1.
France
–
France, officially the French Republic, is a country with territory in western Europe and several overseas regions and territories. The European, or metropolitan, area of France extends from the Mediterranean Sea to the English Channel and the North Sea, Overseas France include French Guiana on the South American continent and several island territories in the Atlantic, Pacific and Indian oceans. France spans 643,801 square kilometres and had a population of almost 67 million people as of January 2017. It is a unitary republic with the capital in Paris. Other major urban centres include Marseille, Lyon, Lille, Nice, Toulouse, during the Iron Age, what is now metropolitan France was inhabited by the Gauls, a Celtic people. The area was annexed in 51 BC by Rome, which held Gaul until 486, France emerged as a major European power in the Late Middle Ages, with its victory in the Hundred Years War strengthening state-building and political centralisation. During the Renaissance, French culture flourished and a colonial empire was established. The 16th century was dominated by civil wars between Catholics and Protestants. France became Europes dominant cultural, political, and military power under Louis XIV, in the 19th century Napoleon took power and established the First French Empire, whose subsequent Napoleonic Wars shaped the course of continental Europe. Following the collapse of the Empire, France endured a succession of governments culminating with the establishment of the French Third Republic in 1870. Following liberation in 1944, a Fourth Republic was established and later dissolved in the course of the Algerian War, the Fifth Republic, led by Charles de Gaulle, was formed in 1958 and remains to this day. Algeria and nearly all the colonies became independent in the 1960s with minimal controversy and typically retained close economic. France has long been a centre of art, science. It hosts Europes fourth-largest number of cultural UNESCO World Heritage Sites and receives around 83 million foreign tourists annually, France is a developed country with the worlds sixth-largest economy by nominal GDP and ninth-largest by purchasing power parity. In terms of household wealth, it ranks fourth in the world. France performs well in international rankings of education, health care, life expectancy, France remains a great power in the world, being one of the five permanent members of the United Nations Security Council with the power to veto and an official nuclear-weapon state. It is a member state of the European Union and the Eurozone. It is also a member of the Group of 7, North Atlantic Treaty Organization, Organisation for Economic Co-operation and Development, the World Trade Organization, originally applied to the whole Frankish Empire, the name France comes from the Latin Francia, or country of the Franks

2.
Nancy, France
–
Nancy is the capital of the north-eastern French department of Meurthe-et-Moselle, and formerly the capital of the Duchy of Lorraine, and then the French province of the same name. The metropolitan area of Nancy had a population of 410,509 inhabitants at the 1999 census,103,602 of whom lived in the city of Nancy proper. The motto of the city is Non inultus premor, Latin for Im not touched with impunity—a reference to the thistle, the earliest signs of human settlement in the area date back to 800 BC. Early settlers were attracted by easily mined iron ore and a ford in the Meurthe River. A small fortified town named Nanciacum was built by Gérard, Duke of Lorraine around 1050, Duke Charles the Bold of Burgundy, was defeated and killed in the Battle of Nancy in 1477, René II, Duke of Lorraine became the ruler. In 1736 Emperor Charles arranged her marriage to Duke François of Lorraine, exiled Polish king Stanisław Leszczyński, father-in-law of French king Louis XV, was given the vacant duchy instead. Under his nominal rule, Nancy experienced growth and a flowering of Baroque culture and architecture, with his death in 1766, the duchy became a regular French province and Nancy lost its position as a residential capital city with its own princely court and patronage. As unrest surfaced within the French armed forces during the French Revolution, a few reliable units laid siege to the town and shot or imprisoned the mutineers. In 1871, Nancy remained French when Prussia annexed Alsace-Lorraine, the flow of refugees reaching Nancy doubled its population in three decades. Artistic, academic, financial and industrial excellence flourished, establishing what is still the Capital of Lorraines trademark to this day, Nancy was freed from Nazi Germany by the U. S. Third Army in September 1944, during the Lorraine Campaign of World War II at the Battle of Nancy ), in 1988, Pope John Paul II visited Nancy. In 2005, French President Jacques Chirac, German Chancellor Gerhard Schröder, Nancy is situated on the left bank of the river Meurthe, about 10 km upstream from its confluence with the Moselle. The Marne–Rhine Canal runs through the city, parallel to the Meurthe, Nancy is surrounded by hills that are about 150 m higher than the city center, which is situated at 200 m amsl. The area of Nancy proper is small,15 km2. Its built-up area is continuous with those of its adjacent suburbs, the neighboring communes of Nancy are, Jarville-la-Malgrange, Laxou, Malzéville, Maxéville, Saint-Max, Tomblaine, Vandœuvre-lès-Nancy and Villers-lès-Nancy. Adjacent to its south is the quarter Charles III – Centre Ville and this quarter contains the famous Place Stanislas, the Nancy Cathedral, the Opéra national de Lorraine and the main railway station. The old city centers heritage dates from the Middle Ages to the 18th century, the cathedral of Nancy, the Triumphal Arch and the Place de la Carriere are a fine examples of 18th-century architecture. The Palace of the Dukes of Lorraine is the princely residence of the rulers

