University of Paris
The University of Paris, metonymically known as the Sorbonne, was a university in Paris, active 1150–1793, 1806–1970. Emerging around 1150 as a corporation associated with the cathedral school of Notre Dame de Paris, it was considered the second oldest university in Europe. Chartered in 1200 by King Philip II of France and recognised in 1215 by Pope Innocent III, it was often nicknamed after its theological College of Sorbonne, in turn founded by Robert de Sorbon and chartered by French King Saint Louis around 1257. Internationally reputed for its academic performance in the humanities since the Middle Ages – notably in theology and philosophy – it introduced several academic standards and traditions that have endured since and spread internationally, such as doctoral degrees and student nations. Vast numbers of popes, royalty and intellectuals were educated at the University of Paris. A few of the colleges of the time are still visible close to Pantheon and Luxembourg Gardens: Collège des Bernardins, Hotel de Cluny, College Sainte Barbe, College d'Harcourt, Cordeliers.
In 1793, during the French Revolution, the university was closed and by Item-27 of the Revolutionary Convention, the college endowments and buildings were sold. A new University of France replaced it in 1806 with four independent faculties: the Faculty of Humanities, the Faculty of Law, the Faculty of Science, the Faculty of Medicine and the Faculty of Theology. In 1970, following the May 1968 events, the university was divided into 13 autonomous universities. Although all the thirteen universities that resulted of the original University of Paris split can be considered its inheritors, just three universities of the post-1968 universities embodied direct faculties successors while inheriting the name "Sorbonne", as well as its physical location in the Latin Quarter: the Pantheon-Sorbonne University. From 2010, University of Paris successors started to reorganise themselves into different groups of universities and institutions that were upgraded to "pôles de recherche et d'enseignement supérieur".
As a result, various university groups exist in the Paris area, among them Sorbonne Paris Cité, Sorbonne Universities, the University of Paris-Saclay, Paris Lumiéres, Paris-Seine, so on. In January 2018, two of the inheritors of the old University of Paris, Paris-Sorbonne University and Pierre and Marie Curie University, merged into a single university called Sorbonne University. In 2019, two other inheritors of the University of Paris, namely Paris Diderot University and Paris Descartes University, are expected to merge. In 1150, the future University of Paris was a student-teacher corporation operating as an annex of the Notre-Dame cathedral school; the earliest historical reference to it is found in Matthew of Paris' reference to the studies of his own teacher and his acceptance into "the fellowship of the elect Masters" there in about 1170, it is known that Pope Innocent III completed his studies there in 1182 at the age of 21. The corporation was formally recognised as an "Universitas" in an edict by King Philippe-Auguste in 1200: in it, among other accommodations granted to future students, he allowed the corporation to operate under ecclesiastic law which would be governed by the elders of the Notre-Dame Cathedral school, assured all those completing courses there that they would be granted a diploma.
The university had four faculties: Arts, Medicine and Theology. The Faculty of Arts was the lowest in rank, but the largest, as students had to graduate there in order to be admitted to one of the higher faculties; the students were divided into four nationes according to language or regional origin: France, Normandy and England. The last came to be known as the Alemannian nation. Recruitment to each nation was wider than the names might imply: the English-German nation included students from Scandinavia and Eastern Europe; the faculty and nation system of the University of Paris became the model for all medieval universities. Under the governance of the Church, students wore robes and shaved the tops of their heads in tonsure, to signify they were under the protection of the church. Students followed the rules and laws of the Church and were not subject to the king's laws or courts; this presented problems for the city of Paris, as students ran wild, its official had to appeal to Church courts for justice.
