The Poles referred to as the Polish people, are a nation and West Slavic ethnic group native to Poland in Central Europe who share a common ancestry, culture and are native speakers of the Polish language. The population of self-declared Poles in Poland is estimated at 37,394,000 out of an overall population of 38,538,000, of whom 36,522,000 declared Polish alone. A wide-ranging Polish diaspora exists throughout Europe, the Americas, in Australasia. Today the largest urban concentrations of Poles are within the Warsaw and Silesian metropolitan areas. Poland's history dates back over a thousand years, to c. 930–960 AD, when the Polans – an influential West Slavic tribe in the Greater Poland region, now home to such cities as Poznań, Kalisz and Września – united various Lechitic tribes under what became the Piast dynasty, thus creating the Polish state. The subsequent Christianization of Poland, in 966 CE, marked Poland's advent to the community of Western Christendom. Poles have made important contributions to the world in every major field of human endeavor.
Notable Polish émigrés – many of them forced from their homeland by historic vicissitudes – have included physicists Marie Skłodowska Curie and Joseph Rotblat, mathematician Stanisław Ulam, pianists Fryderyk Chopin and Arthur Rubinstein, actresses Helena Modjeska and Pola Negri, novelist Joseph Conrad, military leaders Tadeusz Kościuszko and Casimir Pulaski, U. S. National Security Advisor Zbigniew Brzezinski, politician Rosa Luxemburg, filmmakers Samuel Goldwyn and the Warner Brothers, cartoonist Max Fleischer, cosmeticians Helena Rubinstein and Max Factor. Slavs have been in the territory of modern Poland for over 1500 years, they organized into tribal units, of which the larger ones were known as the Polish tribes. In the 9th and 10th centuries the tribes gave rise to developed regions along the upper Vistula, the Baltic Sea coast and in Greater Poland; the last tribal undertaking resulted in the 10th century in a lasting political structure and state, one of the West Slavic nations. The concept which has become known as the Piast Idea, the chief proponent of, Jan Ludwik Popławski, is based on the statement that the Piast homeland was inhabited by so-called "native" aboriginal Slavs and Slavonic Poles since time immemorial and only was "infiltrated" by "alien" Celts, Baltic peoples and others.
After 1945 the so-called "autochthonous" or "aboriginal" school of Polish prehistory received official backing in Poland and a considerable degree of popular support. According to this view, the Lusatian Culture which archaeologists have identified between the Oder and the Vistula in the early Iron Age, is said to be Slavonic. In contrast, the critics of this theory, such as Marija Gimbutas, regard it as an unproved hypothesis and for them the date and origin of the westward migration of the Slavs is uncharted. Polish people are the sixth largest national group in the European Union. Estimates vary depending on source, though available data suggest a total number of around 60 million people worldwide. There are 38 million Poles in Poland alone. There are Polish minorities in the surrounding countries including, indigenous minorities in the Czech Republic, Slovakia and eastern Lithuania, western Ukraine, western Belarus. There are some smaller indigenous minorities in nearby countries such as Moldova.
There is a Polish minority in Russia which includes indigenous Poles as well as those forcibly deported during and after World War II. The term "Polonia" is used in Poland to refer to people of Polish origin who live outside Polish borders estimated at around 10 to 20 million. There is a notable Polish diaspora in the United States and Canada. France has a historic relationship with Poland and has a large Polish-descendant population. Poles have lived in France since the 18th century. In the early 20th century, over a million Polish people settled in France during world wars, among them Polish émigrés fleeing either Nazi occupation or Soviet rule. In the United States, a significant number of Polish immigrants settled in Chicago, Detroit, New Jersey, New York City, Pittsburgh and New England; the highest concentration of Polish Americans in a single New England municipality is in New Britain, Connecticut. The majority of Polish Canadians have arrived in Canada since World War II; the number of Polish immigrants increased between 1945 and 1970, again after the end of Communism in Poland in 1989.
