Kristallnacht or Reichskristallnacht referred to as the Night of Broken Glass, Reichspogromnacht or Pogromnacht, Novemberpogrome, was a pogrom against Jews throughout Nazi Germany on 9–10 November 1938, carried out by SA paramilitary forces and civilians. The German authorities looked on without intervening; the name Kristallnacht comes from the shards of broken glass that littered the streets after the windows of Jewish-owned stores and synagogues were smashed. Estimates of the number of fatalities caused by the pogrom have varied. Early reports estimated. Modern analysis of German scholarly sources by historians such as Sir Richard Evans puts the number much higher; when deaths from post-arrest maltreatment and subsequent suicides are included, the death toll climbs into the hundreds. Additionally, 30,000 Jewish men were incarcerated in concentration camps. Jewish homes and schools were ransacked, as the attackers demolished buildings with sledgehammers; the rioters destroyed 267 synagogues throughout Germany and the Sudentenland, over 7,000 Jewish businesses were either destroyed or damaged.
The British historian Martin Gilbert wrote that no event in the history of German Jews between 1933 and 1945 was so reported as it was happening, the accounts from the foreign journalists working in Germany sent shock waves around the world. The British newspaper The Times wrote at the time: "No foreign propagandist bent upon blackening Germany before the world could outdo the tale of burnings and beatings, of blackguardly assaults on defenseless and innocent people, which disgraced that country yesterday."The attacks were retaliation for the assassination of the Nazi German diplomat Ernst vom Rath by Herschel Grynszpan, a seventeen-year-old German-born Polish Jew living in Paris. Kristallnacht was followed by additional economic and political persecution of Jews, it is viewed by historians as part of Nazi Germany's broader racial policy, the beginning of the Final Solution and The Holocaust. In the 1920s, most German Jews were integrated into German society as German citizens, they served in the German army and navy and contributed to every field of German business and culture.
Conditions for the Jews began to change after the appointment of Adolf Hitler as Chancellor of Germany on 30 January 1933, the Enabling Act assumption of power by Hitler after the Reichstag fire of 27 February 1933. From its inception, Hitler's régime moved to introduce anti-Jewish policies. Nazi propaganda singled out the 500,000 Jews in Germany, who accounted for only 0.86% of the overall population, as an enemy within who were responsible for Germany's defeat in the First World War and for its subsequent economic disasters, such as the 1920s hyperinflation and Wall Street Crash Great Depression. Beginning in 1933, the German government enacted a series of anti-Jewish laws restricting the rights of German Jews to earn a living, to enjoy full citizenship and to gain education, including the Law for the Restoration of the Professional Civil Service of 7 April 1933, which forbade Jews to work in the civil service; the subsequent 1935 Nuremberg Laws stripped German Jews of their citizenship and forbade Jews to marry non-Jewish Germans.
These laws resulted in the exclusion of Jews from German political life. Many sought asylum abroad; the international Évian Conference on 6 July 1938 addressed the issue of Jewish and Gypsy immigration to other countries. By the time the conference took place, more than 250,000 Jews had fled Germany and Austria, annexed by Germany in March 1938; as the number of Jews and Gypsies wanting to leave increased, the restrictions against them grew, with many countries tightening their rules for admission. By 1938, Germany "had entered a new radical phase in anti-Semitic activity"; some historians believe that the Nazi government had been contemplating a planned outbreak of violence against the Jews and were waiting for an appropriate provocation. In a 1997 interview, the German historian Hans Mommsen claimed that a major motive for the pogrom was the desire of the Gauleiters of the NSDAP to seize Jewish property and businesses. Mommsen stated: The need for money by the party organization stemmed from the fact that Franz Xaver Schwarz, the party treasurer, kept the local and regional organizations of the party short of money.
