DellaPergola in a rough calculation of Sephardic and Mizrahi Jews , implies that Ashkenazi make up a notably lower figure, less than 74%. Other estimates place Ashkenazi Jews as making up about 75% of Jews worldwide. Jews of mixed background are increasingly common, partly because of intermarriage between Ashkenazi and non-Ashkenazi, and partly because many do not see such historic markers as relevant to their life experiences as Jews. Religious Ashkenazi Jews living in Israel are obliged to follow

3293-484: The arrival of Ashkenazi Jews from central Europe to Eastern Europe, from the Middle Ages to the 16th century, there were a substantial number of non-Ashkenazim Jews already there who later abandoned their original Eastern European Jewish culture in favor of the Ashkenazi one. However, according to more recent research, mass migrations of Yiddish-speaking Ashkenazi Jews occurred to Eastern Europe, from Central Europe in

3382-540: The astronomer. The crater Jacobi on the Moon is named after him. One of Jacobi's greatest accomplishments was his theory of elliptic functions and their relation to the elliptic theta function . This was developed in his great treatise Fundamenta nova theoriae functionum ellipticarum (1829), and in later papers in Crelle's Journal . Theta functions are of great importance in mathematical physics because of their role in

3471-530: The authority of the chief Ashkenazi rabbi in halakhic matters. In this respect, a religiously Ashkenazi Jew is an Israeli who is more likely to support certain religious interests in Israel, including certain political parties. These political parties result from the fact that a portion of the Israeli electorate votes for Jewish religious parties; although the electoral map changes from one election to another, there are generally several small parties associated with

3560-500: The cradle of Germanic tribes, as early as a 6th-century gloss to the Historia Ecclesiastica of Eusebius . In the 10th-century History of Armenia of Yovhannes Drasxanakertc'i (1.15), Ashkenaz was associated with Armenia, as it was occasionally in Jewish usage, where its denotation extended at times to Adiabene , Khazaria , Crimea and areas to the east. His contemporary Saadia Gaon identified Ashkenaz with

3649-662: The culture of the Babylonian Talmud that underlies it became established in southern Italy and then spread north to Ashkenaz. Numerous massacres of Jews occurred throughout Europe during the Christian Crusades . Inspired by the preaching of a First Crusade, crusader mobs in France and Germany perpetrated the Rhineland massacres of 1096, devastating Jewish communities along the Rhine River, including

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3738-459: The customs of their ancestors and do not believe they have the option of picking and choosing. For this reason, observant Jews at times find it important for religious reasons to ascertain who their household's religious ancestors are in order to know what customs their household should follow. These times include, for example, when two Jews of different ethnic background marry, when a non-Jew converts to Judaism and determines what customs to follow for

3827-573: The degree and sources of European admixture , with some focusing on the European genetic origin in Ashkenazi maternal lineages, contrasting with the predominantly Middle Eastern genetic origin in paternal lineages. The name Ashkenazi derives from the biblical figure of Ashkenaz , the first son of Gomer , son of Japhet , son of Noah , and a Japhetic patriarch in the Table of Nations ( Genesis 10 ). The name of Gomer has often been linked to

3916-548: The early Middle Ages, some Jews assimilated into the dominant Greek and Latin cultures, mostly through conversion to Christianity. King Dagobert I of the Franks expelled the Jews from his Merovingian kingdom in 629. Jews in former Roman territories faced new challenges as harsher anti-Jewish Church rulings were enforced. Charlemagne 's expansion of the Frankish empire around 800, including northern Italy and Rome, brought on

4005-462: The early modern period. During the 16th century, as conditions for Italian Jews worsened, many Jews from Venice and the surrounding area migrated to Poland and Lithuania. During the 16th and 17th centuries, some Sephardi Jews and Romaniote Jews from throughout the Ottoman Empire migrated to Eastern Europe, as did Arabic-speaking Mizrahi Jews and Persian Jews . In the first half of

4094-529: The economy, media, and politics of Israel since its founding. During the first decades of Israel as a state, strong cultural conflict occurred between Sephardic and Ashkenazi Jews (mainly east European Ashkenazim). The roots of this conflict, which still exists to a much smaller extent in present-day Israeli society, are chiefly attributed to the concept of the " melting pot ". That is to say, all Jewish immigrants who arrived in Israel were strongly encouraged to "meltdown" their own particular exilic identities within

