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125-480: A profound mathematician, Cauchy had a great influence over his contemporaries and successors; Hans Freudenthal stated: Cauchy was a prolific worker; he wrote approximately eight hundred research articles and five complete textbooks on a variety of topics in the fields of mathematics and mathematical physics . Cauchy was the son of Louis François Cauchy (1760–1848) and Marie-Madeleine Desestre. Cauchy had two brothers: Alexandre Laurent Cauchy (1792–1857), who became

250-481: A topological space . Ends are intended to capture the intuitive idea of a direction in which the space extends to infinity, but have a precise mathematical formulation in terms of covers of the space by nested sequences of compact sets . Ends remain of great importance in topological group theory, Freudenthal's motivating application, and also in other areas of mathematics such as the study of minimal surfaces . In 1936, while working with Brouwer, Freudenthal proved

375-403: A Bourbon Restoration. The opinions expressed in the declaration were largely those of Antoine de Bésiade, Count of Avaray , Louis's closest advisor in exile. Louis XVIII was forced once again to leave Jelgava when Tsar Alexander informed him that his safety could not be guaranteed in continental Europe. In July 1807, Louis boarded a Swedish frigate bound for Stockholm , bringing with him only

500-517: A Knight of the Order of the Holy Spirit . The name of Louis was bestowed because it was typical of a prince of France; Stanislas was chosen to honour his great-grandfather King Stanislaus I of Poland who was still alive at the time; and Xavier was chosen for Saint Francis Xavier , whom his mother's family held as one of their patron saints. At the time of his birth, Louis Stanislas was fourth in line to

625-413: A complex variable in another textbook. In spite of these, Cauchy's own research papers often used intuitive, not rigorous, methods; thus one of his theorems was exposed to a "counter-example" by Abel , later fixed by the introduction of the notion of uniform continuity . In a paper published in 1855, two years before Cauchy's death, he discussed some theorems, one of which is similar to the " Principle of

750-547: A contemporary living there at the time, the Prussian local authorities, wishing to honour the arrivals, had music played, but trying to give this a national and patriotic character, unwittingly chose La Marseillaise , the hymn of the French Republic with unflattering allusions to both Louis XVI and Louis XVIII. They later apologised for their mistake. It was very soon after their arrival that Louis and Marie-Thérèse learned of

875-487: A correspondence with Napoleon Bonaparte (by then First Consul of France ), urging him to restore the Bourbons to their throne, but the future emperor was impervious to this idea and continued to consolidate his own position as ruler of France. Louis XVIII encouraged his niece to write her memoirs, as he wished them to be used as Bourbon propaganda. In 1796 and 1803, Louis also used the diaries of Louis XVI's final attendants in

1000-576: A dozen papers on this topic to the academy. He described and illustrated the signed-digit representation of numbers, an innovation presented in England in 1727 by John Colson . The confounded membership of the Bureau lasted until the end of 1843, when Cauchy was replaced by Poinsot. Throughout the nineteenth century the French educational system struggled over the separation of church and state. After losing control of

1125-403: A few of his best students could reach, and cramming his allotted time with too much material. Henri d'Artois had neither taste nor talent for either mathematics or science. Although Cauchy took his mission very seriously, he did this with great clumsiness, and with surprising lack of authority over Henri d'Artois. During his civil engineering days, Cauchy once had been briefly in charge of repairing

1250-516: A few of the Parisian sewers, and he made the mistake of mentioning this to his pupil; with great malice, Henri d'Artois went about saying Cauchy started his career in the sewers of Paris. Cauchy's role as tutor lasted until Henri d'Artois became eighteen years old, in September 1838. Cauchy did hardly any research during those five years, while Henri d'Artois acquired a lifelong dislike of mathematics. Cauchy

1375-527: A friend of the Cauchy family. On Lagrange's advice, Augustin-Louis was enrolled in the École Centrale du Panthéon , the best secondary school of Paris at that time, in the fall of 1802. Most of the curriculum consisted of classical languages; the ambitious Cauchy, being a brilliant student, won many prizes in Latin and the humanities. In spite of these successes, Cauchy chose an engineering career, and prepared himself for