In the fall of 1938, the increased pressure on Jewish property nourished the party's ambition since Hjalmar Schacht had been ousted as Reich minister for economics. This, was only one aspect of the origin of the November 1938 pogrom; the Polish government threatened to extradite all Jews who were Polish citizens but would stay in Germany, thus creating a burden of responsibility on the German side. The immediate reaction by the Gestapo was to push the Polish Jews—16,000 persons—over the borderline, but this measure failed due to the stubbornness of the Polish customs officers; the loss of prestige as a result of this abortive operation called for some sort of compensation. Thus, the overreaction to Herschel Grynszpan's attempt against t
Jews or Jewish people are an ethnoreligious group and a nation, originating from the Israelites and Hebrews of historical Israel and Judah. Jewish ethnicity and religion are interrelated, as Judaism is the traditional faith of the Jewish people, while its observance varies from strict observance to complete nonobservance. Jews originated as an ethnic and religious group in the Middle East during the second millennium BCE, in the part of the Levant known as the Land of Israel; the Merneptah Stele appears to confirm the existence of a people of Israel somewhere in Canaan as far back as the 13th century BCE. The Israelites, as an outgrowth of the Canaanite population, consolidated their hold with the emergence of the kingdoms of Israel and Judah; some consider that these Canaanite sedentary Israelites melded with incoming nomadic groups known as'Hebrews'. Though few sources mention the exilic periods in detail, the experience of diaspora life, from the Ancient Egyptian rule over the Levant, to Assyrian captivity and exile, to Babylonian captivity and exile, to Seleucid Imperial rule, to the Roman occupation and exile, the historical relations between Jews and their homeland thereafter, became a major feature of Jewish history and memory.
Prior to World War II, the worldwide Jewish population reached a peak of 16.7 million, representing around 0.7% of the world population at that time. 6 million Jews were systematically murdered during the Holocaust. Since the population has risen again, as of 2016 was estimated at 14.4 million by the Berman Jewish DataBank, less than 0.2% of the total world population. The modern State of Israel is the only country, it defines itself as a Jewish and democratic state in the Basic Laws, Human Dignity and Liberty in particular, based on the Declaration of Independence. Israel's Law of Return grants the right of citizenship to Jews who have expressed their desire to settle in Israel. Despite their small percentage of the world's population, Jews have influenced and contributed to human progress in many fields, both and in modern times, including philosophy, literature, business, fine arts and architecture, music and cinema, science and technology, as well as religion. Jews have played a significant role in the development of Western Civilization.
The English word "Jew" continues Iewe. These terms derive from Old French giu, earlier juieu, which through elision had dropped the letter "d" from the Medieval Latin Iudaeus, like the New Testament Greek term Ioudaios, meant both "Jew" and "Judean" / "of Judea"; the Greek term was a loan from Aramaic Y'hūdāi, corresponding to Hebrew יְהוּדִי Yehudi the term for a member of the tribe of Judah or the people of the kingdom of Judah. According to the Hebrew Bible, the name of both the tribe and kingdom derive from Judah, the fourth son of Jacob. Genesis 29:35 and 49:8 connect the name "Judah" with the verb yada, meaning "praise", but scholars agree that the name of both the patriarch and the kingdom instead have a geographic origin—possibly referring to the gorges and ravines of the region; the Hebrew word for "Jew" is יְהוּדִי Yehudi, with the plural יְהוּדִים Yehudim. Endonyms in other Jewish languages include the Yiddish ייִד Yid; the etymological equivalent is in use in other languages, e.g. يَهُودِيّ yahūdī, al-yahūd, in Arabic, "Jude" in German, "judeu" in Portuguese, "Juif" /"Juive" in French, "jøde" in Danish and Norwegian, "judío/a" in Spanish, "jood" in Dutch, "żyd" in Polish etc. but derivations of the word "Hebrew" are in use to describe a Jew, e.g. in Italian, in Persian and Russian.
The German word "Jude" is pronounced, the corresponding adjective "jüdisch" is the origin of the word "Yiddish". According to The American Heritage Dictionary of the English Language, fourth edition, It is recognized that the attributive use of the noun Jew, in phrases such as Jew lawyer or Jew ethics, is both vulgar and offensive. In such contexts Jewish is the only acceptable possibility; some people, have become so wary of this construction that they have extended the stigma to any use of Jew as a noun, a practice that carries risks of its own. In a sentence such as There are now several Jews on the council, unobjectionable, the substitution of a circumlocution like Jewish people or persons of Jewish background may in itself cause offense for seeming to imply that Jew has a negative connotation when used as a noun. Judaism shares some of the characteristics of a nation, an ethnicity, a religion, a culture, making the definition of, a Jew vary depending on whether a religious or national approach to identity is used.