In Brazil the majority of Polish immigrants settled in Paraná State. Smaller, but significant numbers settled in the states of Rio Grande do Sul, Espírito Santo and São Paulo; the city of Curitiba has the second largest Polish diaspora in the world and Polish music and culture are quite common in the region. A recent large migration of Poles took place followi
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work to solve mathematical problems. Mathematics is concerned with numbers, quantity, space and change. One of the earliest known mathematicians was Thales of Miletus, he is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number", it was the Pythagoreans who coined the term "mathematics", with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria, she succeeded her father as Librarian at the Great Library and wrote many works on applied mathematics. Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells.
Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs, it turned out that certain scholars became experts in the works they translated and in turn received further support for continuing to develop certain sciences; as these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many scholars working under Muslim rule in medieval times is that they were polymaths. Examples include the work on optics and astronomy of Ibn al-Haytham; the Renaissance brought an increased emphasis on science to Europe.
During this period of transition from a feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli. As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in the seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle, at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking.” In 1810, Humboldt convinced the King of Prussia to build a university in Berlin based on Friedrich Schleiermacher’s liberal ideas. Thus and laboratories started to evolve. British universities of this period adopted some approaches familiar to the Italian and German universities, but as they enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment, the same influences that inspired Humboldt.
The Universities of Oxford and Cambridge emphasized the importance of research, arguably more authentically implementing Humboldt’s idea of a university than German universities, which were subject to state authority. Overall, science became the focus of universities in the 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge; the German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of the kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of “freedom of scientific research and study.” Mathematicians cover a breadth of topics within mathematics in their undergraduate education, proceed to specialize in topics of their own choice at the graduate level.
In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics. Mathematicians involved with solving problems with applications in real life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of the imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, localized constructs, applied mathematicians work in the study and formulation of mathematical models. Mathematicians and applied mathematicians are considered to be two of the STEM careers; the discipline of applied mathematics concerns
The Russian Empire known as Imperial Russia or Russia, was an empire that existed across Eurasia and North America from 1721, following the end of the Great Northern War, until the Republic was proclaimed by the Provisional Government that took power after the February Revolution of 1917. The third largest empire in world history, at its greatest extent stretching over three continents, Europe and North America, the Russian Empire was surpassed in landmass only by the British and Mongol empires; the rise of the Russian Empire coincided with the decline of neighboring rival powers: the Golden Horde, the Swedish Empire, the Polish–Lithuanian Commonwealth and the Ottoman Empire. It played a major role in 1812–1814 in defeating Napoleon's ambitions to control Europe and expanded to the west and south; the House of Romanov ruled the Russian Empire from 1721 until 1762, its matrilineal branch of patrilineal German descent the House of Holstein-Gottorp-Romanov ruled from 1762. At the beginning of the 19th century, the Russian Empire extended from the Arctic Ocean in the north to the Black Sea in the south, from the Baltic Sea on the west to the Pacific Ocean, into Alaska and Northern California in America on the east.
With 125.6 million subjects registered by the 1897 census, it had the third-largest population in the world at the time, after Qing China and India. Like all empires, it included a large disparity in terms of economics and religion. There were numerous dissident elements. Economically, the empire had a predominantly agricultural base, with low productivity on large estates worked by serfs, Russian peasants; the economy industrialized with the help of foreign investments in railways and factories. The land was ruled by a nobility from the 10th through the 17th centuries, subsequently by an emperor. Tsar Ivan III laid the groundwork for the empire that emerged, he tripled the territory of his state, ended the dominance of the Golden Horde, renovated the Moscow Kremlin, laid the foundations of the Russian state. Emperor Peter the Great fought numerous wars and expanded an huge empire into a major European power, he moved the capital from Moscow to the new model city of St. Petersburg, led a cultural revolution that replaced some of the traditionalist and medieval social and political mores with a modern, Europe-oriented, rationalist system.