3.
Mathematics
–
Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times

4.
University of St Andrews
–
The University of St Andrews is a British public research university in St Andrews, Fife, Scotland. It is the oldest of the four ancient universities of Scotland, St Andrews was founded between 1410 and 1413, when the Avignon Antipope Benedict XIII issued a papal bull to a small founding group of Augustinian clergy. St Andrews is made up from a variety of institutions, including three constituent colleges and 18 academic schools organised into four faculties, the university occupies historic and modern buildings located throughout the town. The academic year is divided into two terms, Martinmas and Candlemas, in term time, over one-third of the towns population is either a staff member or student of the university. It is ranked as the third best university in the United Kingdom in national league tables, the Times Higher Education World Universities Ranking names St Andrews among the worlds Top 50 universities for Social Sciences, Arts and Humanities. St Andrews has the highest student satisfaction amongst all multi-faculty universities in the United Kingdom, St Andrews has many notable alumni and affiliated faculty, including eminent mathematicians, scientists, theologians, philosophers, and politicians. Six Nobel Laureates are among St Andrews alumni and former staff, a charter of privilege was bestowed upon the society of masters and scholars by the Bishop of St Andrews, Henry Wardlaw, on 28 February 1411. Wardlaw then successfully petitioned the Avignon Pope Benedict XIII to grant the university status by issuing a series of papal bulls. King James I of Scotland confirmed the charter of the university in 1432, subsequent kings supported the university with King James V confirming privileges of the university in 1532. A college of theology and arts called St Johns College was founded in 1418 by Robert of Montrose, St Salvators College was established in 1450, by Bishop James Kennedy. St Leonards College was founded in 1511 by Archbishop Alexander Stewart, St Johns College was refounded by Cardinal James Beaton under the name St Marys College in 1538 for the study of divinity and law. Some university buildings that date from this period are still in use today, such as St Salvators Chapel, St Leonards College Chapel, at this time, the majority of the teaching was of a religious nature and was conducted by clerics associated with the cathedral. During the 17th and 18th centuries, the university had mixed fortunes and was beset by civil. He described it as pining in decay and struggling for life, in the second half of the 19th century, pressure was building upon universities to open up higher education to women. In 1876, the University Senate decided to allow women to receive an education at St Andrews at a roughly equal to the Master of Arts degree that men were able to take at the time. The scheme came to be known as the L. L. A and it required women to pass five subjects at an ordinary level and one at honours level and entitled them to hold a degree from the university. In 1889 the Universities Act made it possible to admit women to St Andrews. Agnes Forbes Blackadder became the first woman to graduate from St Andrews on the level as men in October 1894

5.
Nicolas Bourbaki
–
With the goal of grounding all of mathematics on set theory, the group strove for rigour and generality. Their work led to the discovery of several concepts and terminologies still used, in 1934, young French mathematicians from various French universities felt the need to form a group to jointly produce textbooks that they could all use for teaching. André Weil organized the first meeting on 10 December 1934 in the basement of a Parisian grill room, Bourbakis main work is the Elements of Mathematics series. This series aims to be a completely self-contained treatment of the areas of modern mathematics. Assuming no special knowledge of mathematics, it takes up mathematics from the beginning, proceeds axiomatically. The volume on spectral theory from 1967 was for almost four decades the last new book to be added to the series, after that several new chapters to existing books as well as revised editions of existing chapters appeared until the publication of chapters 8-9 of Commutative Algebra in 1983. Then a long break in publishing activity occurred, leading many to suspect the end of the publishing project, however, chapter 10 of Commutative Algebra appeared in 1998, and after another long break a completely re-written and expanded chapter 8 of Algèbre was published in 2012. More importantly, the first four chapters of a new book on algebraic topology were published in 2016. Besides the Éléments de mathématique series, lectures from the Séminaire Bourbaki also have been published in monograph form since 1948. Notations introduced by Bourbaki include the symbol ∅ for the empty set and a dangerous bend symbol ☡, and the terms injective, surjective, and bijective. The emphasis on rigour may be seen as a reaction to the work of Henri Poincaré, the impact of Bourbakis work initially was great on many active research mathematicians world-wide. For example, Our time is witnessing the creation of a monumental work and it provoked some hostility, too, mostly on the side of classical analysts, they approved of rigour but not of high abstraction. This led to a gulf with the way theoretical physics was practiced, Bourbakis direct influence has decreased over time. This is partly because certain concepts which are now important, such as the machinery of category theory, are not covered in the treatise. It also mattered that, while especially algebraic structures can be defined in Bourbakis terms. On the other hand, the approach and rigour advocated by Bourbaki have permeated the current mathematical practices to such extent that the task undertaken was completed and this is particularly true for the less applied parts of mathematics. The Bourbaki seminar series founded in post-WWII Paris continues, it has going on since 1948. It is an important source of survey articles, with sketches of proofs, the topics range through all branches of mathematics, including sometimes theoretical physics