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1500-400: A generous pension, though later discontinued payment. Marie-Thérèse finally joined Louis XVIII at Jelgava in 1799. In the winter of 1798–1799, Louis XVIII wrote a biography of Marie Antoinette titled Réflexions historiques sur Marie Antoinette . Moreover, being surrounded at Jelgava with many old courtiers, he attempted to recreate the court life of Versailles, re-establishing various of

1625-426: A harmonious relationship and often quarrelled, as did their wives. Louis Stanislas did impregnate his wife in 1774, having conquered his aversion. However, the pregnancy ended in a miscarriage. A second pregnancy in 1781 also miscarried, and the marriage remained childless. On 27 April 1774, Louis XV fell ill after contracting smallpox and died a few days later on 10 May, aged 64. Louis Stanislas' elder brother,

1750-500: A hostile stance against this rejection, and Louis XVI had to implement a "bed of justice" ( Lit de justice ), which automatically registered an edict in the Parlement of Paris, to ratify the desired reforms. On 8 May, two of the leading members of the Parlement of Paris were arrested. There was rioting in Brittany , Provence, Burgundy and Béarn in reaction to their arrest. This unrest

1875-587: A human activity where students should open a scientific eye on the world around them, mathematizing real situations, in a context that makes sense for the students. This approach is called Realistic Mathematics Education (RME). Freudenthal published the Impossible Puzzle , a mathematical puzzle that appears to lack sufficient information for a solution, in 1969. He also designed a constructed language , Lincos , to make possible communication with extraterrestrial intelligence . In 1951, Freudenthal became

2000-623: A loyalty oath from all state functionaries, including university professors. This time a cabinet minister was able to convince the Emperor to exempt Cauchy from the oath. In 1853, Cauchy was elected an International Member of the American Philosophical Society . Cauchy remained a professor at the university until his death at the age of 67. He received the Last Rites and died of a bronchial condition at 4 a.m. on 23 May 1857. His name

2125-484: A manifesto in response to Louis XVII's death. The manifesto, known as the " Declaration of Verona ", was Louis XVIII's attempt to introduce the French people to his politics. The Declaration of Verona beckoned France back into the arms of the monarchy, "which for fourteen centuries was the glory of France". Louis XVIII negotiated the release of Marie-Thérèse from her Paris prison in 1795. He desperately wanted her to marry her first cousin, Louis Antoine, Duke of Angoulême ,

2250-854: A member of the Royal Netherlands Academy of Arts and Sciences . He was also an honorary member of the International Academy of the History of Science . He was awarded the Gouden Ganzenveer award in 1984. In 2000, the International Commission on Mathematical Instruction instituted an award named in honor of Freudenthal, the Hans Freudenthal Medal. It is given in odd-numbered years (beginning in 2003) for an "outstanding achievement in mathematics education research" in

2375-448: A new property tax, and new elected provincial assemblies which would have a say in local taxation. Calonne's proposition was rejected outright by the notables, and, as a result, Louis XVI dismissed him. The Archbishop of Toulouse, Étienne Charles de Loménie de Brienne , acquired Calonne's ministry. Brienne attempted to salvage Calonne's reforms, but ultimately failed to convince the notables to approve them. A frustrated Louis XVI dissolved

2500-458: A president of a division of the court of appeal in 1847 and a judge of the court of cassation in 1849, and Eugene François Cauchy (1802–1877), a publicist who also wrote several mathematical works. From his childhood he was good at math. Cauchy married Aloise de Bure in 1818. She was a close relative of the publisher who published most of Cauchy's works. They had two daughters, Marie Françoise Alicia (1819) and Marie Mathilde (1823). Cauchy's father

2625-522: A rift between Liouville and Cauchy. Another dispute with political overtones concerned Jean-Marie Constant Duhamel and a claim on inelastic shocks. Cauchy was later shown, by Jean-Victor Poncelet , to be wrong. Hans Freudenthal Hans Freudenthal (17 September 1905 – 13 October 1990) was a Jewish German -born Dutch mathematician . He made substantial contributions to algebraic topology and also took an interest in literature , philosophy , history and mathematics education . Freudenthal

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2750-527: A suspension of a lower-dimensional sphere) and eventually formed the basis of stable homotopy theory . The Freudenthal magic square is a construction in Lie algebra developed by Freudenthal (and independently by Jacques Tits ) in the 1950s and 1960s, associating each Lie algebra to a pair of division algebras . In 1968, Freudenthal founded the journal, Educational Studies in Mathematics (ESM). Becoming one of

