Berlin is the capital and largest city of Germany by both area and population. Its 3,748,148 inhabitants make it the second most populous city proper of the European Union after London; the city is one of Germany's 16 federal states. It is surrounded by the state of Brandenburg, contiguous with its capital, Potsdam; the two cities are at the center of the Berlin-Brandenburg capital region, which is, with about six million inhabitants and an area of more than 30,000 km², Germany's third-largest metropolitan region after the Rhine-Ruhr and Rhine-Main regions. Berlin straddles the banks of the River Spree, which flows into the River Havel in the western borough of Spandau. Among the city's main topographical features are the many lakes in the western and southeastern boroughs formed by the Spree and Dahme rivers. Due to its location in the European Plain, Berlin is influenced by a temperate seasonal climate. About one-third of the city's area is composed of forests, gardens, rivers and lakes; the city lies in the Central German dialect area, the Berlin dialect being a variant of the Lusatian-New Marchian dialects.
First documented in the 13th century and situated at the crossing of two important historic trade routes, Berlin became the capital of the Margraviate of Brandenburg, the Kingdom of Prussia, the German Empire, the Weimar Republic, the Third Reich. Berlin in the 1920s was the third largest municipality in the world. After World War II and its subsequent occupation by the victorious countries, the city was divided. East Berlin was declared capital of East Germany. Following German reunification in 1990, Berlin once again became the capital of all of Germany. Berlin is a world city of culture, politics and science, its economy is based on high-tech firms and the service sector, encompassing a diverse range of creative industries, research facilities, media corporations and convention venues. Berlin serves as a continental hub for air and rail traffic and has a complex public transportation network; the metropolis is a popular tourist destination. Significant industries include IT, biomedical engineering, clean tech, biotechnology and electronics.
Berlin is home to world-renowned universities, orchestras and entertainment venues, is host to many sporting events. Its Zoological Garden is one of the most popular worldwide. With the world's oldest large-scale movie studio complex, Berlin is an popular location for international film productions; the city is well known for its festivals, diverse architecture, contemporary arts and a high quality of living. Since the 2000s Berlin has seen the emergence of a cosmopolitan entrepreneurial scene. Berlin lies in northeastern Germany, east of the River Saale, that once constituted, together with the River Elbe, the eastern border of the Frankish Realm. While the Frankish Realm was inhabited by Germanic tribes like the Franks and the Saxons, the regions east of the border rivers were inhabited by Slavic tribes; this is why most of the villages in northeastern Germany bear Slavic-derived names. Typical Germanised place name suffixes of Slavic origin are -ow, -itz, -vitz, -witz, -itzsch and -in, prefixes are Windisch and Wendisch.
The name Berlin has its roots in the language of West Slavic inhabitants of the area of today's Berlin, may be related to the Old Polabian stem berl-/birl-. Since the Ber- at the beginning sounds like the German word Bär, a bear appears in the coat of arms of the city, it is therefore a canting arm. Of Berlin's twelve boroughs, five bear a Slavic-derived name: Pankow, Steglitz-Zehlendorf, Marzahn-Hellersdorf, Treptow-Köpenick and Spandau. Of its ninety-six neighborhoods, twenty-two bear a Slavic-derived name: Altglienicke, Alt-Treptow, Buch, Gatow, Kladow, Köpenick, Lankwitz, Lübars, Marzahn, Prenzlauer Berg, Schmöckwitz, Stadtrandsiedlung Malchow, Steglitz and Zehlendorf; the neighborhood of Moabit bears a French-derived name, Französisch Buchholz is named after the Huguenots. The earliest evidence of settlements in the area of today's Berlin are a wooden beam dated from 1192, remnants of a house foundation dated to 1174, found in excavations in Berlin Mitte; the first written records of towns in the area of present-day Berlin date from the late 12th century.