In modern secular usage Jews include three groups: people who were born to a Jewish family regardless of whether or not they follow the religion, those who have some Jewish ancestral background or lineage, people without any Jewish ancestral background or lineage who have formally converted to Judaism and therefore are followers of the religion. Historical definitions of Jewish identity have traditionally been based on halakhic definitions of matrilineal descent, halakhic conversions; these definitions of, a Jew date back to the codification of the Oral
The Baltic Germans are ethnic German inhabitants of the eastern shores of the Baltic Sea, in what today are Estonia and Latvia. Since their expulsion from Estonia and Latvia and resettlement during the upheavals and aftermath of the Second World War, Baltic Germans have markedly declined as a geographically determined ethnic group; the largest groups of present-day descendants of the Baltic Germans are found in Canada. It is estimated that several thousand still reside in Estonia. For centuries Baltic Germans and the Baltic nobility constituted a ruling class over native non-German serfs; the emerging Baltic-German middle class was urban and professional. In the 12th and 13th centuries Catholic Germans, both traders and crusaders, began settling in the eastern Baltic territories. After the Livonian Crusade, they assumed control of government, economics and culture of these lands, ruling for more than 700 years until 1918 — in alliance with Polish, Swedish or Russian overlords. With the decline of Latin, German became the language of all official documents, commerce and government.
At first the majority of German settlers lived in military castles. Their elite formed the Baltic nobility, acquiring large rural estates and comprising the social, commercial and cultural elite of Latvia and Estonia for several centuries. After 1710 many of these men took high positions in the military and civilian life of the Russian Empire in Saint Petersburg. Baltic Germans held citizenship in the Russian Empire until the Revolution of 1918, they held Estonian or Latvian citizenship until the occupation and annexation of these areas by the Soviet Union in 1939–1940. The Baltic German population never surpassed more than 10% of the total population. In 1881 there were 180,000 Baltic Germans in Russia's Baltic provinces, but by 1914 this number had declined to 162,000. In 1881 there were 46,700 Germans in Estonia. According to the Russian Empire Census of 1897, there were 120,191 Germans in Latvia, or 6.2% of the population. Baltic German history and presence in the Baltics came to an end in late 1939, following the signing of the Molotov–Ribbentrop Pact and the subsequent Nazi–Soviet population transfers.
All the Baltic Germans were resettled by Nazi Germany under the Heim ins Reich program into the newly formed Reichsgaue of Wartheland and Danzig-West Prussia. In 1945, most ethnic Germans were expelled from these lands by the Soviet army. Resettlement was planned for the territory remaining to Germany under terms of the border changes promulgated at the Potsdam Conference, i.e. west of the Oder–Neisse line, or elsewhere in the world. Ethnic Germans from East Prussia and Lithuania are sometimes incorrectly considered Baltic Germans for reasons of cultural and historical affinities, but the Germans of East Prussia held Prussian, after 1871, German citizenship, because the territory they lived in was part of the Kingdom of Prussia. Baltic Germans were not a purely German ethnic group; the early crusaders and craftsmen married local women, as there were no German women available. Some noble families, such as the Lievens, claimed descent through such women from native chieftains. Many of the German Livonian Order soldiers died during the Livonian War.
New German arrivals came to the area. During this time the Low German of the original settlers was replaced by the High German of the new settlers. In the course of their 700-year history, Baltic German families had ethnic German roots, but had extensive intermarriage with Estonians and Latvians, as well as with other Northern or Central European people, such as Danes, Irish, Scots, Poles and Dutch. In cases where intermarriage occurred, members of the other ethnic groups assimilated into German culture, adopting language and German family names, they were considered Germans, leading to the ethnogenesis of the Baltic Germans. Barclay de Tolly and George Armitstead, who emigrated from the British Isles, married into and became part of the Baltic-German community. Baltic German settlements in the Baltic area consisted of the following territories: Estland the northern half of present-day Estonia. Livland the southern half of present-day Estonia and the northern and eastern part of today's Latvia.