Students were very young, entering the school at 13 or 14 years of age and staying for six to 12 years. Three schools were famous in Paris: the palatine or palace school, the school of Notre-Dame, that of Sainte-Geneviève Abbey; the decline of royalty brought about the decline of the first. The other two did not have much visibility in the early centuries; the glory of the palatine school doubtless eclipsed theirs, until it gave way to them. These two centres were much frequented and many of their masters were esteemed for their learning; the first renowned professor at the school of Ste-Geneviève was Hubold, who lived in the tenth century. Not content with the courses at Liège, he continued his studies at Paris, entered or allied himself with the chapter of Ste-Geneviève, attracted many pupils via his teaching. Distinguished professors from the school of Notre-Dame in the eleventh century incl
Grigore Constantin Moisil was a Romanian mathematician, computer pioneer, member of the Romanian Academy. His research was in the fields of mathematical logic, algebraic logic, MV-algebra, differential equations, he is viewed as the father of computer science in Romania. Moisil was a member of the Academy of Sciences of Bologna and of the International Institute of Philosophy. In 1996, the IEEE Computer Society awarded him posthumously the Computer Pioneer Award. Grigore Moisil was born in 1906 in Tulcea into an intellectual family, his great-grandfather, Grigore Moisil, a clergyman, was one of the founders of the first Romanian high school in Năsăud. His father, Constantin Moisil, was a history professor and numismatist, his mother, was a teacher in Tulcea the director of "Maidanul Dulapului" school in Bucharest. Grigore Moisil attended primary school in Bucharest high school in Vaslui and Bucharest between 1916 and 1922. In 1924 he was admitted to the Civil Engineering School of the Polytechnic University of Bucharest, the Mathematics School of the University of Bucharest.
He showed a stronger interest in mathematics, so he quit the Polytechnic University in 1929, despite having passed all the third-year exams. In 1929 he defended his Ph. D. thesis, La mécanique analytique des systemes continus, before a commission led by Gheorghe Ţiţeica, with Dimitrie Pompeiu and Anton Davidoglu as members. The thesis was published the same year by the Gauthier-Villars publishing house in Paris, received favourable comments from Vito Volterra, Tullio Levi-Civita, Paul Lévy. In 1930 Moisil went to the University of Paris for further study in mathematics, which he finalized the next year with the paper On a class of systems of equations with partial derivatives from mathematical physics. In 1931 he returned to Romania, where he was appointed in a teaching position at the Mathematics School of the University of Iaşi. Shortly after, he left for a one-year Rockefeller Foundation scholarship to study in Rome. In 1932 he returned to Iaşi, where he remained for 10 years, developing a close relationship with professor Alexandru Myller.
He taught the first modern algebra course in Romania, named Logic and theory of proof, at the University of Iaşi. During that time, he started writing a series of papers based on the works of Jan Łukasiewicz in multi-valued logic, his research in mathematical logic laid the foundation for significant work done afterwards in Romania, as well as Argentina, Yugoslavia and Hungary. While in Iaşi, he completed research remarkable for the many new ideas and for his way of finding and using new connections between concepts from different areas of mathematics, he was promoted to Full Professor in November 1939. In 1941, a position of professor at the University of Bucharest opened up, Moisil applied for it. However, Gheorghe Vrânceanu, Dan Barbilian, Miron Nicolescu applied for the position, Vrânceanu got it. Moisil approached the Ministry of Education, arguing that it would be a great opportunity for mathematics in Romania if all four could be appointed; as a result of his appeal, all four mathematicians were hired.
Moisil moved to Bucharest, where he became a Professor in the School of Mathematics at the University of Bucharest, on 30 December 1941. From 1946 to 1948, Moisil took a leave of absence. While in Turkey, he gave several series of mathematics lectures at Istanbul University and Istanbul Technical University. In 1948, he resumed teaching at the University of Bucharest; that same year, he was elected to the Romanian Academy, a member of the Institute of Mathematics of the Romanian Academy. After 1965, one of his outstanding students – George Georgescu – worked with him on multi-valued logics, after the emergence of Romania from dictatorship in 1989, he became a Professor of Mathematics and Logic at the same university and department as Moisil in 1991, his student published extensive, original work on algebraic logic, MV-algebra, algebraic topology, categories of MV-algebras, category theory and Łukasiewicz–Moisil algebra. Moisil published papers on mechanics, mathematical analysis, geometry and mathematical logic.