Spandau is first mentioned in 1197 and Köpenick in 1209, although these areas did not join Berlin until 1920. The central part of Berlin can be traced back to two towns. Cölln on the Fischerinsel is first mentioned in a 1237 document, Berlin, across the Spree in what is now called the Nikolaiviertel, is referenced in a document from 1244. 1237 is considered the founding date of the city. The two towns over time formed close economic and social ties, profited from the staple right on the two important trade routes Via Imperii and from Bruges to Novgorod. In 1307, they formed an alliance with a common external policy, their internal administrations still being separated. In 1415, Frederick I became the elector of the Margraviate of Brandenburg, which he ruled until 1440. During the 15th century, his successors established Berlin-Cölln as capital of the margraviate, subsequent members of the Hohenzol
ETH Zurich is a science, technology and mathematics university in the city of Zürich, Switzerland. Like its sister institution EPFL, it is an integral part of the Swiss Federal Institutes of Technology Domain, directly subordinate to Switzerland's Federal Department of Economic Affairs and Research; the school was founded by the Swiss Federal Government in 1854 with the stated mission to educate engineers and scientists, serve as a national center of excellence in science and technology and provide a hub for interaction between the scientific community and industry. In the 2019 edition of the QS World University Rankings ETH Zurich is ranked 7th in the world, is ranked 10th in the world by the Times Higher Education World Rankings 2018. In the 2019 QS World University Rankings by subject it is ranked 3rd in the world for engineering and technology, 1st for Earth & Marine Science; as of August 2018, 32 Nobel laureates, 4 Fields Medalists, 1 Turing Award winner have been affiliated with the Institute, including Albert Einstein.
It is a founding member of the IDEA League and the International Alliance of Research Universities and a member of the CESAER network. ETH was founded on 7 February 1854 by the Swiss Confederation and began giving its first lectures on 16 October 1855 as a polytechnic institute at various sites throughout the city of Zurich, it was composed of six faculties: architecture, civil engineering, mechanical engineering, forestry, an integrated department for the fields of mathematics, natural sciences and social and political sciences. It is locally still known as Polytechnikum, or as Poly, derived from the original name eidgenössische polytechnische Schule, which translates to "federal polytechnic school". ETH is a federal institute; the decision for a new federal university was disputed at the time. In the beginning, both universities were co-located in the buildings of the University of Zürich. From 1905 to 1908, under the presidency of Jérôme Franel, the course program of ETH was restructured to that of a real university and ETH was granted the right to award doctorates.
In 1909 the first doctorates were awarded. In 1911, it was given Eidgenössische Technische Hochschule. In 1924, another reorganization structured the university in 12 departments. However, it now has 16 departments. ETH Zurich, the EPFL, four associated research institutes form the "ETH Domain" with the aim of collaborating on scientific projects. ETH Zurich is ranked among the top universities in the world. Popular rankings place the institution as the best university in continental Europe and ETH Zurich is ranked among the top 1-5 universities in Europe, among the top 3-10 best universities of the world. ETH Zurich has achieved its reputation in the fields of chemistry and physics. There are 32 Nobel Laureates who are associated with ETH; the most recent Nobel Laureate is Richard F. Heck, awarded the Nobel Prize in chemistry in 2010. Albert Einstein is its most famous alumnus. In 2018, the QS World University Rankings placed ETH Zurich at 7th overall in the world. In 2015, ETH was ranked 5th in the world in Engineering and Technology, just behind the Massachusetts Institute of Technology, Stanford University, Cambridge University and National University of Singapore.
In 2015, ETH ranked 6th in the world in Natural Sciences, in 2016 ranked 1st in the world for Earth & Marine Sciences for the second consecutive year. In 2016, Times Higher Education World University Rankings ranked ETH Zurich 9th overall in the world and 8th in the world in the field of Engineering & Technology, just behind the Massachusetts Institute of Technology, Stanford University, California Institute of Technology, Princeton University, Cambridge University, Imperial College London and Oxford University. In a comparison of Swiss universities by swissUP Ranking and in rankings published by CHE comparing the universities of German-speaking countries, ETH Zurich traditionally is ranked first in natural sciences, computer science and engineering sciences. In the survey CHE ExcellenceRanking on the quality of Western European graduate school programmes in the fields biology, chemistry and mathematics, ETH was assessed as one of the three institutions to have excellent graduate programmes in all considered fields, the other two being the Imperial College London and the University of Cambridge.
