Laurent Schwartz
Laurent-Moïse Schwartz was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function, he was awarded the Fields Medal in 1950 for his work on the theory of distributions. For several years he taught at the École polytechnique. Laurent Schwartz came from a Jewish family of Alsatian origin, with a strong scientific background: his father was a well-known surgeon, his uncle Robert Debré was a famous pediatrician, his great-uncle-in-law, Jacques Hadamard, was a famous mathematician. During his training at Lycée Louis-le-Grand to enter the École Normale Supérieure, he fell in love with Marie-Hélène Lévy, daughter of the probabilist Paul Lévy, teaching at the École polytechnique, they would have two children, Marc-André and Claudine. Marie-Hélène was gifted in mathematics as well, as she contributed to the geometry of singular analytic spaces and taught at the University of Lille. Angelo Guerraggio describes "Mathematics and butterflies" as his "three great loves".
According to his teachers, Schwartz was an exceptional student. He was gifted in Latin and mathematics. One of his teachers told his parents: "Beware, some will say your son has a gift for languages, but he is only interested in the scientific and mathematical aspect of languages: he should become a mathematician." In 1934, he was admitted at the École Normale Supérieure, in 1937 he obtained the agrégation. As a man of Trotskyist affinities and Jewish descent, life was difficult for Schwartz during World War II, he had to change his identity to avoid being deported after Nazi Germany overran France. He worked for the University of Strasbourg under the name of Laurent-Marie Sélimartin, while Marie-Hélène used the name Lengé instead of Lévy. Unlike other mathematicians at Clermont-Ferrand such as Feldbau, the couple managed to escape the Nazis. Schwartz taught at École Polytechnique, from 1958 to 1980. At the end of the war, he spent one year in Grenoble in 1945 joined the University of Nancy on the advice of Jean Delsarte and Jean Dieudonné, where he spent seven years.
He was both an influential researcher and teacher, with students such as Bernard Malgrange, Jacques-Louis Lions, François Bruhat and Alexander Grothendieck. He joined the science faculty of the University of Paris in 1952. In 1958 he became a teacher at the École polytechnique after having at first refused this position. From 1961 to 1963 the École polytechnique suspended his right to teach, because of his having signed the Manifesto of the 121 about the Algerian war, a gesture not appreciated by Polytechnique's military administration. However, Schwartz had a lasting influence on mathematics at the École polytechnique, having reorganized both teaching and research there. In 1973 he was elected corresponding member of the French Academy of Sciences, was promoted to full membership in 1975. In 1950 at the ICM, Schwartz was a plenary speaker and was awarded the Fields medal for his work on distributions, he was the first French mathematician to receive the Fields medal. Because of his sympathy for Trotskyism, Schwartz encountered serious problems trying to enter the United States to receive the medal.
The theory of distributions clarifies the mysteries of the Dirac delta function and Heaviside step function. It helps to extend the theory of Fourier transform and is now of capital importance to the theory of partial differential equations. Throughout his life, Laurent Schwartz worked to promote science and bring it closer to the general audience. Laurent says: What are mathematics helpful for? Mathematics are helpful for physics. Physics helps us make fridges. Fridges are made to contain spiny lobsters, spiny lobsters help mathematicians who eat them and have hence better abilities to do mathematics, which are helpful for physics, which helps us make fridges which... His mother, passionate about natural science passed on her taste for entomology to Laurent, his personal collection of 20, 000 Lepidoptera specimens, collected during his various travels was bequeathed to the Muséum national d'histoire naturelle), the Science Museum of Lyon, the Museum of Toulouse and the Museo de Historia Natural Alcide d’Orbigny in Cochabamba.
Several species discovered by Laurent Schwartz bear his name. Apart from his scientific work, Schwartz was a well-known outspoken intellectual; as a young socialist influenced by Leon Trotsky, Schwartz opposed the totalitarianism of the Soviet Union under Joseph Stalin. Schwartz rejected Trotskyism for democratic socialism. On his religious views, Schwartz called himself an atheist. Étude des sommes d'exponentielles réelles. Hermann, 1943, new edn. 1959 Théorie des distributions. Hermann, 2 vols. 1950/1951, new edn. 1966 Lectures on complex analytic manifolds. Springer, 1986 Séminaire Schwartz in Paris 1953 bis 1961. Online edition: Mathematics for the physical sciences. Hermann, 1966 Analyse mathématique. 2 vols. Hermann, 1967 Application of distributions to the theory of elementary particles in quantum mechanics. Gordon and Breach, 1968, 1988 Radon measures on arbitrary topological spaces and cylindrical measures. Oxford University Press, 1973 Tenseurs. Hermann, 1975 Analyse hilbertienne. Hermann, 1979 Semi-martingales sur des variétés et martingales conformes sur des variétés analytiques complexes.