He developed a multi-dimensional extension of Pompeiu's areolar derivative, studied monogenic functions of one hypercomplex variable with applications to mechanics. Moisil introduced some many-valued algebras, which he called Łukasiewicz algebras, used them in logic and the study of automata theory, he created new methods to analyze finite automata, had many contributions to the field of automata theory in algebra. Moisil had important contributions in the creation of the first Romanian computers, he played a fundamental role in the development of computer science in Romania, in raising the first generations of Romanian computer scientists. In 1996, he was awarded by exception posthumously the Computer Pioneer Award by the Institute of Electrical and Electronics Engineers Computer Society. Boolean logic De Morgan algebra Jan ŁukasiewiczŁukasiewicz logic Ternary logic Lattices Multi-valued logic:Łukasiewicz–Moisil algebras Quantum logic:Quantum computers Algebraic logic:MV-algebra Symbolic logic:Mathematical logic Algebra Category theory:Categorical logic, Adjoint functors Institute of Electrica
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics. By extension, use of complex analysis has applications in engineering fields such as nuclear, aerospace and electrical engineering; as a differentiable function of a complex variable is equal to the sum of its Taylor series, complex analysis is concerned with analytic functions of a complex variable. Complex analysis is one of the classical branches in mathematics, with roots in the 18th century and just prior. Important mathematicians associated with complex numbers include Euler, Riemann, Cauchy and many more in the 20th century. Complex analysis, in particular the theory of conformal mappings, has many physical applications and is used throughout analytic number theory. In modern times, it has become popular through a new boost from complex dynamics and the pictures of fractals produced by iterating holomorphic functions.
Another important application of complex analysis is in string theory which studies conformal invariants in quantum field theory. A complex function is a function from complex numbers to complex numbers. In other words, it is a function that has a subset of the complex numbers as a domain and the complex numbers as a codomain. Complex functions are supposed to have a domain that contains a nonempty open subset of the complex plane. For any complex function, the values z from the domain and their images f in the range may be separated into real and imaginary parts: z = x + i y and f = f = u + i v, where x, y, u, v are all real-valued. In other words, a complex function f: C → C may be decomposed into u: R 2 → R and v: R 2 → R, i.e. into two real-valued functions of two real variables. Any complex-valued function f on an arbitrary set X can be considered as an ordered pair of two real-valued functions: or, alternatively, as a vector-valued function from X into R 2; some properties of complex-valued functions are nothing more than the corresponding properties of vector valued functions of two real variables.
Other concepts of complex analysis, such as differentiability are direct generalizations of the similar concepts for real functions, but may have different properties. In particular, every differentiable complex function is analytic, two differentiable functions that are equal in a neighborhood of a point are equal on the intersection of their domain; the latter property is the basis of the principle of analytic continuation which allows extending every real analytic function in a unique way for getting a complex analytic function whose domain is the whole complex plane with a finite number of curve arcs removed. Many basic and special complex functions are defined in this way, including exponential functions, logarithmic functions, trigonometric functions. Complex functions that are differentiable at every point of an open subset Ω of the complex plane are said to be holomorphic on Ω. In the context of complex analysis, the derivative of f at z 0 is defined to be f ′ = lim z → z 0 f − f z − z 0, z ∈ C.