ETH Zurich had a total budget of 1.885 billion CHF in the year 2017. For Swiss students, ETH is not selective in its undergraduate admission procedures. Like every public university in Switzerland, ETH is obliged to grant admission to every Swiss resident who took the Matura. Applicants from foreign countries are required to take either the reduced entrance exam or the comprehensive entrance exam although some applicants from several European countries are exempted from this rule. An applicant can be admitted to ETH without any verifiable educational records by passing the comprehensive entrance exam; as at all universities in Switzerland, the academic year is divided into two semesters. Examinations are held durin
Humboldt University of Berlin
Humboldt University of Berlin is a university in the central borough of Mitte in Berlin, Germany. It was established by Frederick William III on the initiative of Wilhelm von Humboldt, Johann Gottlieb Fichte and Friedrich Ernst Daniel Schleiermacher as the University of Berlin in 1809, opened in 1810, making it the oldest of Berlin's four universities. From 1810 until its closure in 1945, it was named Friedrich Wilhelm University. During the Cold War the university found itself in East Berlin and was de facto split in two when the Free University of Berlin opened in West Berlin; the university received its current name in honour of Alexander and Wilhelm von Humboldt in 1949. The university is divided into nine faculties, including its medical school shared with the Free University of Berlin, has a student enrollment of around 32,000 students, offers degree programmes in some 189 disciplines from undergraduate to postdoctorate level, its main campus is located on the Unter den Linden boulevard in central Berlin.
The university is known worldwide for pioneering the Humboldtian model of higher education, which has influenced other European and Western universities, the university has been called "the mother of all modern universities."As of 2017, the university has been associated with 55 Nobel Prize winners, is considered one of the best universities in Europe as well as one of the most prestigious universities in the world for arts and humanities. It was regarded as the world's preeminent university for the natural sciences during the 19th and early 20th century, is linked to major breakthroughs in physics and other sciences by its professors such as Albert Einstein. Former faculty and notable alumni include eminent philosophers, artists, politicians, mathematicians and Heads of State; the University of Berlin was established on 16 August 1809, on the initiative of the liberal Prussian educational politician Wilhelm von Humboldt by King Friedrich Wilhelm III, during the period of the Prussian Reform Movement.
The university was located in a palace constructed from 1748-1766 for the late Prince Henry, the younger brother of Frederick the Great. After his widow and her ninety-member staff moved out, the first unofficial lectures were given in the building in the winter of 1809. Humboldt faced great resistance to his ideas, he submitted his resignation to the King in April 1810, was not present when the school opened that fall. The first students were admitted on 6 October 1810, the first semester started on 10 October 1810, with 256 students and 52 lecturers in faculties of law, medicine and philosophy under rector Theodor Schmalz; the university celebrates 15 October 1810 as the date of its opening. From 1828 to 1945, the school was named the Friedrich Wilhelm University, in honor of its founder. Ludwig Feuerbach one of the students, made a comment on the university in 1826: "There is no question here of drinking and plesant communal outings. Compared to this temple of work, the other universities appear like public houses."The university has been home to many of Germany's greatest thinkers of the past two centuries, among them the subjective idealist philosopher Johann Gottlieb Fichte, the theologian Friedrich Schleiermacher, the absolute idealist philosopher G.
W. F. Hegel, the Romantic legal theorist Friedrich Carl von Savigny, the pessimist philosopher Arthur Schopenhauer, the objective idealist philosopher Friedrich Schelling, cultural critic Walter Benjamin, famous physicists Albert Einstein and Max Planck; the founders of Marxist theory Karl Marx and Friedrich Engels attended the university, as did poet Heinrich Heine, novelist Alfred Döblin, founder of structuralism Ferdinand de Saussure, German unifier Otto von Bismarck, Communist Party of Germany founder Karl Liebknecht, African American Pan Africanist W. E. B. Du Bois and European unifier Robert Schuman, as well as the influential surgeon Johann Friedrich Dieffenbach in the early half of the 1800s; the structure of German research-intensive universities served as a model for institutions like Johns Hopkins University. Further, it has been claimed that "the'Humboldtian' university became a model for the rest of Europe with its central principle being the union of teaching and research in the work of the individual scholar or scientist."