2875-584: A thesis on the ends of topological groups in 1930, and was officially awarded a degree in October 1931. After defending his thesis in 1930, he moved to Amsterdam to take up a position as assistant to Brouwer. In this pre-war period in Amsterdam, he was promoted to lecturer at the University of Amsterdam , and married his wife, Suus Lutter, a Dutch teacher. Although he was a German Jew, Freudenthal's position in

3000-545: Is now known as the Cauchy stress tensor . In elasticity , he originated the theory of stress , and his results are nearly as valuable as those of Siméon Poisson . Other significant contributions include being the first to prove the Fermat polygonal number theorem . Cauchy is most famous for his single-handed development of complex function theory . The first pivotal theorem proved by Cauchy, now known as Cauchy's integral theorem ,

3125-524: Is one of the 72 names inscribed on the Eiffel Tower . The genius of Cauchy was illustrated in his simple solution of the problem of Apollonius —describing a circle touching three given circles—which he discovered in 1805, his generalization of Euler's formula on polyhedra in 1811, and in several other elegant problems. More important is his memoir on wave propagation, which obtained the Grand Prix of

3250-479: Is said to have a pole of order n in the point a . If n = 1, the pole is called simple. The coefficient B 1 is called by Cauchy the residue of function f at a . If f is non-singular at a then the residue of f is zero at a . Clearly, the residue is in the case of a simple pole equal to where we replaced B 1 by the modern notation of the residue. In 1831, while in Turin, Cauchy submitted two papers to

3375-504: Is the important thing and goes to show that human beings can get by with little. I should tell you that for my children's pap I still have a bit of fine flour, made from wheat that I grew on my own land. I had three bushels, and I also have a few pounds of potato starch . It is as white as snow and very good, too, especially for very young children. It, too, was grown on my own land. In any event, he inherited his father's staunch royalism and hence refused to take oaths to any government after

3500-537: The Ancien Régime . Accordingly, in 1805 he reformulated his public policies with a view to reclaiming his throne, issuing a declaration that was far more liberal than his earlier pronouncements. This repudiated his Declaration of Verona, promised to abolish conscription, retain the Napoleonic administrative and judicial system, reduce taxes, eliminate political prisons, and guarantee amnesty to everyone who did not oppose

3625-668: The Austrian Netherlands in conjunction with the royal family's failed Flight to Varennes in June 1791. When the Count of Provence arrived in the Low Countries , he proclaimed himself regent of France. He exploited a document that he and Louis XVI had written before the latter's failed escape to Varennes-en-Argonne . The document gave him the regency in the event of his brother's death or inability to perform his role as king. He would join

3750-529: The Bureau des Longitudes . This Bureau bore some resemblance to the academy; for instance, it had the right to co-opt its members. Further, it was believed that members of the Bureau could "forget about" the oath of allegiance, although formally, unlike the Academicians, they were obliged to take it. The Bureau des Longitudes was an organization founded in 1795 to solve the problem of determining position at sea — mainly

3875-490: The Comte de Blacas as his principal political advisor. Queen Marie Joséphine died on 13 November 1810. That same winter, Louis had a particularly severe attack of gout , which was a recurring problem for him at Hartwell, and he had to take to a wheelchair. In 1812, Napoleon I embarked on an invasion of Russia , initiating a war which would prove to be the turning point in his fortunes. The expedition failed miserably, and Napoleon

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4000-580: The Duchy of Alençon in December 1774. The duchy was given to enhance Louis Stanislas's prestige. However, the appanage generated only 300,000 livres a year, an amount much lower than it had been at its peak in the fourteenth century. Louis Stanislas travelled about France more than other members of the Royal Family, who rarely left the Île-de-France . In 1774, he accompanied his sister Clotilde to Chambéry on

4125-521: The Duchy of Brunswick after his departure from Verona. He lived in a modest two-bedroom apartment over a shop. Louis XVIII was forced to leave Blankenburg when King Frederick William II of Prussia died. In light of this, Marie-Thérèse decided to wait a while longer before reuniting with her uncle. In 1798, Tsar Paul I of Russia offered Louis the use of Jelgava Palace in Courland (now Latvia). The Tsar also guaranteed Louis' safety and bestowed on him