Springer, 1980 Geometry and probability in Banach Spaces. Springer, 1981 Cours d' Analyse. Hermann, 1981 Pour sauver l’université. Editions
French Algeria
French Algeria known as Colonial Algeria, began in 1830 with the invasion of Algiers and lasted until 1962, under a variety of governmental systems. From 1848 until independence, the whole Mediterranean region of Algeria was administered as an integral part of France. One of France's longest-held overseas territories, Algeria became a destination for hundreds of thousands of European immigrants known as colons and as pieds-noirs. However, the indigenous Muslim population remained a majority of the territory's population throughout its history. Dissatisfaction among the Muslim population with its lack of political and economic status fueled calls for greater political autonomy, independence from France. Tensions between the two population groups came to a head in 1954, when the first violent events began of what was called the Algerian War; the war concluded in 1962, when Algeria gained independence following the March 1962 Evian agreements and the July 1962 self-determination referendum. During its last years of existence, French Algeria was the founding member state of the United Nations, NATO and the European Economic Community.
Since the 1516 capture of Algiers by the Ottoman admirals, the brothers Ours and Hayreddin Barbarossa, Algeria had been a base for conflict and piracy in the Mediterranean. In 1681, Louis XIV asked Admiral Abraham Duquesne to fight the Berber pirates and ordered a large-scale attack on Algiers between 1682 and 1683 on the pretext of assisting Christian captives. Again, Jean II d'Estrées bombarded Tripoli and Algiers from 1685 to 1688. An ambassador from Algiers visited the Court in Versailles, a Treaty was signed in 1690 that provided peace throughout the 18th century. During the Directory regime of the First French Republic, the Bacri and the Busnach, Jewish negotiators of Algiers, provided important quantities of grain for Napoleon's soldiers who participated in the Italian campaign of 1796. However, Bonaparte refused claiming it was excessive. In 1820, Louis XVIII paid back half of the Directory's debts; the dey, who had loaned to the Bacri 250,000 francs, requested from France the rest of the money.
The Dey of Algiers himself was weak politically and militarily. Algeria was part of the Barbary States, along with today's Tunisia – which depended on the Ottoman Empire led by Mahmud II — but enjoyed relative independence; the Barbary Coast was the stronghold of the Berber pirates, which carried out raids against European and American ships. Conflicts between the Barbary States and the newly independent United States of America culminated in the First and Second Barbary Wars. An Anglo-Dutch force, led by Admiral Lord Exmouth, carried out a punitive expedition, the August 1816 bombardment of Algiers; the Dey was forced to sign the Barbary treaties, while the technological advance of U. S. British, French forces overwhelmed the Algerians' expertise at naval warfare; the name of "Algeria" itself came from the French. Following the conquest under the July monarchy, the Algerian territories, disputed with the Ottoman Empire, were first named "French possessions in North Africa" before being called "Algeria" by Marshal General Jean-de-Dieu Soult, Duke of Dalmatia, in 1839.
The conquest of Algeria was initiated in the last days of the Bourbon Restoration by Charles X, as an attempt to increase his popularity amongst the French people in Paris, where many veterans of the Napoleonic Wars lived. His intention was to bolster patriotic sentiment, distract attention from ineptly handled domestic policies by "skirmishing against the dey". In the 1790s, France had contracted to purchase wheat for the French army from two merchants in Algiers, Messrs. Bacri and Boushnak, was in arrears paying them; these merchants and Boushnak who had debts to the dey, claimed inability to pay those debts until France paid its debts to them. The dey had unsuccessfully negotiated with Pierre Deval, the French consul, to rectify this situation, he suspected Deval of collaborating with the merchants against him when the French government made no provisions for repaying the merchants in 1820. Deval's nephew Alexandre, the consul in Bône, further angered the dey by fortifying French storehouses in Bône and La Calle against the terms of prior agreements.
After a contentious meeting in which Deval refused to provide satisfactory answers on 29 April 1827, the dey struck Deval with his fly whisk. Charles X used this slight against his diplomatic representative to first demand an apology from the dey, to initiate a blockade against the port of Algiers. France demanded; when the dey responded with cannon fire directed toward one of the blockading ships, the French determined that more forceful action was required. Pierre Deval and other French residents of Algiers left for France, while the Minister of War, Clermont-Tonnerre, proposed a military expedition. However, the Count of Villèle, an ultra-royalist, President of the Council and the monarch's heir, opposed any military action; the Restoration decided to blockade Algiers for three years, but the overpowering presence of the French naval force prevented an incursion beyond the coastal perimeter. Meanwhile, the Berber pirates were able to exploit the geography of the coast with ease. Before the failure of the blockade, the Restoration decided on 31 January 1830 to engage a military expedition against Algiers.