In addition to the strong anchoring of traditional subjects, such as science, philosophy, history and medicine, the university developed to encompass numerous new scientific disciplines. Alexander von Humboldt, brother of the founder William, promoted the new learning. With the construction of modern research facilities in the second half of the 19th Century teaching of the natural sciences began. Famous researchers, such as the chemist August Wilhelm Hofmann, the physicist Hermann von Helmholtz, the mathematicians Ernst Eduard Kummer, Leopold Kronecker, Karl Weierstrass, the physicians Johannes Peter Müller, Albrecht von Graefe, Rudolf Virchow and Robert Koch, contributed to Berlin University's scientific fame. During this period of enlargement, the university expanded to incorporate other separate colleges in Berlin. An example would be the Pépinière and the Collegium Medico-chirurgicum. In 1717, King Friedrich I had built a quarantine house for Plague at the city gates, which in 1727 was rechristened by the "soldier king" Friedrich
Switzerland the Swiss Confederation, is a country situated in western and southern Europe. It consists of 26 cantons, the city of Bern is the seat of the federal authorities; the sovereign state is a federal republic bordered by Italy to the south, France to the west, Germany to the north, Austria and Liechtenstein to the east. Switzerland is a landlocked country geographically divided between the Alps, the Swiss Plateau and the Jura, spanning a total area of 41,285 km2. While the Alps occupy the greater part of the territory, the Swiss population of 8.5 million people is concentrated on the plateau, where the largest cities are to be found: among them are the two global cities and economic centres Zürich and Geneva. The establishment of the Old Swiss Confederacy dates to the late medieval period, resulting from a series of military successes against Austria and Burgundy. Swiss independence from the Holy Roman Empire was formally recognized in the Peace of Westphalia in 1648; the country has a history of armed neutrality going back to the Reformation.
It pursues an active foreign policy and is involved in peace-building processes around the world. In addition to being the birthplace of the Red Cross, Switzerland is home to numerous international organisations, including the second largest UN office. On the European level, it is a founding member of the European Free Trade Association, but notably not part of the European Union, the European Economic Area or the Eurozone. However, it participates in the Schengen Area and the European Single Market through bilateral treaties. Spanning the intersection of Germanic and Romance Europe, Switzerland comprises four main linguistic and cultural regions: German, French and Romansh. Although the majority of the population are German-speaking, Swiss national identity is rooted in a common historical background, shared values such as federalism and direct democracy, Alpine symbolism. Due to its linguistic diversity, Switzerland is known by a variety of native names: Schweiz. On coins and stamps, the Latin name – shortened to "Helvetia" – is used instead of the four national languages.
Switzerland is one of the most developed countries in the world, with the highest nominal wealth per adult and the eighth-highest per capita gross domestic product according to the IMF. Switzerland ranks at or near the top globally in several metrics of national performance, including government transparency, civil liberties, quality of life, economic competitiveness and human development. Zürich and Basel have all three been ranked among the top ten cities in the world in terms of quality of life, with the first ranked second globally, according to Mercer in 2018; the English name Switzerland is a compound containing Switzer, an obsolete term for the Swiss, in use during the 16th to 19th centuries. The English adjective Swiss is a loan from French Suisse in use since the 16th century; the name Switzer is from the Alemannic Schwiizer, in origin an inhabitant of Schwyz and its associated territory, one of the Waldstätten cantons which formed the nucleus of the Old Swiss Confederacy. The Swiss began to adopt the name for themselves after the Swabian War of 1499, used alongside the term for "Confederates", used since the 14th century.
The data code for Switzerland, CH, is derived from Latin Confoederatio Helvetica. The toponym Schwyz itself was first attested in 972, as Old High German Suittes perhaps related to swedan ‘to burn’, referring to the area of forest, burned and cleared to build; the name was extended to the area dominated by the canton, after the Swabian War of 1499 came to be used for the entire Confederation. The Swiss German name of the country, Schwiiz, is homophonous to that of the canton and the settlement, but distinguished by the use of the definite article; the Latin name Confoederatio Helvetica was neologized and introduced after the formation of the federal state in 1848, harking back to the Napoleonic Helvetic Republic, appearing on coins from 1879, inscribed on the Federal Palace in 1902 and after 1948 used in the official seal.. Helvetica is derived from the Helvetii, a Gaulish tribe living on the Swiss plateau before the Roman era. Helvetia appears as a national personification of the Swiss confederacy in the 17th century with a 1672 play by Johann Caspar Weissenbach.