Superficially, this definition is formally analogous to that of the derivative of a real function. However, complex derivatives and differentiable functions behave in different ways compared to their real counterparts. In particular, for this limit to exist, the value of the difference quotient must approach the same complex number, regardless of the manner in which we
The Romanians are a Romance ethnic group and nation native to Romania, that share a common Romanian culture and speak the Romanian language, the most widespread spoken Eastern Romance language, descended from the Latin language. According to the 2011 Romanian census, just under 89% of Romania's citizens identified themselves as ethnic Romanians. In one interpretation of the census results in Moldova, the Moldovans are counted as Romanians, which would mean that the latter form part of the majority in that country as well. Romanians are an ethnic minority in several nearby countries situated in Central Eastern Europe in Hungary, Czech Republic, Ukraine and Bulgaria. Today, estimates of the number of Romanian people worldwide vary from 26 to 30 million according to various sources, evidently depending on the definition of the term'Romanian', Romanians native to Romania and Republic of Moldova and their afferent diasporas, native speakers of Romanian, as well as other Eastern Romance-speaking groups considered by most scholars and the Romanian Academy as a constituent part of the broader Romanian people Aromanians, Megleno-Romanians, Istro-Romanians, Vlachs in Serbia, in Croatia, in Bulgaria, or in Bosnia and Herzegovina.
Inhabited by the ancient Dacians, part of today's territory of Romania was conquered by the Roman Empire in 106, when Trajan's army defeated the army of Dacia's ruler Decebalus. The Roman administration withdrew two centuries under the pressure of the Goths and Carpi. Two theories account for the origin of the Romanian people. One, known as the Daco-Roman continuity theory, posits that they are descendants of Romans and Romanized indigenous peoples living in the Roman Province of Dacia, while the other posits that the Romanians are descendants of Romans and Romanized indigenous populations of the former Roman provinces of Illyria, Moesia and Macedon, the ancestors of Romanians migrated from these Roman provinces south of the Danube into the area which they inhabit today. According to the first theory, the Romanians are descended from indigenous populations that inhabited what is now Romania and its immediate environs: Thracians and Roman legionnaires and colonists. In the course of the two wars with the Roman legions, between AD 101–102 and AD 105–106 the emperor Trajan succeeded in defeating the Dacians and the greatest part of Dacia became a Roman province.
The colonisation with Roman or Romanized elements, the use of the Latin language and the assimilation of Roman civilisation as well as the intense development of urban centres led to the Romanization of part of the autochthonous population in Dacia. This process was concluded by the 10th century when the assimilation of the Slavs by the Daco-Romanians was completed. According to the south-of-the-Danube origin theory, the Romanians' ancestors, a combination of Romans and Romanized peoples of Illyria and Thrace, moved northward across the Danube river into modern-day Romania. Small population groups speaking several versions of Romanian still exist south of the Danube in Greece, Macedonia and Serbia, but it is not known whether they themselves migrated from more northern parts of the Balkans, including Dacia; the south-of-the Danube theory favours northern Albania and/or Moesia as the more specific places of Romanian ethnogenesis. Small genetic differences were found among Southeastern European populations and those of the Dniester–Carpathian region.
Despite this low level of differentiation between them, tree reconstruction and principal component analyses allowed a distinction between Balkan–Carpathian and Balkan Mediterranean population groups. The genetic affinities among Dniester–Carpathian and southeastern European populations do not reflect their linguistic relationships. According to the report, the results indicate that the ethnic and genetic differentiations occurred in these regions to a considerable extent independently of each other. During the Middle Ages Romanians were known as Vlachs, a blanket term of Germanic origin, from the word Walha, used by ancient Germanic peoples to refer to Romance-speaking and Celtic neighbours. Besides the separation of some groups during the Age of Migration, many Vlachs could be found all over the Balkans, in Transylvania, across Carpathian Mountains as far north as Poland and as far west as the regions of Moravia, some went as far east as Volhynia of western Ukraine, the present-day Croatia where the Morlachs disappeared, while the Catholic and Orthodox Vlachs took Croat and Serb national identity.