4250-619: The Faculté des sciences de Paris  [ fr ] . In July 1830, the July Revolution occurred in France. Charles X fled the country, and was succeeded by Louis-Philippe . Riots, in which uniformed students of the École Polytechnique took an active part, raged close to Cauchy's home in Paris. These events marked a turning point in Cauchy's life, and a break in his mathematical productivity. Shaken by

4375-519: The Freudenthal spectral theorem on the existence of uniform approximations by simple functions in Riesz spaces . In 1937 he proved the Freudenthal suspension theorem , showing that the suspension operation on topological spaces shifts by one their low-dimensional homotopy groups ; this result was important in understanding the homotopy groups of spheres (since every sphere can be formed topologically as

4500-727: The National Convention abolished the monarchy and deposed Louis XVI, who was later executed by guillotine . When his young nephew Louis XVII died in prison in June 1795, the Count of Provence claimed the throne as Louis XVIII. Following the French Revolution and during the Napoleonic era , Louis XVIII lived in exile in Prussia , Great Britain , and Russia . When the Sixth Coalition first defeated Napoleon in 1814, Louis XVIII

4625-530: The Première Classe (First Class) of the Institut de France . Cauchy's first two manuscripts (on polyhedra ) were accepted; the third one (on directrices of conic sections ) was rejected. In September 1812, at 23 years old, Cauchy returned to Paris after becoming ill from overwork. Another reason for his return to the capital was that he was losing interest in his engineering job, being more and more attracted to

4750-650: The Storming of the Bastille two days later. On 16 July, the King's brother, Charles, Comte d'Artois , left France with his wife and children, along with many other courtiers. Artois and his family took up residence in Turin , the capital city of his father-in-law's ( Carlo Emanuele Ferdinando Maria IV ) Kingdom of Sardinia , with the family of Louis Joseph, Prince de Condé . The Count of Provence decided to remain at Versailles. When

4875-651: The Tuileries Palace . In March 1791, the National Assembly created a law outlining the regency of Louis Charles in case his father died while he was still too young to reign. This law awarded the regency to Louis Charles' nearest male relative in France (at that time the Count of Provence), and after him, the Duke of Orleans , thus bypassing the Count of Artois. If Orleans were unavailable, the regency would be submitted to election. The Count of Provence and his wife fled to

5000-432: The longitudinal coordinate, since latitude is easily determined from the position of the sun. Since it was thought that position at sea was best determined by astronomical observations, the Bureau had developed into an organization resembling an academy of astronomical sciences. In November 1839 Cauchy was elected to the Bureau, and discovered that the matter of the oath was not so easily dispensed with. Without his oath,

5125-769: The École des Ponts et Chaussées (School for Bridges and Roads). He graduated in civil engineering, with the highest honors. After finishing school in 1810, Cauchy accepted a job as a junior engineer in Cherbourg, where Napoleon intended to build a naval base. Here Cauchy stayed for three years, and was assigned the Ourcq Canal project and the Saint-Cloud Bridge project, and worked at the Harbor of Cherbourg. Although he had an extremely busy managerial job, he still found time to prepare three mathematical manuscripts, which he submitted to

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5250-504: The "dual representation" proposal. Louis Stanislas was the only notable to vote to increase the size of the Third Estate. Necker disregarded the notables' judgment, and convinced Louis XVI to grant the extra representation. The king duly obliged on 27 December. The Estates-General were convened in May 1789 to ratify financial reforms. The Count of Provence favoured a stalwart position against

5375-471: The Academy of Sciences of Turin. In the first he proposed the formula now known as Cauchy's integral formula , where f ( z ) is analytic on C and within the region bounded by the contour C and the complex number a is somewhere in this region. The contour integral is taken counter-clockwise. Clearly, the integrand has a simple pole at z = a . In the second paper he presented the residue theorem , where

5500-535: The Bourbons were forced to assume pseudonyms. With Louis XVIII using the title Comte d'Isle , named after his estate in Languedoc and at times spelt as Comte de Lille. After an arduous journey from Jelgava, he and his family took up residence in the years 1801–1804 at the Łazienki Palace in Warsaw , which after the partitions of Poland became part of the province of South Prussia . According to Wirydianna Fiszerowa ,