Kurland the western half of present-day Latvia. Ösel belonging to present-day Estonia. Small numbers of Ethnic Germans began to settle in the area in the late 12th century when traders and Christian missionaries began to visit the coastal lands inhabited by tribes who spoke Finnic and Baltic languages. Systematic conquest and settlement of these lands was completed during the Northern Crusades of the 12th and 13th centuries which resulted in creation of the Terra Mariana confederation, under the protection of Roman Popes and Holy Roman Empire. After the heavy defeat in the 1236 Battle of Saule the Livonian Brothers of the Sword became a part of
Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to
Estonia the Republic of Estonia, is a country in North East Europe. It is bordered to the north by the Gulf of Finland with Finland on the other side, to the west by the Baltic Sea with Sweden on the other side, to the south by Latvia, to the east by Lake Peipus and Russia; the territory of Estonia consists of a mainland and 2,222 islands in the Baltic Sea, covering a total area of 45,227 km2, water 2,839 km2, land area 42,388 km2, is influenced by a humid continental climate. The official language of the country, Estonian, is the third most spoken Finno-Ugric language; the territory of Estonia has been inhabited since at least 9,000 B. C. Ancient Estonians were some of the last European pagans to be Christianized, following the Livonian Crusade in the 13th century. After centuries of successive rule by Germans, Swedes and Russians, a distinct Estonian national identity began to emerge in the 19th and early 20th centuries; this culminated in independence from Russia in 1920 after a brief War of Independence at the end of World War I.
Democratic, after the Great Depression Estonia was governed by authoritarian rule since 1934 during the Era of Silence. During World War II, Estonia was contested and occupied by the Soviet Union and Germany being incorporated into the former as the Estonian Soviet Socialist Republic. After the loss of its de facto independence, Estonia's de jure state continuity was preserved by diplomatic representatives and the government-in-exile. In 1987 the peaceful Singing Revolution began against Soviet rule, resulting in the restoration of de facto independence on 20 August 1991; the sovereign state of Estonia is a democratic unitary parliamentary republic divided into fifteen counties. Its capital and largest city is Tallinn. With a population of 1.3 million, it is one of the least-populous member states of the European Union since joining in 2004, the economic monetary Eurozone, Organisation for Economic Co-operation and Development, Schengen Area, of the Western military alliance of the North Atlantic Treaty Organization.
It is a developed country with an advanced, high-income economy, among the fastest-growing in the EU. Estonia ranks high in the Human Development Index, performs favourably in measurements of economic freedom, civil liberties and press freedom. Estonian citizens are provided with universal health care, free education, the longest-paid maternity leave in the OECD. One of the world's most digitally advanced societies, in 2005 Estonia became the first state to hold elections over the Internet, in 2014 the first state to provide e-residency. In the Estonian language the oldest known endonym of the Estonians was maarahvas, meaning "country people" or "people of the soil"; the land inhabited by Estonians was called Maavald meaning "Country Realm" or "Land Realm". One hypothesis regarding the modern name of Estonia derives it from the Aesti, a people described by the Roman historian Tacitus in his Germania; the historic Aesti were Baltic people, whereas the modern Estonians are Finno-Ugric. The geographical areas of the Aesti and of Estonia do not match, with the Aesti living farther south.
Ancient Scandinavian sagas refer to an area called Eistland, as the country is still called in Icelandic, with close parallels to the Danish, Dutch and Norwegian terms Estland for the country. Early Latin and other ancient versions of the name include Hestia. Esthonia was a common alternative English spelling before 1921. Human settlement in Estonia became possible 13,000 to 11,000 years ago, when the ice from the last glacial era melted; the oldest known settlement in Estonia is the Pulli settlement, on the banks of the river Pärnu, near the town of Sindi, in south-western Estonia. According to radiocarbon dating it was settled around 11,000 years ago; the earliest human inhabitation during the Mesolithic period is connected to the Kunda culture, named after the town of Kunda in northern Estonia. At that time the country was covered with forests, people lived in semi-nomadic communities near bodies of water. Subsistence activities consisted of hunting and fishing. Around 4900 BC appear ceramics of the neolithic period, known as Narva culture.