Empress Catherine the Great presided over a golden age. Emperor Alexander II promoted numerous reforms, most the emancipation of all 23 million serfs in 1861, his policy in Eastern Europe involved protecting the Orthodox Christians under the rule of the Ottoman Empire. That connection by 1914 led to Russia's entry into the First World War on the side of France, the United Kingdom, Serbia, against the German and Ottoman empires; the Russian Empire functioned as an absolute monarchy on principles of Orthodoxy and Nationality until the Revolution of 1905 and became a de jure constitutional monarchy. The empire collapsed during the February Revolution of 1917 as a result of massive failures in its participation in the First World War. Though the Empire was only proclaimed by Tsar Peter I following the Treaty of Nystad, some historians would argue that it was born either when Ivan III of Russia conquered Veliky Novgorod in 1478, or when Ivan the Terrible conquered the Khanate of Kazan in 1552. According to another point of view, the term Tsardom, used after the coronation of Ivan IV in 1547, was a contemporary Russian word for empire.
Much of Russia's expansion occurred in the 17th century, culminating in the first Russian colonization of the Pacific in the mid-17th century, the Russo-Polish War that incorporated left-bank Ukraine, the Russian conquest of Siberia. Poland was divided in the 1790 -- 1815 era, with much of the population going to Russia. Most of the 19th-century growth came from adding territory in Asia, south of Siberia. Peter I the Great played a major role in introducing Russia to the European state system. While the vast land had a population of 14 million, grain yields trailed behind those of agriculture in the West, compelling nearly the entire population to farm. Only a small percentage lived in towns; the class of kholops, close in status to slavery, remained a major institution in Russia until 1723, when Peter converted household kholops into house serfs, thus including them in poll taxation. Russian agricultural kholops were formally converted into serfs earlier in 1679. Peter's first military efforts were directed against the Ottoman Turks.
His attention turned to the North. Peter still lacked a secure northern seaport, except at Archangel on the White Sea, where the harbor was frozen for nine months a year. Access to the Baltic was blocked by Sweden. Peter's ambitions for a "window to the sea" led him to make a secret alliance in 1699 with Saxony, the Polish–Lithuanian Commonwealth and Denmark against Sweden, resulting in the Great Northern War; the war ended in 1721. Peter acquired four provinces situated east of the Gulf of Finland; the coveted access to the sea was now secured. There he built Russia's new capital, Saint Petersburg, to replace Moscow, which had long been Russia's cultural center. In 1722, he tur
Poland the Republic of Poland, is a country located in Central Europe. It is divided into 16 administrative subdivisions, covering an area of 312,696 square kilometres, has a temperate seasonal climate. With a population of 38.5 million people, Poland is the sixth most populous member state of the European Union. Poland's capital and largest metropolis is Warsaw. Other major cities include Kraków, Łódź, Wrocław, Poznań, Gdańsk, Szczecin. Poland is bordered by the Baltic Sea, Russia's Kaliningrad Oblast and Lithuania to the north and Ukraine to the east and Czech Republic, to the south, Germany to the west; the establishment of the Polish state can be traced back to AD 966, when Mieszko I, ruler of the realm coextensive with the territory of present-day Poland, converted to Christianity. The Kingdom of Poland was founded in 1025, in 1569 it cemented its longstanding political association with the Grand Duchy of Lithuania by signing the Union of Lublin; this union formed the Polish–Lithuanian Commonwealth, one of the largest and most populous countries of 16th and 17th century Europe, with a uniquely liberal political system which adopted Europe's first written national constitution, the Constitution of 3 May 1791.