5625-481: The Children of France , as he was her favourite among his siblings. Louis Stanislas was taken away from his governess when he turned seven, the age at which the education of boys of royal blood and of the nobility was turned over to men. Antoine de Quélen de Stuer de Caussade, Duke of La Vauguyon  [ fr ] , a friend of his father, was named as his governor. Louis Stanislas was an intelligent boy, excelling in

5750-741: The Dauphin Louis Joseph . Louis Stanislas and his brother, the Count of Artois , served as godfathers by proxy for Joseph II, Holy Roman Emperor , the Queen's brother. When Marie Antoinette gave birth to her second son, Louis Charles , in March 1785, Louis Stanislas slid further down the line of succession. In 1780, Anne Nompar de Caumont , Countess of Balbi, entered the service of Marie Joséphine. Louis Stanislas soon fell in love with his wife's new lady-in-waiting and installed her as his mistress, which resulted in

5875-491: The Dauphin Louis Auguste, succeeded their grandfather as King Louis XVI. As eldest brother of the King, Louis Stanislas received the title Monsieur . Louis Stanislas longed for political influence. He attempted to gain admittance to the King's council in 1774, but failed. Louis Stanislas was left in a political limbo that he called "a gap of 12 years in my political life". Louis XVI granted Louis Stanislas revenues from

6000-935: The Duke of Angoulême. This stay in Sweden was short-lived since in November 1807 he disembarked at Great Yarmouth , on the Eastern coast of England. He then took up residence in Gosfield Hall in Essex, leased to him by the Marquess of Buckingham . In 1808, Louis brought his wife and queen, Marie Joséphine, to join him in England. His stay at Gosfield Hall did not last long; he soon moved to Hartwell House in Buckinghamshire, where over one hundred courtiers were housed. The King paid £500 in rent each year to

6125-703: The French . In July, Louis XVIII and his nephew departed for Sweden for a Bourbon family conference, where Louis XVIII, the Count of Artois, and the Duke of Angoulême issued a statement condemning Napoleon's move. When the King of Prussia decreed that Louis XVIII would have to leave Prussian territory, and hence Warsaw, Tsar Alexander I invited Louis XVIII to resume residence in Jelgava, which he did. However, having to live under less generous conditions than those enjoyed under Paul I, Louis XVIII decided to embark for England as soon as possible. As time went on, Louis XVIII realised that France would never accept an attempt to return to

6250-509: The French Academy of Sciences in 1816. Cauchy's writings covered notable topics. In the theory of series he developed the notion of convergence and discovered many of the basic formulas for q-series . In the theory of numbers and complex quantities, he was the first to define complex numbers as pairs of real numbers. He also wrote on the theory of groups and substitutions, the theory of functions, differential equations and determinants. In

6375-571: The Irish during the Great Famine of Ireland . His royalism and religious zeal made him contentious, which caused difficulties with his colleagues. He felt that he was mistreated for his beliefs, but his opponents felt he intentionally provoked people by berating them over religious matters or by defending the Jesuits after they had been suppressed. Niels Henrik Abel called him a "bigoted Catholic" and added he

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6500-589: The Legislative Assembly declared that all of the émigrés were traitors to France. Their property and titles were confiscated. The monarchy of France was abolished by the National Convention on 21 September 1792. Louis XVI was executed in January 1793 . This left his young son, Louis Charles, as the titular King. The princes-in-exile proclaimed Louis Charles "King Louis XVII ". The Count of Provence now unilaterally declared himself regent for his nephew, who

6625-648: The Netherlands insulated him from the anti-Jewish laws that had been passed in Germany beginning with the Nazi rise to power in 1933. However, in 1940 the Germans invaded the Netherlands , following which Freudenthal was suspended from duties at the University of Amsterdam by the Nazis. In 1943 Freudenthal was sent to a labor camp in the village of Havelte in the Netherlands, but with

6750-441: The Queen gave birth to a daughter, who was named Marie-Thérèse Charlotte de France and given the honorific title Madame Royale . That the baby was a girl came as a relief to the Count of Provence, who kept his position as heir to Louis XVI, since Salic Law excluded women from acceding to the throne of France. However, Louis Stanislas did not remain heir to the throne much longer. On 22 October 1781, Marie Antoinette gave birth to