4183-655: The emancipation, Zionism developed in central Europe. Other Jews, particularly those in the Pale of Settlement , turned to socialism . These tendencies would be united in Labor Zionism , the founding ideology of the State of Israel. Of the estimated 8.8 million Jews living in Europe at the beginning of World War II , the majority of whom were Ashkenazi, about 6 million – more than two-thirds – were systematically murdered in

4272-402: The far north, the others being Minni and Ararat (corresponding to Urartu ), called on by God to resist Babylon. In the Yoma tractate of the Babylonian Talmud the name Gomer is rendered as Germania , which elsewhere in rabbinical literature was identified with Germanikia in northwestern Syria, but later became associated with Germania . Ashkenaz is linked to Scandza/Scanzia , viewed as

4361-411: The father of Ashkenaz, is translated by Germamia , which evidently stands for Germany, and which was suggested by the similarity of the sound. In later times, the word Ashkenaz is used to designate southern and western Germany, the ritual of which sections differs somewhat from that of eastern Germany and Poland. Thus the prayer-book of Isaiah Horowitz , and many others, give the piyyutim according to

4450-444: The favor. Further evidence of German communities in the holy city comes in the form of halakhic questions sent from Germany to Jerusalem during the second half of the 11th century. Material relating to the history of German Jews has been preserved in the communal accounts of certain communities on the Rhine, a Memorbuch , and a Liebesbrief , documents that are now part of the Sassoon Collection. Heinrich Graetz also added to

4539-538: The first time, or when a lapsed or less observant Jew returns to traditional Judaism and must determine what was done in his or her family's past. In this sense, "Ashkenazic" refers both to a family ancestry and to a body of customs binding on Jews of that ancestry. Reform Judaism , which does not necessarily follow those minhagim, did nonetheless originate among Ashkenazi Jews. Fundamenta nova theoriae functionum ellipticarum Fundamenta nova theoriae functionum ellipticarum (from Latin : New Foundations of

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4628-438: The forces of Herod the Great with assistance from Roman forces in 37 BCE. It is known that Jewish war captives were sold into slavery after the suppression of a minor Jewish revolt in 53 BCE, and some were probably taken to southern Europe. Regarding Jewish settlements founded in southern Europe during the Roman era, E. Mary Smallwood wrote that "no date or origin can be assigned to the numerous settlements eventually known in

4717-432: The functional equation and the Jacobi triple product formula, as well as many other results on q-series and hypergeometric series . The solution of the Jacobi inversion problem for the hyperelliptic Abel map by Weierstrass in 1854 required the introduction of the hyperelliptic theta function and later the general Riemann theta function for algebraic curves of arbitrary genus . The complex torus associated to

4806-436: The general social "pot" in order to become Israeli. As of 2020, 63% of American Jews are Ashkenazim. A disproportionate amount of Ashkenazi Americans are religious compared to American Jews of other racial groups. They live in large populations in the states of New York, California, Florida, and New Jersey. The majority of American Ashkenazi Jewish voters vote for the Democratic Party , although Orthodox ones tend to support

4895-401: The history of German Jewry in modern times in the abstract of his seminal work, History of the Jews , which he entitled "Volksthümliche Geschichte der Juden." In an essay on Sephardi Jewry, Daniel Elazar at the Jerusalem Center for Public Affairs summarized the demographic history of Ashkenazi Jews in the last thousand years. He noted that at the end of the 11th century, 97% of world Jewry

4984-409: The idea that Jews had the know-how and capacity to jump-start the economy, improve revenues, and enlarge trade seems to have played a prominent role. Typically, Jews relocated close to the markets and churches in town centres, where, though they came under the authority of both royal and ecclesiastical powers, they were accorded administrative autonomy. In the 11th century, both Rabbinic Judaism and

5073-409: The interests of religious Ashkenazi Jews. The role of religious parties, including small religious parties that play important roles as coalition members, results in turn from Israel's composition as a complex society in which competing social, economic, and religious interests stand for election to the Knesset , a unicameral legislature with 120 seats. Ashkenazi Jews have played a prominent role in