Starting from around 3200 BC the Corded Ware culture appeared. The Bronze Age started around 1800 BC, saw the establishment of the first hill fort settlements. A transition from hunting-fishing-gathering subsistence to single-farm-based settlement started around 1000 BC, was complete by the beginning of the Iron Age around 500 BC; the large amount of bronze objects indicate the existence of active communication with Scandinavian and Germanic tribes. A more troubled and war-ridden middle Iron Age followed, with external threats appearing from different directions. Several Scandinavian sagas referred to major confrontations with Estonians, notably when Estonians defeated and killed the Swedish king Ingvar. Similar threats appeared in the east. In 1030 Yaroslav the Wise established a fort in modern-day Tartu. Around the 11th century, the Scandinavian Viking era around the Baltic Sea was succeeded by the Baltic Viking era, with seaborne
Lothar Collatz was a German mathematician, born in Arnsberg, Westphalia. The 3x + 1 problem is known as the Collatz conjecture, named after him and still unsolved; the Collatz–Wielandt formula for the Perron–Frobenius eigenvalue of a positive square matrix was named after him. Collatz's 1957 paper with Ulrich Sinogowitz, killed in the bombing of Darmstadt in World War II, founded the field of spectral graph theory. Collatz studied at universities in Germany including the University of Berlin under Alfred Klose, receiving his doctorate in 1935 for a dissertation entitled Das Differenzenverfahren mit höherer Approximation für lineare Differentialgleichungen. For his many contributions to the field, Collatz had many honors bestowed upon him in his lifetime, including: election to the Academy of Sciences Leopoldina, the Academy of Sciences of the Institute of Bologna and the Academy at Modena in Italy. Honorary member of the Hamburg Mathematical Society honorary degrees by the University of São Paulo, the Technical University of Vienna, the University of Dundee in Scotland, Brunel University in England, the University of Hanover in 1981, the Technical University of Dresden.
He died unexpectedly from a heart attack in Varna, while attending a mathematics conference. Das Differenzenverfahren mit höherer Approximation für lineare Differentialgleichungen, Leipzig 1935 Eigenwertprobleme und ihre numerische Behandlung. Leipzig 1945 Eigenwertaufgaben mit technischen Anwendungen. Leipzig 1949, 1963 Numerische Behandlung von Differentialgleichungen. Berlin 1951, 1955 Differentialgleichungen für Ingenieure. Stuttgart 1960 with Wolfgang Wetterling: Optimierungsaufgaben Berlin 1966, 1971 Funktionalanalysis und Numerische Mathematik. Berlin 1964 Differentialgleichungen. Eine Einführung unter besonderer Berücksichtigung der Anwendungen. Stuttgart, Teubner Verlag, 1966, 7th edn. 1990 with Julius Albrecht: Aufgaben aus der angewandten Mathematik I. Gleichungen in einer und mehreren Variablen. Approximationen. Berlin 1972 Numerische Methoden der Approximationstheorie. Vol. 2. Vortragsauszüge der Tagung über Numerische Methoden der Approximationstheorie vom 3.-9. Juni 1973 im Mathematischen Forschungsinstitut Oberwolfach, Stuttgart 1975 Approximationstheorie: Tschebyscheffsche Approximation und Anwendungen.
Teubner 1973 Lothar Collatz, Journal of Approximation Theory, vol. 65, issue 1, April 1991, page II by Günter Meinardus and Günther Nürnberger Collatz, Lothar, "Einschließungssatz für die charakteristischen Zahlen von Matrizen", Mathematische Zeitschrift, 48: 221–226, doi:10.1007/BF01180013 J Albrecht, P Hagedorn and W Velte, Lothar Collatz, Numerical treatment of eigenvalue problems, vol. 5, Oberwolfach, 1990, viii–ix. R Ansorge, Lothar Collatz, Mitt. Ges. Angew. Math. Mech. No. 1, 4–9. U Eckhardt, Der Einfluss von Lothar Collatz auf die angewandte Mathematik, Numerical mathematics, Sympos. Inst. Appl. Math. Univ. Hamburg, Hamburg, 1979, 9–23. L Elsner and K P Hadeler, Lothar Collatz – on the occasion of his 75th birthday, Linear Algebra Appl. 68, vi. R B Guenther, Obituary: Lothar Collatz, 1910–1990, Aequationes Mathematicae 43, 117–119. H Heinrich, Zum siebzigsten Geburtstag von Lothar Collatz, Z. Angew. Math. Mech. 60, 274–275. G Meinardus, G Nürnberger, Th Riessinger and G Walz, In memoriam: the work of Lothar Collatz in approximation theory, J. Approx.
Theory 67, 119–128. G Meinardus and G Nürnberger, In memoriam: Lothar Collatz, J. Approx. Theory 65, i. J R Whiteman, In memoriam: Lothar Collatz, Internat. J. Numer. Methods Engrg. 31, 1475–1476. O'Connor, John J.. Lothar Collatz at the Mathematics Genealogy Project