6875-481: The Revolution) would be compensated for their losses. Allied troops entered Paris on 31 March 1814. Louis, unable to walk, had sent the Count of Artois to France in January 1814 and issued letters patent appointing Artois Lieutenant-General of the Kingdom in the event of his being restored as king. On 11 April, five days after the French Senate had invited Louis to resume the throne of France, Napoleon I abdicated. The Count of Artois ruled as Lieutenant-General of

7000-410: The Royal Family plotted to abscond from Versailles to Metz , Provence advised the King not to leave, a suggestion he accepted. The Royal Family was forced to leave the palace at Versailles on the day after the Women's March on Versailles , 5 October 1789. They were taken to Paris. There, the Count of Provence and his wife lodged in the Luxembourg Palace , while the rest of the Royal Family stayed in

7125-413: The Swiss magnate Jacques Necker . In November 1788, a second Assembly of Notables was convened by Jacques Necker, to consider the makeup of the next Estates-General. The Parlement of Paris recommended that the Estates should be the same as they were at the last assembly, in 1614 (this would mean that the clergy and nobility would have more representation than the Third Estate ). The notables rejected

7250-408: The Third Estate and its demands for tax reform. On 17 June, the Third Estate declared itself a National Assembly , an Assembly not of the Estates, but of the people. The Count of Provence urged the King to act strongly against the declaration, while the King's popular minister Jacques Necker aimed at reaching a compromise with the new assembly. Louis XVI was characteristically indecisive. On 9 July,

7375-464: The abstract beauty of mathematics; in Paris, he would have a much better chance to find a mathematics related position. When his health improved in 1813, Cauchy chose not to return to Cherbourg. Although he formally kept his engineering position, he was transferred from the payroll of the Ministry of the Marine to the Ministry of the Interior. The next three years Cauchy was mainly on unpaid sick leave; he spent his time fruitfully, working on mathematics (on

7500-415: The argument " in many modern textbooks on complex analysis. In modern control theory textbooks, the Cauchy argument principle is quite frequently used to derive the Nyquist stability criterion , which can be used to predict the stability of negative feedback amplifier and negative feedback control systems. Thus Cauchy's work has a strong impact on both pure mathematics and practical engineering. Cauchy

7625-408: The assembly declared itself a National Constituent Assembly that would give France a Constitution. On 11 July, Louis XVI dismissed Necker, which led to widespread rioting across Paris. On 12 July, the sabre charge of the Régiment Royal–Allemand Cavalerie (Royal German Cavalry Regiment) of Charles-Eugène de Lorraine, Prince de Lambesc , against a crowd gathered at the Tuileries gardens , sparked

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7750-503: The assembly. Brienne's reforms were then submitted to the Parlement of Paris in the hopes that they would be approved. (A parlement was responsible for ratifying the King's edicts; each province had its own parlement , but the Parlement of Paris was the most significant of all.) The Parlement of Paris refused to accept Brienne's proposals and declared that any new taxation would have to be approved by an Estates-General (the nominal parliament of France). Louis XVI and Brienne took

7875-428: The beginning of the Differential Calculus. Laugwitz (1989) and Benis-Sinaceur (1973) point out that Cauchy continued to use infinitesimals in his own research as late as 1853. Cauchy gave an explicit definition of an infinitesimal in terms of a sequence tending to zero. There has been a vast body of literature written about Cauchy's notion of "infinitesimally small quantities", arguing that they lead from everything from

8000-486: The classics. His education was of the same quality and consistency as that of his older brother, Louis Auguste, despite the fact that Louis Auguste was heir and Louis Stanislas was not. Louis Stanislas's education was quite religious in nature; several of his teachers were priests, such as Jean-Gilles du Coëtlosquet , Bishop of Limoges; the Abbé Jean-Antoine Nollet ; and the Jesuit Guillaume-François Berthier . La Vauguyon drilled into young Louis Stanislas and his brothers

8125-494: The couple's already limited affection for each other cooling entirely. Louis Stanislas commissioned a pavilion for his mistress on a parcel of land at Versailles which became known as the Parc Balbi . Louis Stanislas lived a quiet and sedentary lifestyle at this point, not having a great deal to do since his self-proclaimed political exclusion in 1774. He kept himself occupied with his vast library of over 11,000 books at Balbi's pavilion, reading for several hours each morning. In