Switzerland has existed as a state in its present form since the adoption of the Swiss Federal Constitution in 1848. The precursors of Switzerland established a protective alliance at the end of the 13th century, forming a loose confederation of states which persisted for centuries; the oldest traces of hominid existence in Switzerland date back about 150,000 years. The oldest known farming settlements in Switzerland, which were found at Gächlingen, have been dated to around 5300 BC; the earliest known cultural tribes of the area were members of the Hallstatt and La Tène cultures, named after the archaeological site of La Tène on the north side of Lake Neuchâtel. La Tène culture developed and flourished during the late Iron Age from around 450 BC under some influence from the Gree
The Weimar Republic is an unofficial historical designation for the German state from 1918 to 1933. The name derives from the city of Weimar; the official name of the republic remained Deutsches Reich unchanged from 1871, because of the German tradition of substates. Although translated as "German Empire", the word Reich here better translates as "realm", in that the term does not have monarchical connotations in itself; the Reich was changed from a constitutional monarchy into a republic. In English, the country was known as Germany. Germany became a de facto republic on 9 November 1918 when Kaiser Wilhelm II abdicated the German and Prussian thrones with no agreement made on a succession by his son Crown Prince Wilhelm, became a de jure republic in February 1919 when the position of President of Germany was created. A national assembly was convened in Weimar, where a new constitution for Germany was written and adopted on 11 August 1919. In its fourteen years, the Weimar Republic faced numerous problems, including hyperinflation, political extremism as well as contentious relationships with the victors of the First World War.
Resentment in Germany towards the Treaty of Versailles was strong on the political right where there was great anger towards those who had signed the Treaty and submitted to fulfill the terms of it. The Weimar Republic fulfilled most of the requirements of the Treaty of Versailles although it never met its disarmament requirements and paid only a small portion of the war reparations. Under the Locarno Treaties, Germany accepted the western borders of the country by abandoning irredentist claims on France and Belgium, but continued to dispute the eastern borders and sought to persuade German-speaking Austria to join Germany as one of Germany's states. From 1930 onwards President Hindenburg used emergency powers to back Chancellors Heinrich Brüning, Franz von Papen and General Kurt von Schleicher; the Great Depression, exacerbated by Brüning's policy of deflation, led to a surge in unemployment. In 1933, Hindenburg appointed Adolf Hitler as Chancellor with the Nazi Party being part of a coalition government.
The Nazis held two out of the remaining ten cabinet seats. Von Papen as Vice Chancellor was intended to be the "éminence grise" who would keep Hitler under control, using his close personal connection to Hindenburg. Within months, the Reichstag Fire Decree and the Enabling Act of 1933 had brought about a state of emergency: it wiped out constitutional governance and civil liberties. Hitler's seizure of power was permissive of government by decree without legislative participation; these events brought the republic to an end – as democracy collapsed, the founding of a single-party state began the dictatorship of the Nazi era. The Weimar Republic is so called because the assembly that adopted its constitution met at Weimar, from 6 February 1919 to 11 August 1919, but this name only became mainstream after 1933. Between 1919 and 1933 there was no single name for the new state that gained widespread acceptance, why the old name Deutsches Reich remained though hardly anyone used it during the Weimar period.
To the right of the spectrum the politically engaged rejected the new democratic model and cringed to see the honour of the traditional word Reich associated with it. The Catholic Centre party, Zentrum favoured the term Deutscher Volksstaat while on the moderate left the Chancellor's SPD preferred Deutsche Republik. By 1925, Deutsche Republik was used by most Germans, but for the anti-democratic right the word Republik was, along with the relocation of the seat of power to Weimar, a painful reminder of a government structure, imposed by foreign statesmen, along with the expulsion of Kaiser Wilhelm in the wake of massive national humiliation; the first recorded mention of the term Republik von Weimar came during a speech delivered by Adolf Hitler at a National Socialist German Worker's Party rally in Munich on 24 February 1929—it was a few weeks that the term Weimarer Republik was first used in a newspaper article. Only during the 1930s did the term become mainstream, both within and outside Germany.
According to historian Richard J. Evans: The continued use of the term'German Empire', Deutsches Reich, by the Weimar Republic....conjured up an image among educated Germans that resonated far beyond the institutional structures Bismarck created: the successor to the Roman Empire. After the introduction of the republic, the flag and coat of arms of Germany were altered to reflect the political changes; the Weimar Republic without the symbols of the former Monarchy. This left the black eagle with one head, facing to the right, with open wings but closed feathers, with a red beak and claws and white highlighting. By reason of a decision of the Reich's Government I hereby announce, that the Imperial coat of arms on a gold-yellow shield shows the one headed black eagle, the head turned to the right, the wings open but with closed feathering, beak and claws in red color. If the Reich's Eagle is shown without a frame, the same charg
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
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