More than a century after the Partitions of Poland at the end of the 18th century, Poland regained its independence in 1918 with the Treaty of Versailles. In September 1939, World War II started with the invasion of Poland by Germany, followed by the Soviet Union invading Poland in accordance with the Molotov–Ribbentrop Pact. More than six million Polish citizens, including 90% of the country's Jews, perished in the war. In 1947, the Polish People's Republic was established as a satellite state under Soviet influence. In the aftermath of the Revolutions of 1989, most notably through the emergence of the Solidarity movement, Poland reestablished itself as a presidential democratic republic. Poland is regional power, it has the fifth largest economy by GDP in the European Union and one of the most dynamic economies in the world achieving a high rank on the Human Development Index. Additionally, the Polish Stock Exchange in Warsaw is the largest and most important in Central Europe. Poland is a developed country, which maintains a high-income economy along with high standards of living, life quality, safety and economic freedom.
Having a developed school educational system, the country provides free university education, state-funded social security, a universal health care system for all citizens. Poland has 15 UNESCO World Heritage Sites. Poland is a member state of the European Union, the Schengen Area, the United Nations, NATO, the OECD, the Three Seas Initiative, the Visegrád Group; the origin of the name "Poland" derives from the West Slavic tribe of Polans that inhabited the Warta river basin of the historic Greater Poland region starting in the 6th century. The origin of the name "Polanie" itself derives from the early Slavic word "pole". In some languages, such as Hungarian, Lithuanian and Turkish, the exonym for Poland is Lechites, which derives from the name of a semi-legendary ruler of Polans, Lech I. Early Bronze Age in Poland begun around 2400 BC, while the Iron Age commenced in 750 BC. During this time, the Lusatian culture, spanning both the Bronze and Iron Ages, became prominent; the most famous archaeological find from the prehistory and protohistory of Poland is the Biskupin fortified settlement, dating from the Lusatian culture of the early Iron Age, around 700 BC.
Throughout the Antiquity period, many distinct ancient ethnic groups populated the regions of what is now Poland in an era that dates from about 400 BC to 500 AD. These groups are identified as Celtic, Slavic and Germanic tribes. Recent archeological findings in the Kujawy region, confirmed the presence of the Roman Legions on the territory of Poland; these were most expeditionary missions sent out to protect the amber trade. The exact time and routes of the original migration and settlement of Slavic peoples lacks written records and can only be defined as fragmented; the Slavic tribes who would form Poland migrated to these areas in the second half of the 5th century AD. Up until the creation of Mieszko's state and his subsequent conversion to Christianity in 966 AD, the main religion of Slavic tribes that inhabited the geographical area of present-day Poland was Slavic paganism. With the Baptism of Poland the Polish rulers accepted Christianity and the religious authority of the Roman Church.
However, the transition from paganism was not a smooth and instantaneous process for the rest of the population as evident from the pagan reaction of the 1030s. Poland began to form into a recognizable unitary and territorial entity around the middle of the 10th century under the Piast dynasty. Poland's first documented ruler, Mieszko I, accepted Christianity with the Baptism of Poland in 966, as the new official religion of his subjects; the bulk of the population converted in the course of the next few centuries. In 1000, Boleslaw the Brave, continuing the policy of his father Mieszko, held a Congress of Gniezno and created the metropolis of Gniezno and the dioceses of Kraków, Kołobrzeg, Wrocław. However, the pagan unrest led to the transfer of the capital to Kraków in 1038 by Casimir I the Restorer. In 1109, Prince Bolesław III Wrymouth defeated the King of Germany Henry V at the Battle of Hundsfeld, stopping the Ge
Russia the Russian Federation, is a transcontinental country in Eastern Europe and North Asia. At 17,125,200 square kilometres, Russia is by far or by a considerable margin the largest country in the world by area, covering more than one-eighth of the Earth's inhabited land area, the ninth most populous, with about 146.77 million people as of 2019, including Crimea. About 77 % of the population live in the European part of the country. Russia's capital, Moscow, is one of the largest cities in the world and the second largest city in Europe. Extending across the entirety of Northern Asia and much of Eastern Europe, Russia spans eleven time zones and incorporates a wide range of environments and landforms. From northwest to southeast, Russia shares land borders with Norway, Estonia, Latvia and Poland, Ukraine, Azerbaijan, China and North Korea, it shares maritime borders with Japan by the Sea of Okhotsk and the U. S. state of Alaska across the Bering Strait. However, Russia recognises two more countries that border it, Abkhazia and South Ossetia, both of which are internationally recognized as parts of Georgia.