Admiral Duperré commandeered an armada of 600 ships that originated from Toulon, leading it to Algiers. Using Napoleon's 1808 contingency plan f
William Daniel Phillips
William Daniel Phillips is an American physicist. He shared the Nobel Prize in Physics, with Steven Chu and Claude Cohen-Tannoudji. Phillips was born to William Cornelius Phillips of Juniata and Mary Catherine Savino of Ripacandida, Italy, he is of Welsh descent on his father's side. His parents moved to Camp Hill in 1959, where he attended high school and graduated valedictorian of his class, he graduated from Juniata College in 1970 summa cum laude. After that he received his physics doctorate from the Massachusetts Institute of Technology. In 1978 he joined NIST. In 1996, he received the Albert A. Michelson Medal from The Franklin Institute. Phillips' doctoral thesis concerned the magnetic moment of the proton in H2O, he did some work with Bose–Einstein condensates. In 1997 he won the Nobel Prize in Physics together with Claude Cohen-Tannoudji and Steven Chu for his contributions to laser cooling, a technique to slow the movement of gaseous atoms in order to better study them, at the National Institute of Standards and Technology, for his invention of the Zeeman slower.
Phillips is a professor of physics, part of the University of Maryland College of Computer and Natural Sciences at University of Maryland, College Park. He was one of the 35 Nobel laureates who signed a letter urging President Obama to provide a stable $15 billion per year support for clean energy research and demonstration, he is one of three well-known scientists and Methodist laity who have involved themselves in the religion and science dialogue. The other two scientists and fellow Methodists are chemist Charles Coulson and 1981 Nobel laureate Arthur Leonard Schawlow. In Oct 2010 Phillips participated in the USA Science and Engineering Festival's Lunch with a laureate program where middle and high school students got to engage in an informal conversation with a Nobel Prize–winning scientist over a brown-bag lunch. Phillips is a member of the USA Science and Engineering Festival's Advisory Board. Phillips married Jane Van Wynen shortly before he went to MIT. Neither had been regular churchgoers early in their marriage.
However, in 1979, they joined the Fairhaven United Methodist Church in Gaithersburg, Maryland because they appreciated its diversity. He is a founding member of the International Society for Religion, he and his wife have two daughters. During a seminar at the UMCP Department of Chemistry and Biochemistry titled Coherent Atoms in Optical Lattices Phillips stated, "Rubidium is God's gift to Bose–Einstein condensates." Nobel autobiography Curriculum Vitae from NIST. Atoms floating in optical molasses. Press Release: The 1997 Nobel Prize in Physics-for development of methods to cool and trap atoms with laser light. "Nobelist William Phillips Addresses ASA'99"
Stable distribution
In probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable; the stable distribution family is sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the four parameters defining the family, most attention has been focused on the stability parameter, α. Stable distributions have 0 < α ≤ 2, with the upper bound corresponding to the normal distribution, α = 1 to the Cauchy distribution. The distributions have undefined variance for α < 2, undefined mean for α ≤ 1. The importance of stable probability distributions is that they are "attractors" for properly normed sums of independent and identically distributed random variables; the normal distribution defines a family of stable distributions. By the classical central limit theorem the properly normed sum of a set of random variables, each with finite variance, will tend toward a normal distribution as the number of variables increases.
Without the finite variance assumption, the limit may be a stable distribution, not normal. Mandelbrot referred to such distributions after Vilfredo Pareto. In particular, he referred to those maximally skewed in the positive direction with 1 < α < 2 as "Pareto–Lévy distributions", which he regarded as better descriptions of stock and commodity prices than normal distributions. A non-degenerate distribution is a stable distribution if it satisfies the following property: Let X1 and X2 be independent copies of a random variable X. X is said to be stable if for any constants a > 0 and b > 0 the random variable aX1 + bX2 has the same distribution as cX + d for some constants c > 0 and d. The distribution is said to be stable if this holds with d = 0. Since the normal distribution, the Cauchy distribution, the Lévy distribution all have the above property, it follows that they are special cases of stable distributions; such distributions form a four-parameter family of continuous probability distributions parametrized by location and scale parameters μ and c and two shape parameters β and α corresponding to measures of asymmetry and concentration, respectively.