Because of the migrations that followed – such as those of Slavs, Bulgars and Tatars – the Romanians were organised in agricultural communes, developing large centralised states only in the 14th century, when the Danubian Principalities of Moldavia and Wallachia emerged to fight the Ottoman Empire. During the late Middle Ages, prominent medieval Romanian monarchs such as Bogdan of Moldavia, Stephen the Great, Mircea the Elder, Michael the Brave, or Vlad the Impaler took part in the history of Central Europe by waging tumultuous wars and leading noteworthy crusades against the continuously expanding Ottoman Empire, at ti
Peter Henrici (mathematician)
Peter Karl Henrici was a Swiss mathematician best known for his contributions to the field of numerical analysis. Henrici was studied law for two years at University of Basel. After World War II he transferred to ETH Zürich where he received a diploma in electrical engineering and a doctorate in mathematics with Eduard Stiefel as his advisor. In 1951 he moved to the United States and worked on a joint contract with American University and the National Bureau of Standards. From 1956 to 1962, he taught at University of California, Los Angeles where he became a professor. In 1962 he returned to ETH Zürich as a professor, a position he kept for the rest of his life, though he held a part-time appointment as William R. Kenan, Jr. Distinguished Professor of Mathematics at the University of North Carolina at Chapel Hill from 1985. An internationally recognized numerical analyst, who published 11 books and more than 80 research papers, Henrici was a gifted pianist and a regarded teacher, he was an editor of a number of scientific journals, including Numerische Mathematik and Zeitschrift für Angewandte Mathematik und Physik.
In 1962, he was a speaker at the International Congress of Mathematicians, in 1978 he gave the SIAM John von Neumann Lecture. Every four years since 1999, the Peter Henrici Prize is awarded by ETH Zürich and SIAM for "original contributions to applied analysis and numerical analysis and/or for exposition appropriate for applied mathematics and scientific computing". Henrici, Peter. Discrete variable methods in ordinary differential equations. Wiley. Henrici, Peter. Error propagation for difference methods. SIAM series in applied mathematics. Wiley. Henrici, Peter. Elements of numerical analysis. Wiley. Henrici, Peter. Applied and computational complex analysis, Volume 1: Power series—integration—conformal mapping—location of zeros. Wiley. ISBN 0-471-37244-7. Henrici, Peter. Applied and computational complex analysis, Volume 2: Special functions—integral transforms—asymptotics—continued fractions. Wiley. ISBN 0-471-01525-3. Henrici, Peter. Computational Analysis with the HP-25 Pocket Calculator. Wiley. ISBN 0-471-02938-6.
Henrici, Peter. Applied and computational complex analysis, Volume 3: Discrete Fourier analysis—Cauchy integrals—construction of conformal maps—univalent functions. Wiley. ISBN 0-471-08703-3. Peter Henrici at the Mathematics Genealogy Project O'Connor, John J..
Gaetano Fichera was an Italian mathematician, working in mathematical analysis, linear elasticity, partial differential equations and several complex variables. He was born in Acireale, died in Rome, he was born in Acireale, a town near Catania in Sicily, the elder of the four sons of Giuseppe Fichera and Marianna Abate. His father Giuseppe was a professor of mathematics and influenced the young Gaetano starting his lifelong passion. In his young years he was a talented football player. On 1 February 1943 he was in the Italian Army and during the events of September 1943 he was taken prisoner by the Nazist troops, kept imprisoned in Teramo and sent to Verona: he succeeded in escaping from there and reached the Italian region of Emilia-Romagna, spending with partisans the last year of war. After the war he was first in Rome and in Trieste, where he met Matelda Colautti, who become his wife in 1952. After graduating from the liceo classico in only two years, he entered the University of Catania at the age of 16, being there from 1937 to 1939 and studying under Pia Nalli.