The East Slavs emerged as a recognizable group in Europe between the 3rd and 8th centuries AD. Founded and ruled by a Varangian warrior elite and their descendants, the medieval state of Rus arose in the 9th century. In 988 it adopted Orthodox Christianity from the Byzantine Empire, beginning the synthesis of Byzantine and Slavic cultures that defined Russian culture for the next millennium. Rus' disintegrated into a number of smaller states; the Grand Duchy of Moscow reunified the surrounding Russian principalities and achieved independence from the Golden Horde. By the 18th century, the nation had expanded through conquest and exploration to become the Russian Empire, the third largest empire in history, stretching from Poland on the west to Alaska on the east. Following the Russian Revolution, the Russian Soviet Federative Socialist Republic became the largest and leading constituent of the Union of Soviet Socialist Republics, the world's first constitutionally socialist state; the Soviet Union played a decisive role in the Allied victory in World War II, emerged as a recognized superpower and rival to the United States during the Cold War.
The Soviet era saw some of the most significant technological achievements of the 20th century, including the world's first human-made satellite and the launching of the first humans in space. By the end of 1990, the Soviet Union had the world's second largest economy, largest standing military in the world and the largest stockpile of weapons of mass destruction. Following the dissolution of the Soviet Union in 1991, twelve independent republics emerged from the USSR: Russia, Belarus, Uzbekistan, Azerbaijan, Kyrgyzstan, Tajikistan and the Baltic states regained independence: Estonia, Lithuania, it is governed as a federal semi-presidential republic. Russia's economy ranks as the twelfth largest by nominal GDP and sixth largest by purchasing power parity in 2018. Russia's extensive mineral and energy resources are the largest such reserves in the world, making it one of the leading producers of oil and natural gas globally; the country is one of the five recognized nuclear weapons states and possesses the largest stockpile of weapons of mass destruction.
Russia is a great power as well as a regional power and has been characterised as a potential superpower. It is a permanent member of the United Nations Security Council and an active global partner of ASEAN, as well as a member of the Shanghai Cooperation Organisation, the G20, the Council of Europe, the Asia-Pacific Economic Cooperation, the Organization for Security and Co-operation in Europe, the World Trade Organization, as well as being the leading member of the Commonwealth of Independent States, the Collective Security Treaty Organization and one of the five members of the Eurasian Economic Union, along with Armenia, Belarus and Kyrgyzstan; the name Russia is derived from Rus', a medieval state populated by the East Slavs. However, this proper name became more prominent in the history, the country was called by its inhabitants "Русская Земля", which can be translated as "Russian Land" or "Land of Rus'". In order to distinguish this state from other states derived from it, it is denoted as Kievan Rus' by modern historiography.
The name Rus itself comes from the early medieval Rus' people, Swedish merchants and warriors who relocated from across the Baltic Sea and founded a state centered on Novgorod that became Kievan Rus. An old Latin version of the name Rus' was Ruthenia applied to the western and southern regions of Rus' that were adjacent to Catholic Europe; the current name of the country, Россия, comes from the Byzantine Greek designation of the Rus', Ρωσσία Rossía—spelled Ρωσία in Modern Greek. The standard way to refer to citizens of Russia is rossiyane in Russian. There are two Russian words which are commonly
Second Polish Republic
The Second Polish Republic known as interwar Poland, refers to the country of Poland in the period between the First and Second World Wars. Known as the Republic of Poland, sometimes Commonwealth of Poland, the Polish state was re-established in 1918, in the aftermath of World War I. When, after several regional conflicts, the borders of the state were fixed in 1922, Poland's neighbours were Czechoslovakia, the Free City of Danzig, Latvia and the Soviet Union, it had side of the city of Gdynia. Between March and August 1939, Poland shared a border with the then-Hungarian governorate of Subcarpathia; the Second Republic ceased to exist in 1939, when Poland was invaded by Nazi Germany, the Soviet Union and the Slovak Republic, marking the beginning of the European theatre of World War II. In 1938, the Second Republic was the sixth largest country in Europe. According to the 1921 census, the number of inhabitants was 27.2 million. By 1939, just before the outbreak of World War II, this had grown to an estimated 35.1 million.