5162-517: The introduction of the Jacobi symbol ; contributions to higher reciprocity laws, investigations of continued fractions , and the invention of Jacobi sums . He was also one of the early founders of the theory of determinants. In particular, he invented the Jacobian determinant formed from the n partial derivatives of n given functions of n independent variables, which plays an important part in changes of variables in multiple integrals, and in many analytical investigations. In 1841 he reintroduced

5251-454: The inverse problem for periodic and quasi-periodic flows. The equations of motion are integrable in terms of Jacobi's elliptic functions in the well-known cases of the pendulum , the Euler top , the symmetric Lagrange top in a gravitational field , and the Kepler problem (planetary motion in a central gravitational field). He also made fundamental contributions in the study of differential equations and to classical mechanics , notably

5340-405: The invitation of local Christian rulers. Thus Baldwin V, Count of Flanders , invited Jacob ben Yekutiel and his fellow Jews to settle in his lands; and soon after the Norman conquest of England , William the Conqueror likewise extended a welcome to continental Jews to take up residence there. Bishop Rüdiger Huzmann called on the Jews of Mainz to relocate to Speyer . In all of these decisions,

5429-488: The land of Israel/Judaea. They collected an annual temple tax from Jews both in and outside of Israel. The revolts in and suppression of diaspora communities in Egypt, Libya and Crete during the Kitos War of 115–117 CE had a severe impact on the Jewish diaspora. A substantial Jewish population emerged in northern Gaul by the Middle Ages, but Jewish communities existed in 465 CE in Brittany , in 524 CE in Valence , and in 533 CE in Orléans . Throughout this period and into

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5518-437: The majority of the American Jewish community since 1750. In the context of the European Enlightenment , Jewish emancipation began in 18th century France and spread throughout Western and Central Europe. Disabilities that had limited the rights of Jews since the Middle Ages were abolished, including the requirements to wear distinctive clothing, pay special taxes, and live in ghettos isolated from non-Jewish communities and

5607-407: The mid-first century became widely accepted, including by Louis Feldman . However, contemporary scholars now accept that Bar Hebraeus based his figure on a census of total Roman citizens and thus included non-Jews, the figure of 6,944,000 being recorded in Eusebius' Chronicon . Louis Feldman, previously an active supporter of the figure, now states that he and Baron were mistaken. Philo gives

5696-418: The migration patterns of Jews from Southern and Western Europe to Central and Eastern Europe. In 1740, a family from Lithuania became the first Ashkenazi Jews to settle in the Jewish Quarter of Jerusalem. In the generations after emigration from the west, Jewish communities in places like Poland, Russia, and Belarus enjoyed a comparatively stable socio-political environment. A thriving publishing industry and

5785-435: The movement was by no means a singular, centralized event, and a Jewish diaspora had already been established before. During both of these rebellions, many Jews were captured and sold into slavery by the Romans. According to the Jewish historian Josephus , 97,000 Jews were sold as slaves in the aftermath of the first revolt. In one occasion, Vespasian reportedly ordered 6,000 Jewish prisoners of war from Galilee to work on

5874-413: The nature of elliptic and theta functions. In his 1835 paper, Jacobi proved the following basic result classifying periodic (including elliptic) functions: If a univariate single-valued function is multiply periodic , then such a function cannot have more than two periods, and the ratio of the periods cannot be a real number. He discovered many of the fundamental properties of theta functions, including

5963-781: The official religion of Rome and Constantinople in 380 CE, Jews were increasingly marginalized. The Synagogue in the Agora of Athens is dated to the period between 267 and 396 CE. The Stobi Synagogue in Macedonia was built on the ruins of a more ancient synagogue in the 4th century, while later in the 5th century, the synagogue was transformed into a Christian basilica. Hellenistic Judaism thrived in Antioch and Alexandria , and many of these Greek-speaking Jews would convert to Christianity. Sporadic epigraphic evidence in gravesite excavations, particularly in Brigetio ( Szőny ), Aquincum ( Óbuda ), Intercisa ( Dunaújváros ), Triccinae ( Sárvár ), Savaria ( Szombathely ), Sopianae ( Pécs ) in Hungary, and Mursa ( Osijek ) in Croatia, attest to

6052-475: The possible exception of Trier and Cologne , the archeological evidence suggests at most a fleeting presence of very few Jews, primarily itinerant traders or artisans. Estimating the number of Jews in antiquity is a task fraught with peril due to the nature of and lack of accurate documentation. The number of Jews in the Roman Empire for a long time was based on the accounts of Syrian Orthodox bishop Bar Hebraeus who lived between 1226 and 1286 CE, who stated by