8250-418: The court of Versailles. The marriage remained unconsummated for years. Biographers disagree about the reason. The most common theories propose Louis Stanislas' alleged impotence (according to biographer Antonia Fraser ) or his unwillingness to sleep with his wife due to her poor personal hygiene. She never brushed her teeth, plucked her eyebrows, or used any perfumes. At the time of his marriage, Louis Stanislas

8375-493: The death of Tsar Paul I. Louis hoped that Paul's successor, Alexander I , would repudiate his father's banishment of the Bourbons, which he later did. Louis then intended to set off to the Kingdom of Naples . The Count of Artois asked Louis to send his son, Louis-Antoine, and daughter-in-law, Marie-Thérèse, to him in Edinburgh , but the King did not do so at that time. Artois had an allowance from King George III of Great Britain and he sent some money to Louis, whose court-in-exile

8500-522: The early 1780s, he also incurred huge debts totalling 10 million livres, which his brother Louis XVI paid. An Assembly of Notables (the members consisted of magistrates, mayors, nobles and clergy) was convened in February 1787 to ratify the financial reforms sought by the Controller-General of Finance Charles Alexandre de Calonne . This provided the Count of Provence, who abhorred the radical reforms proposed by Calonne, his long-awaiting opportunity to establish himself in politics. The reforms proposed

8625-424: The effects of the absence of Catholic university education in France. These activities did not make Cauchy popular with his colleagues, who, on the whole, supported the Enlightenment ideals of the French Revolution. When a chair of mathematics became vacant at the Collège de France in 1843, Cauchy applied for it, but received just three of 45 votes. In 1848 King Louis-Philippe fled to England. The oath of allegiance

8750-445: The entrance examination to the École Polytechnique . In 1805, he placed second of 293 applicants on this exam and was admitted. One of the main purposes of this school was to give future civil and military engineers a high-level scientific and mathematical education. The school functioned under military discipline, which caused Cauchy some problems in adapting. Nevertheless, he completed the course in 1807, at age 18, and went on to

8875-428: The fall of the government and moved by a deep hatred of the liberals who were taking power, Cauchy left France to go abroad, leaving his family behind. He spent a short time at Fribourg in Switzerland, where he had to decide whether he would swear a required oath of allegiance to the new regime. He refused to do this, and consequently lost all his positions in Paris, except his membership of the academy, for which an oath

9000-638: The family to Arcueil during the French Revolution . Their life there during that time was apparently hard; Augustin-Louis's father, Louis François, spoke of living on rice, bread, and crackers during the period. A paragraph from an undated letter from Louis François to his mother in Rouen says: We never had more than a one-half pound (230 g) of bread — and sometimes not even that. This we supplement with little supply of hard crackers and rice that we are allotted. Otherwise, we are getting along quite well, which

9125-450: The first mathematician besides Cauchy to make a substantial contribution (his work on what are now known as Laurent series , published in 1843). In his book Cours d'Analyse Cauchy stressed the importance of rigor in analysis. Rigor in this case meant the rejection of the principle of Generality of algebra (of earlier authors such as Euler and Lagrange) and its replacement by geometry and infinitesimals . Judith Grabiner wrote Cauchy

9250-480: The following year a Foreign Honorary Member of the American Academy of Arts and Sciences . In August 1833 Cauchy left Turin for Prague to become the science tutor of the thirteen-year-old Duke of Bordeaux, Henri d'Artois (1820–1883), the exiled Crown Prince and grandson of Charles X. As a professor of the École Polytechnique, Cauchy had been a notoriously bad lecturer, assuming levels of understanding that only

9375-454: The form of "a major cumulative program of research". Recipients of the medal have included Celia Hoyles , Paul Cobb, Anna Sfard , Yves Chevallard , Luis Radford and Frederick Leung . The asteroid 9689 Freudenthal is named after him. Louis XVIII Louis XVIII (Louis Stanislas Xavier; 17 November 1755 – 16 September 1824), known as the Desired (French: le Désiré ),

9500-587: The former court ceremonies, including the lever and coucher (ceremonies that accompanied waking and bedding, respectively). On 9 June 1799, Marie-Thérèse married her cousin Louis-Antoine at the Jelgava Palace. Desperate to display to the world a united family, Louis XVIII ordered his wife Queen Marie Joséphine , who at the time was living apart from her husband in Schleswig-Holstein , to attend