A third of population came from minority groups: 13.9% Ruthenians. At the same time, a significant number of ethnic Poles lived outside the country's borders; the political conditions of the Second Republic were influenced by the aftermath of World War I and conflicts with neighbouring states and the emergence of Nazi Germany. The Second Republic maintained moderate economic development; the cultural hubs of interwar Poland – Warsaw, Kraków, Poznań, Wilno and Lwów – became major European cities and the sites of internationally acclaimed universities and other institutions of higher education. After more than a century of Partitions between the Austrian, the Prussian, the Russian imperial powers, Poland re-emerged as a sovereign state at the end of the First World War in Europe in 1917-1918; the victorious Allies of World War I confirmed the rebirth of Poland in the Treaty of Versailles of June 1919. It was one of the great stories of the 1919 Paris Peace Conference. Poland solidified its independence in a series of border wars fought by the newly formed Polish Army from 1918 to 1921.
The extent of the eastern half of the interwar territory of Poland was settled diplomatically in 1922 and internationally recognized by the League of Nations. In the course of World War I, Germany gained overall dominance on the Eastern Front as the Imperial Russian Army fell back. German and Austro-Hungarian armies seized the Russian-ruled part of. In a failed attempt to resolve the Polish question as as possible, Berlin set up a German puppet state on 5 November 1916, with a governing Provisional Council of State and a Regency Council; the Council administered the country under German auspices, pending the election of a king. A month before Germany surrendered on 11 November 1918 and the war ended, the Regency Council had dissolved the Council of State, announced its intention to restore Polish independence. With the notable exception of the Marxist-oriented Social Democratic Party of the Kingdom of Poland and Lithuania, most Polish political parties supported this move. On 23 October the Regency Council appointed a new government under Józef Świeżyński and began conscription into the Polish Army.
In 1918–1919, over 100 workers' councils sprang up on Polish territories. On 6 November socialists proclaimed the Republic of Tarnobrzeg at Tarnobrzeg in Austrian Galicia; the same day the Socialist, Ignacy Daszyński, set up a Provisional People's Government of the Republic of Poland in Lublin. On Sunday, 10 November at 7 a.m. Józef Piłsudski, newly freed from 16 months in a German prison in Magdeburg, returned by train to Warsaw. Piłsudski, together with Colonel Kazimierz Sosnkowski, was greeted at Warsaw's railway station by Regent Zdzisław Lubomirski and by Colonel Adam Koc. Next day, due to his popularity and support from most political parties, the Regency Council appointed Piłsudski as Commander in Chief of the Polish Armed Forces. On 14 November, the Council dissolved itself and transferred all its authority to Piłsudski as Chief of State. After consultation with Piłsudski, Daszyński's government dissolved itself and a new government formed under Jędrzej Moraczewski. In 1918 Italy became the first country in Europe to recognise Poland's renewed sovereignty.