He went to the university of Rome, where in 1941 he earned his laurea with magna cum laude under the direction of Mauro Picone, when he was only 19. He was appointed by Picone as an assistant professor to his chair and as a researcher at the Istituto Nazionale per le Applicazioni del Calcolo, becoming his pupil. After the war he went back to Rome working with Mauro Picone: in 1948 he became "Libero Docente" of mathematical analysis and in 1949 he was appointed as full professor at the University of Trieste; as he remembers in, in both cases one of the members of the judging commission was Renato Caccioppoli, which become a close friend of him. From 1956 onward he was full professor at the University of Rome in the chair of mathematical analysis and at the Istituto Nazionale di Alta Matematica in the chair of higher analysis, succeeding to Luigi Fantappiè, he retired from university teaching in 1992, but was professionally active until his death in 1996: as a member of the Accademia Nazionale dei Lincei and first director of the journal Rendiconti Lincei – Matematica e Applicazioni, he succeeded in reviving its reputation.
He was member of several academies, notably of the Accademia Nazionale dei Lincei, the Accademia Nazionale delle Scienze detta dei XL and of the Russian Academy of Science. His lifelong friendship with his teacher Mauro Picone is remembered by him in several occasions; as recalled by Colautti Fichera, his father Giuseppe was an assistant professor to the chair of Picone while he was teaching at the University of Catania: they become friends and their friendship lasted when Giuseppe was forced to leave the academic career for economic reasons, being the father of two sons, until Giuseppe's death. The young, in effect child, was kept by Picone in his arms. From 1939 to 1941 the young Fichera developed his research directly under the supervision of Picone: as he remembers, it was a time of intense work, but when he was back from the front in April 1945 he met Picone while he was in Roma in his way back to Sicily, his advisor was so happy to see him as a father can be seeing its living child. Another mathematician Fichera was influenced by and acknowledged as one of his teachers and inspirators was Pia Nalli: she was an outstanding analyst, teaching for several years at the University of Catania, being his teacher of mathematical analysis from 1937 to 1939.
Antonio Signorini and Francesco Severi were two of Fichera's teachers of the Roman period: the first one introduced him and inspired his research in the field of linear elasticity while the second inspired his research in the field he taught him i.e. the theory of analytic functions of several complex variables. Signorini had a strong long-time friendship with Picone: on a wall of the apartment building where they lived, in Via delle Tre Madonne, 18 in Rome, a memorial tablet which commemorates the two friends is placed, as Fichera recalls; the two great mathematicians extended their friendship to the young Fichera, as a consequence this led to the solution of the Signorini problem and the foundation of the theory of variational inequalities. Fichera's relations with Severi were not as friendly as with Signorini and Picone: Severi, one of the most influential Italian mathematicians of the first half of the 20th century, esteemed the young mathematician. During a course on the theory of analytic functions of several complex variables taught at the Istituto Nazionale di Alta Matematica from the fall of 1956 and the beginning of the 1957, whose lectures were collected in the book, Severi posed the problem of generalizing his theorem on the Dirichlet problem for holomorphic function of several variables, as Fichera recalls: the result was the paper, a masterpiece, although not acknowledged for various reasons described by Range.
Other scientists he had as teachers during the period 1939–1941 were Enrico Bompiani, Leonida Tonelli and Giuseppe Armellini: he remembered them with great respect and admiration if he did not share all their opinions and ideas, as Colautti Fichera recalls. A complete list of Fichera's friends includes some of the best scientists and mathematicians of the 20th century: Olga Oleinik, Olga Ladyzhenskaya, Israel Gel'fand, Ivan Petrovsky, Vladimir Maz'ya, Nikoloz Muskhelishvili, Ilia Vekua, Richard Courant, Fritz John, Kurt Friedrichs, Peter Lax, Louis Nirenberg, Ronald Rivlin, Hans Lewy, Clifford Truesdell, Edmund Hlawka, Ian Sneddon, Jean Leray, Alexander Weinstein, Alexander Ostrowski, Renato Caccioppoli, Solomon Mikhlin, P
France the French Republic, is a country whose territory consists of metropolitan France in Western Europe and several overseas regions and territories. The metropolitan area of France extends from the Mediterranean Sea to the English Channel and the North Sea, from the Rhine to the Atlantic Ocean, it is bordered by Belgium and Germany to the northeast and Italy to the east, Andorra and Spain to the south. The overseas territories include French Guiana in South America and several islands in the Atlantic and Indian oceans; the country's 18 integral regions span a combined area of 643,801 square kilometres and a total population of 67.3 million. France, a sovereign state, is a unitary semi-presidential republic with its capital in Paris, the country's largest city and main cultural and commercial centre. Other major urban areas include Lyon, Toulouse, Bordeaux and Nice. During the Iron Age, what is now metropolitan France was inhabited by a Celtic people. Rome annexed the area in 51 BC, holding it until the arrival of Germanic Franks in 476, who formed the Kingdom of Francia.