6.
Mathematician
–
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, one of the earliest known mathematicians was Thales of Miletus, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, 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, and 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 works on applied mathematics. Because of a dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked. Science and mathematics in the Islamic world during the Middle Ages followed various models and it was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. 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 working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham, the Renaissance brought an increased emphasis on mathematics and science to Europe. As time passed, many gravitated towards universities. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking. ”Thus, seminars, overall, science became the focus of universities in the 19th and 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. ”Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then 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 an understanding of mathematics, the students, who pass, are permitted to work on a doctoral dissertation. Mathematicians involved with solving problems with applications in life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their knowledge and professional methodology. With professional focus on a variety of problems, theoretical systems

7.
Mathematical analysis
–
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions. These theories are studied in the context of real and complex numbers. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis, analysis may be distinguished from geometry, however, it can be applied to any space of mathematical objects that has a definition of nearness or specific distances between objects. Mathematical analysis formally developed in the 17th century during the Scientific Revolution, early results in analysis were implicitly present in the early days of ancient Greek mathematics. For instance, a geometric sum is implicit in Zenos paradox of the dichotomy. The explicit use of infinitesimals appears in Archimedes The Method of Mechanical Theorems, in Asia, the Chinese mathematician Liu Hui used the method of exhaustion in the 3rd century AD to find the area of a circle. Zu Chongzhi established a method that would later be called Cavalieris principle to find the volume of a sphere in the 5th century, the Indian mathematician Bhāskara II gave examples of the derivative and used what is now known as Rolles theorem in the 12th century. In the 14th century, Madhava of Sangamagrama developed infinite series expansions, like the power series and his followers at the Kerala school of astronomy and mathematics further expanded his works, up to the 16th century. The modern foundations of analysis were established in 17th century Europe. During this period, calculus techniques were applied to approximate discrete problems by continuous ones, in the 18th century, Euler introduced the notion of mathematical function. Real analysis began to emerge as an independent subject when Bernard Bolzano introduced the definition of continuity in 1816. In 1821, Cauchy began to put calculus on a firm logical foundation by rejecting the principle of the generality of algebra widely used in earlier work, instead, Cauchy formulated calculus in terms of geometric ideas and infinitesimals. Thus, his definition of continuity required a change in x to correspond to an infinitesimal change in y. He also introduced the concept of the Cauchy sequence, and started the theory of complex analysis. Poisson, Liouville, Fourier and others studied partial differential equations, the contributions of these mathematicians and others, such as Weierstrass, developed the -definition of limit approach, thus founding the modern field of mathematical analysis. In the middle of the 19th century Riemann introduced his theory of integration, the last third of the century saw the arithmetization of analysis by Weierstrass, who thought that geometric reasoning was inherently misleading, and introduced the epsilon-delta definition of limit. Then, mathematicians started worrying that they were assuming the existence of a continuum of numbers without proof. Around that time, the attempts to refine the theorems of Riemann integration led to the study of the size of the set of discontinuities of real functions, also, monsters began to be investigated

8.
Integrated Authority File
–
The Integrated Authority File or GND is an international authority file for the organisation of personal names, subject headings and corporate bodies from catalogues. It is used mainly for documentation in libraries and increasingly also by archives, the GND is managed by the German National Library in cooperation with various regional library networks in German-speaking Europe and other partners. The GND falls under the Creative Commons Zero license, the GND specification provides a hierarchy of high-level entities and sub-classes, useful in library classification, and an approach to unambiguous identification of single elements. It also comprises an ontology intended for knowledge representation in the semantic web, available in the RDF format

9.
Virtual International Authority File
–
The Virtual International Authority File is an international authority file. It is a joint project of national libraries and operated by the Online Computer Library Center. The project was initiated by the US Library of Congress, the German National Library, the National Library of France joined the project on October 5,2007. The project transitions to a service of the OCLC on April 4,2012, the aim is to link the national authority files to a single virtual authority file. In this file, identical records from the different data sets are linked together, a VIAF record receives a standard data number, contains the primary see and see also records from the original records, and refers to the original authority records. The data are available online and are available for research and data exchange. Reciprocal updating uses the Open Archives Initiative Protocol for Metadata Harvesting protocol, the file numbers are also being added to Wikipedia biographical articles and are incorporated into Wikidata. VIAFs clustering algorithm is run every month, as more data are added from participating libraries, clusters of authority records may coalesce or split, leading to some fluctuation in the VIAF identifier of certain authority records