6141-407: The presence of Jews after the 2nd and 3rd centuries where Roman garrisons were established. There was a sufficient number of Jews in Pannonia to form communities and build a synagogue. Jewish troops were among the Syrian soldiers transferred there, and replenished from the Middle East. After 175 CE Jews and especially Syrians came from Antioch , Tarsus , and Cappadocia . Others came from Italy and

6230-457: The present, Jewish life in northern Europe is well documented. By the 11th century, when Rashi of Troyes wrote his commentaries, Jews in what came to be known as "Ashkenaz" were known for their halakhic learning , and Talmudic studies . They were criticized by Sephardim and other Jewish scholars in Islamic lands for their lack of expertise in Jewish jurisprudence and general ignorance of Hebrew linguistics and literature. Yiddish emerged as

6319-413: The printing of hundreds of biblical commentaries precipitated the development of the Hasidic movement as well as major Jewish academic centers. After two centuries of comparative tolerance in the new nations, massive westward emigration occurred in the 19th and 20th centuries in response to pogroms in the east and the economic opportunities offered in other parts of the world. Ashkenazi Jews have made up

6408-485: The prohibitions on certain professions. Laws were passed to integrate Jews into their host countries, forcing Ashkenazi Jews to adopt family names (they had formerly used patronymics ). Newfound inclusion into public life led to cultural growth in the Haskalah , or Jewish Enlightenment, with its goal of integrating modern European values into Jewish life. As a reaction to increasing antisemitism and assimilation following

6497-399: The relation between elliptic integrals and the Jacobi or Weierstrass elliptic functions. Jacobi was the first to apply elliptic functions to number theory , for example proving Fermat's two-square theorem and Lagrange's four-square theorem , and similar results for 6 and 8 squares. His other work in number theory continued the work of Gauss : new proofs of quadratic reciprocity , and

6586-537: The revolution, to his royal grant being cut off – but his fame and reputation were such that it was soon resumed, thanks to the personal intervention of Alexander von Humboldt . Jacobi died in 1851 from a smallpox infection. His grave is preserved at a cemetery in the Kreuzberg section of Berlin, the Friedhof I der Dreifaltigkeits-Kirchengemeinde (61 Baruther Street). His grave is close to that of Johann Encke ,

6675-423: The same time converted to Christianity. Now qualifying for teaching university classes, the 21-year-old Jacobi lectured in 1825/26 on the theory of curves and surfaces at the University of Berlin. In 1826, Jacobi became a private lecturer , in the next year an extraodinary professor , and in finally 1829, a tenured professor of mathematics at Königsberg University , and held the chair until 1842. He suffered

6764-576: The same year he became qualified to teach secondary school and was offered a position at the Joachimsthal Gymnasium in Berlin. Jacobi decided instead to continue to work towards a university position. In 1825, he obtained the degree of Doctor of Philosophy with a dissertation on the partial fraction decomposition of rational fractions defended before a commission led by Enno Dirksen . He followed immediately with his Habilitation and at

6853-472: The seminars of Böckh , drawing the professor's attention with his talent. Jacobi did not follow a lot of mathematics classes at the time, finding the level of mathematics taught at Berlin University too elementary. He continued, instead, with his private study of the more advanced works of Euler , Lagrange and Laplace . By 1823 he understood that he needed to make a decision between his competing interests and chose to devote all his attention to mathematics. In

6942-469: The senior class until 1821. He used this time to advance his knowledge, showing interest in all subjects, including Latin, Greek, philology, history and mathematics. During this period he also made his first attempts at research, trying to solve the quintic equation by radicals . In 1821 Jacobi went to study at Berlin University , where he initially divided his attention between his passions for philology and mathematics . In philology, he participated in

7031-438: The synagogue there, but occasionally also with regard to certain other observances. In the literature of the 13th century, references to the land and the language of Ashkenaz often occur. Examples include Solomon ben Aderet 's Responsa (vol. i., No. 395); the Responsa of Asher ben Jehiel (pp. 4, 6); his Halakot (Berakot i. 12, ed. Wilna, p. 10); the work of his son Jacob ben Asher , Tur Orach Chayim (chapter 59);