The Treaty of Verdun of 843 partitioned Francia into Middle Francia and West Francia. West Francia which became the Kingdom of France in 987 emerged as a major European power in the Late Middle Ages following its victory in the Hundred Years' War. During the Renaissance, French culture flourished and a global colonial empire was established, which by the 20th century would become the second largest in the world; the 16th century was dominated by religious civil wars between Protestants. France became Europe's dominant cultural and military power in the 17th century under Louis XIV. In the late 18th century, the French Revolution overthrew the absolute monarchy, established one of modern history's earliest republics, saw the drafting of the Declaration of the Rights of Man and of the Citizen, which expresses the nation's ideals to this day. In the 19th century, Napoleon established the First French Empire, his subsequent Napoleonic Wars shaped the course of continental Europe. Following the collapse of the Empire, France endured a tumultuous succession of governments culminating with the establishment of the French Third Republic in 1870.
France was a major participant in World War I, from which it emerged victorious, was one of the Allies in World War II, but came under occupation by the Axis powers in 1940. Following liberation in 1944, a Fourth Republic was established and dissolved in the course of the Algerian War; the Fifth Republic, led by Charles de Gaulle, remains today. Algeria and nearly all the other colonies became independent in the 1960s and retained close economic and military connections with France. France has long been a global centre of art and philosophy, it hosts the world's fourth-largest number of UNESCO World Heritage Sites and is the leading tourist destination, receiving around 83 million foreign visitors annually. France is a developed country with the world's sixth-largest economy by nominal GDP, tenth-largest by purchasing power parity. In terms of aggregate household wealth, it ranks fourth in the world. France performs well in international rankings of education, health care, life expectancy, human development.
France is considered a great power in global affairs, 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 leading member state of the European Union and the Eurozone, a member of the Group of 7, North Atlantic Treaty Organization, Organisation for Economic Co-operation and Development, the World Trade Organization, La Francophonie. Applied to the whole Frankish Empire, the name "France" comes from the Latin "Francia", or "country of the Franks". Modern France is still named today "Francia" in Italian and Spanish, "Frankreich" in German and "Frankrijk" in Dutch, all of which have more or less the same historical meaning. There are various theories as to the origin of the name Frank. Following the precedents of Edward Gibbon and Jacob Grimm, the name of the Franks has been linked with the word frank in English, it has been suggested that the meaning of "free" was adopted because, after the conquest of Gaul, only Franks were free of taxation.
Another theory is that it is derived from the Proto-Germanic word frankon, which translates as javelin or lance as the throwing axe of the Franks was known as a francisca. However, it has been determined that these weapons were named because of their use by the Franks, not the other way around; the oldest traces of human life in what is now France date from 1.8 million years ago. Over the ensuing millennia, Humans were confronted by a harsh and variable climate, marked by several glacial eras. Early hominids led a nomadic hunter-gatherer life. France has a large number of decorated caves from the upper Palaeolithic era, including one of the most famous and best preserved, Lascaux. At the end of the last glacial period, the climate became milder. After strong demographic and agricultural development between the 4th and 3rd millennia, metallurgy appeared at the end of the 3rd millennium working gold and bronze, iron. France has numerous megalithic sites from the Neolithic period, including the exceptiona