Centers of government that formed at that time in Galicia included the National Council of the Principality of Cieszyn, the Republic of Zakopane and the Polish Liquidation Committee. Soon afterward, the Polish–Ukrainian War broke out in Lwów between forces of the Military Committee of Ukrainians and the Polish irregular units made up of students known as the Lwów Eaglets, who were supported by the Polish Army. Meanwhile, in western Poland, another war of national liberation began under the banner of the Greater Poland uprising. In January 1919 Czechoslovakian forces attacked Polish units in the area of Zaolzie. Soon afterwards the Polish–Lithuanian War began, in August 1919 Polish-speaking residents of Upper Silesia initiated a series of three Silesian Uprisings; the most critical military conflict o
Karl Theodor Wilhelm Weierstrass was a German mathematician cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics and trained as a teacher teaching mathematics, physics and gymnastics. Weierstrass formalized the definition of the continuity of a function, proved the intermediate value theorem and the Bolzano–Weierstrass theorem, used the latter to study the properties of continuous functions on closed bounded intervals. Weierstrass was born in part of Ennigerloh, Province of Westphalia. Weierstrass was the son of Wilhelm Weierstrass, a government official, Theodora Vonderforst, his interest in mathematics began. He was sent to the University of Bonn upon graduation to prepare for a government position; because his studies were to be in the fields of law and finance, he was in conflict with his hopes to study mathematics. He resolved the conflict by paying little heed to his planned course of study, but continued private study in mathematics.
The outcome was to leave the university without a degree. After that he studied mathematics at the Münster Academy and his father was able to obtain a place for him in a teacher training school in Münster, he was certified as a teacher in that city. During this period of study, Weierstrass attended the lectures of Christoph Gudermann and became interested in elliptic functions. In 1843 he taught in Deutsch Krone in West Prussia and since 1848 he taught at the Lyceum Hosianum in Braunsberg. Besides mathematics he taught physics and gymnastics. Weierstrass may have had an illegitimate child named Franz with the widow of his friend Carl Wilhelm Borchardt. After 1850 Weierstrass suffered from a long period of illness, but was able to publish papers that brought him fame and distinction; the University of Königsberg conferred an honorary doctor's degree on him on 31 March 1854. In 1856 he took a chair at the Gewerbeinstitut, which became the Technical University of Berlin. In 1864 he became professor at the Friedrich-Wilhelms-Universität Berlin, which became the Humboldt Universität zu Berlin.
At the age of fifty-five, Weierstrass met Sonya Kovalevsky whom he tutored after failing to secure her admission to the University. They had a fruitful intellectual, but troubled personal relationship that "far transcended the usual teacher-student relationship"; the misinterpretation of this relationship and Kovalevsky's early death in 1891 was said to have contributed to Weierstrass' ill-health. He was immobile for the last three years of his life, died in Berlin from pneumonia. Weierstrass was interested in the soundness of calculus, at the time, there were somewhat ambiguous definitions regarding the foundations of calculus, hence important theorems could not be proven with sufficient rigour. While Bolzano had developed a reasonably rigorous definition of a limit as early as 1817 his work remained unknown to most of the mathematical community until years and many mathematicians had only vague definitions of limits and continuity of functions. Delta-epsilon proofs are first found in the works of Cauchy in the 1820s.
Cauchy did not distinguish between continuity and uniform continuity on an interval. Notably, in his 1821 Cours d'analyse, Cauchy argued that the limit of continuous functions was itself continuous, a statement interpreted as being incorrect by many scholars; the correct statement is. This required the concept of uniform convergence, first observed by Weierstrass's advisor, Christoph Gudermann, in an 1838 paper, where Gudermann noted the phenomenon but did not define it or elaborate on it. Weierstrass saw the importance of the concept, both formalized it and applied it throughout the foundations of calculus; the formal definition of continuity of a function, as formulated by Weierstrass, is as follows: f is continuous at x = x 0 if ∀ ε > 0 ∃ δ > 0 such that for every x in the domain of f, | x − x 0 | < δ ⇒ | f − f | < ε. In simple English, f is continuous at a point x = x 0 if for each ε > 0 there exists a δ > 0 such that the function f lies between f − ε and f