Although the probability density function for a general stable distribution cannot be written analytically, the general characteristic function can be. Any probability distribution is given by the Fourier transform of its probability density function, or its characteristic function φ by: f = 1 2 π ∫ − ∞ ∞ φ e − i x t d t A random variable X is called stable if its characteristic function can be written as φ = exp where sgn is just the sign of t and Φ = { tan α ≠ 1 − 2 π log | t | α = 1 μ ∈ R is a shift parameter, β ∈, called the skewness parameter, is a measure of asymmetry. Notice that in this context the usual skewness is not well defined, as for α < 2 the distribution does not admit 2nd or higher moments, the usual skewness definition is the 3rd central moment. The reason this gives a stable distribution is that the characteristic function for the sum of two random variables equals the product of the two corresponding characteristic functions. Adding two random variables from a stable distribution gives something with the same values of α and β, but different values of μ and c.
Not every function is the characteristic function of a legitimate probability distribution, but the characteristic functions given above will be legitimate so long as the parameters are in their ranges. The value of the characteristic function at some value t is the complex conjugate of its value at −t as it should be so that the probability distribution function will be real. In the simplest case β = 0, the characteristic function is just a stretched exponential function; when α < 1 and β = 1, the distribution is supported by [
Serge Haroche
Serge Haroche is a French physicist, awarded the 2012 Nobel Prize for Physics jointly with David J. Wineland for "ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems", a study of the particle of light, the photon; this and his other works developed laser spectroscopy. Since 2001, Haroche holds the Chair of Quantum Physics. In 1971 he defended his doctoral thesis in physics at the University of Paris VI, his research has been conducted under the direction of Claude Cohen-Tannoudji. Serge Haroche was born in Casablanca, Morocco, to Albert Haroche, from a Moroccan Jewish family, Valentine Haroche, née Roubleva a teacher, born in Odessa to a Jewish family of physicians who relocated to Morocco in the early 1920s, his father, a lawyer trained in Rabat, was one of seven children born to a family of teachers who worked at the École de l’Alliance israélite. Both paternal grandparents of Serge Haroche had been AIU students in their respective hometowns of Marrakesh and Tétouan.
Haroche settled in France in 1956, at the end of the French protectorate treaty. He lives in Paris, he is the uncle of French singer -- actor Raphaël Haroche. Haroche worked in the Centre national de la recherche scientifique as a research scientist from 1967 to 1975, spent a year as a visiting post-doc in Stanford University, in Arthur Leonard Schawlow's team. In 1975 he moved to a professor position at Paris VI University. At the same time he taught in other institutions, in particular at the École polytechnique, MIT, Harvard University, Yale University and Conservatoire national des arts et métiers, he was head of the Physics department at the École normale supérieure from 1994 to 2000. Since 2001, Haroche has been a Professor at the Collège de France and holds the Chair of Quantum Physics, he is a member of the Société Française de Physique, the European Physical society and a fellow and member of the American Physical Society. In September 2012, Serge Haroche was elected by his peers to the position of administrator of the Collège de France.
On 9 October 2012 Haroche was awarded the Nobel Prize in Physics, together with the American physicist David Wineland, for their work regarding measurement and manipulation of individual quantum systems. Haroche works in atomic physics and quantum optics, he is principally known for proving quantum decoherence by experimental observation, while working with colleagues at the École normale supérieure in Paris in 1996. After a PhD dissertation on dressed atoms under the supervision of Claude Cohen-Tannoudji from 1967 to 1971, he developed new methods for laser spectroscopy, based on the study of quantum beats and superradiance, he moved on to Rydberg atoms, giant atomic states sensitive to microwaves, which makes them well adapted for studying the interactions between light and matter. He showed that such atoms, coupled to a superconducting cavity containing a few photons, are well-suited to the testing of quantum decoherence and to the realization of quantum logic operations necessary for the treatment of quantum information.