7120-413: The time of the destruction of the Second Temple in 70 CE, as many as six million Jews were already living in the Roman Empire, a conclusion which has been contested as highly exaggerated. The 13th-century author Bar Hebraeus gave a figure of 6,944,000 Jews in the Roman world. Salo Wittmayer Baron considered the figure convincing. The figure of seven million within and one million outside the Roman world in

7209-531: The victims were Ashkenazi Jews, their percentage dropped from an estimate of 92% of world Jewry in 1930 to nearly 80% of world Jewry today. The Holocaust also effectively put an end to the dynamic development of the Yiddish language in the previous decades , as the vast majority of the Jewish victims of the Holocaust, around 5 million, were Yiddish speakers. Many of the surviving Ashkenazi Jews emigrated to countries such as Israel, Canada, Argentina, Australia , and

7298-590: The west, and some may have been founded as a result of the dispersal of Palestinian Jews after the revolts of AD 66–70 and 132–135, but it is reasonable to conjecture that many, such as the settlement in Puteoli attested in 4 BC, went back to the late republic or early empire and originated in voluntary emigration and the lure of trade and commerce." The first and second centuries CE saw a series of unsuccessful large-scale Jewish revolts against Rome . The Roman suppression of these revolts led to wide-scale destruction,

7387-518: The west, who due to high birth rates absorbed and largely replaced the preceding non-Ashkenazi Jewish groups of Eastern Europe (whose numbers the demographer Sergio Della Pergola considers to have been small). Genetic evidence also indicates that Yiddish-speaking Eastern European Jews largely descend from Ashkenazi Jews who migrated from central to eastern Europe and subsequently experienced high birthrates and genetic isolation. Some Jewish immigration from southern Europe to Eastern Europe continued into

7476-446: Was 15.3 million. Israeli demographer and statistician Sergio D. Pergola implied that Ashkenazim comprised 65–70% of Jews worldwide in 2000, while other estimates suggest more than 75%. As of 2013 , the population was estimated to be between 10 million and 11.2 million. Genetic studies indicate that Ashkenazim have both Levantine and European (mainly southern European) ancestry. These studies draw diverging conclusions about

7565-558: Was Sephardic and 3% Ashkenazi; in the mid-17th century, "Sephardim still outnumbered Ashkenazim three to two"; by the end of the 18th century, "Ashkenazim outnumbered Sephardim three to two, the result of improved living conditions in Christian Europe versus the Ottoman Muslim world." By 1930, Arthur Ruppin estimated that Ashkenazi Jews accounted for nearly 92% of world Jewry. These factors are sheer demography showing

7654-598: Was denominated Sefarad ( Obadiah 20), France was called Tsarefat ( 1 Kings 17:9 ), and Bohemia was called the Land of Canaan . By the high medieval period, Talmudic commentators like Rashi began to use Ashkenaz/Eretz Ashkenaz to designate Germany , earlier known as Loter , where, especially in the Rhineland communities of Speyer , Worms and Mainz , the most important Jewish communities arose. Rashi uses leshon Ashkenaz (Ashkenazi language) to describe Yiddish, and Byzantium and Syrian Jewish letters referred to

7743-594: Was especially difficult to differentiate Jews from the Syrians. After Pannonia was ceded to the Huns in 433, the garrison populations were withdrawn to Italy, and only a few, enigmatic traces remain of a possible Jewish presence in the area some centuries later. No evidence has yet been found of a Jewish presence in antiquity in Germany beyond its Roman border, nor in Eastern Europe. In Gaul and Germany itself, with

7832-478: Was focused on trade, business management, and financial services, due to several presumed factors: Christian European prohibitions restricting certain activities by Jews, preventing certain financial activities (such as " usurious " loans) between Christians, high rates of literacy, near-universal male education, and ability of merchants to rely upon and trust family members living in different regions and countries. In Poland, Jews were granted special protection by

7921-556: Was renamed Syria Palaestina . Jews were prohibited from entering the city on pain of death. Jewish presence in the region significantly dwindled after the failure of the Bar Kokhba revolt. With their national aspirations crushed and widespread devastation in Judea, despondent Jews migrated out of Judea in the aftermath of both revolts, and many settled in southern Europe. In contrast to the earlier Assyrian and Babylonian captivities,

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