Commander of the French Legion of Honour 1988 Einstein Prize for Laser Science. 1992 The Humboldt Prize 1993 Albert A. Michelson Medal by the Franklin Institute 2007 Charles Hard Townes Award by the OSA 2009 CNRS Gold medal 2012 Nobel Prize in Physics 2017 IEEE Honorary Membership Serge Haroche, Jean-Michel Raimond, Exploring the quantum. Atoms and photons, Oxford University Press, 2006
Algiers
Algiers is the capital and largest city of Algeria. In 2011, the city's population was estimated to be around 3,500,000. An estimate puts the population of the larger metropolitan city to be around 5,000,000. Algiers is located in the north-central portion of Algeria. Algiers is situated on the west side of a bay of the Mediterranean Sea; the modern part of the city is built on the level ground by the seashore. The casbah and the two quays form a triangle; the city's name is derived via French and Catalan Alger from the Arabic name Al-Jazā’ir, "The Islands". This name refers to the four former islands which lay off the city's coast before becoming part of the mainland in 1525. Al-Jazā’ir is itself a truncated form of the city's older name Jaza'ir Bani Mazghana, "The Islands of the Sons of Mazghana", used by early medieval geographers such as al-Idrisi and Yaqut al-Hamawi. In antiquity, the Greeks knew the town as Ikosion, Latinized as Icosium under Roman rule; the Greeks explained the name as coming from their word for "twenty" because it had been founded by 20 companions of Hercules when he visited the Atlas Mountains during his labors.
In fact, the name transcribed the Punic name ʿWYKSM, "Seagull Island", again named after the site's former islands. Algiers is known as El-Behdja or "Algiers the White" for its whitewashed buildings, seen rising from the sea. A small Phoenician colony on Algiers's former islands was established and taken over by the Carthaginians sometime before the 3rd century BC. After the Punic Wars, the Romans took over administration of the town, which they called Icosium, its ruins now form part of the modern city's marine quarter, with the Rue de la Marine following a former Roman road. Roman cemeteries existed near Bab Azoun; the city was given Latin rights by the emperor Vespasian. The bishops of Icosium are mentioned as late as the 5th century, but the ancient town fell into obscurity during the Muslim conquest of North Africa; the present city was founded in 944 by Bologhine ibn Ziri, the founder of the Berber Zirid–Sanhaja dynasty. He had earlier built a Sanhaja center at Ashir, just south of Algiers.
Although his Zirid dynasty was overthrown by Roger II of Sicily in 1148, the Zirids had lost control of Algiers to their cousins the Hammadids in 1014. The city was wrested from the Hammadids by the Almohads in 1159, in the 13th century came under the dominion of the Ziyanid sultans of Tlemcen. Nominally part of the sultanate of Tlemcen, Algiers had a large measure of independence under amirs of its own due to Oran being the chief seaport of the Ziyanids; the Peñón of Algiers, an islet in front of Algiers harbour had been occupied by the Spaniards as early as 1302. Thereafter, a considerable amount of trade began to flow between Spain. However, Algiers continued to be of comparatively little importance until after the expulsion of the Moors from Spain, many of whom sought asylum in the city. In 1510, following their occupation of Oran and other towns on the coast of Africa, the Spaniards fortified the islet of Peñon and imposed a levy intended to suppress corsair activity. In 1516, the amir of Algiers, Selim b.
Teumi, invited the corsair brothers Aruj and Hayreddin Barbarossa to expel the Spaniards. Aruj came to Algiers, ordered the assassination of Selim, seized the town and ousted the Spanish in the Capture of Algiers. Hayreddin, succeeding Aruj after the latter was killed in battle against the Spaniards in the Fall of Tlemcen, was the founder of the pashaluk, which subsequently became the beylik, of Algeria. Barbarossa lost Algiers in 1524 but regained it with the Capture of Algiers, formally invited the Sultan Suleiman the Magnificent to accept sovereignty over the territory and to annex Algiers to the Ottoman Empire. Algiers from this time became the chief seat of the Barbary pirates. In October 1541 in the Algiers expedition, the King of Spain and Holy Roman Emperor Charles V sought to capture the city, but a storm destroyed a great number of his ships, his army of some 30,000, chiefly made up of Spaniards, was defeated by the Algerians under their Pasha, Hassan. Formally part of the Ottoman Empire but free from Ottoman control, starting in the 16th century Algiers turned to piracy and ransoming.
Due to its location on the periphery of both the Ottoman and European economic spheres, depending for its existence on a Mediterranean, controlled by European shipping, backed by European navies, piracy became the primary economic activity. Repeated attempts were made by various nations to subdue the pirates that disturbed shipping in the western Mediterranean and engaged in slave raids as far north as Iceland; the United States fought two wars over Algiers' attacks on shipping. Among the notable people held for ransom was the future Spanish novelist Miguel de Cervantes, captive in Algiers five years, who wrote two plays set in Algiers of the period; the primary source for knowledge of Algiers of this period, since there are no contemporary local sources, is the Topografía e historia general de Argel, published by Diego de Haedo, but whose authorship is disputed. This work describes in detail the city, the behavior of its inhabitants, its military defenses, with the unsuccessful hope of facilitating an attack by Spain so as to end the piracy.
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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