9625-456: The help of his wife (who, as a non-Jew, had not been deported) he escaped in 1944 and went into hiding with his family in occupied Amsterdam. During this period Freudenthal occupied his time in literary pursuits, including winning first prize under a false name in a novel-writing contest. With the war over, Freudenthal's position at the University of Amsterdam was returned to him, but in 1946 he

9750-463: The journey to meet her bridegroom Charles Emmanuel, Prince of Piedmont , heir to the throne of Sardinia . In 1775, he visited Lyon and also his spinster aunts Adélaïde and Victoire while they were taking the waters at Vichy . The four provincial tours that Louis Stanislas took before the year 1791 amounted to a total of three months. On 5 May 1778, Dr. Lassonne, Marie Antoinette's private physician, confirmed her pregnancy. On 19 December 1778,

9875-401: The king appointed Cauchy to take the place of one of them. The reaction of Cauchy's peers was harsh; they considered the acceptance of his membership in the academy an outrage, and Cauchy created many enemies in scientific circles. In November 1815, Louis Poinsot , who was an associate professor at the École Polytechnique, asked to be exempted from his teaching duties for health reasons. Cauchy

10000-407: The king refused to approve his election. For four years Cauchy was in the position of being elected but not approved; accordingly, he was not a formal member of the Bureau, did not receive payment, could not participate in meetings, and could not submit papers. Still Cauchy refused to take any oaths; however, he did feel loyal enough to direct his research to celestial mechanics . In 1840, he presented

10125-659: The liberal Doctrinaires . His reign was further marked by the formation of the Quintuple Alliance and a military intervention in Spain . Louis had no children, and upon his death the crown passed to his brother, Charles X . Louis XVIII was the last king or emperor of France to die a reigning monarch: his successor, Charles X ( r.   1824–1830) abdicated; and both Louis Philippe I ( r.   1830–1848) and Napoleon III ( r.   1852–1870) were deposed. Louis Stanislas Xavier , styled Count of Provence from birth,

10250-592: The other princes-in-exile at Coblenz soon after his escape. It was there that he, the Count of Artois, and the Condé princes proclaimed that their objective was to invade France. Louis XVI was greatly annoyed by his brothers' behaviour. Provence sent emissaries to various European courts asking for financial aid, soldiers, and munition. Artois secured a castle for the court in exile in the Electorate of Trier (or "Treves"), where their maternal uncle, Clemens Wenceslaus of Saxony ,

10375-475: The overthrow of Charles X. He was an equally staunch Catholic and a member of the Society of Saint Vincent de Paul . He also had links to the Society of Jesus and defended them at the academy when it was politically unwise to do so. His zeal for his faith may have led to his caring for Charles Hermite during his illness and leading Hermite to become a faithful Catholic. It also inspired Cauchy to plead on behalf of

10500-649: The owner of the estate, Sir George Lee. The Prince of Wales (the future George IV of the United Kingdom) was very charitable to the exiled Bourbons. As Prince Regent, he granted them permanent right of asylum and extremely generous allowances. The Count of Artois did not join the court-in-exile in Hartwell, preferring to continue his frivolous life in London. Louis's friend the Count of Avaray left Hartwell for Madeira in 1809, and died there in 1811. Louis replaced Avaray with

10625-521: The public education system, the Catholic Church sought to establish its own branch of education and found in Cauchy a staunch and illustrious ally. He lent his prestige and knowledge to the École Normale Écclésiastique , a school in Paris run by Jesuits, for training teachers for their colleges. He took part in the founding of the Institut Catholique . The purpose of this institute was to counter

10750-627: The related topics of symmetric functions , the symmetric group and the theory of higher-order algebraic equations). He attempted admission to the First Class of the Institut de France but failed on three different occasions between 1813 and 1815. In 1815 Napoleon was defeated at Waterloo, and the newly installed king Louis XVIII took the restoration in hand. The Académie des Sciences was re-established in March 1816; Lazare Carnot and Gaspard Monge were removed from this academy for political reasons, and

10875-552: The same way. In January 1801, Tsar Paul told Louis XVIII that he could no longer live in Russia. The court at Jelgava was so low on funds that it had to auction some of its possessions to afford the journey out of Russia. Marie-Thérèse even sold a diamond necklace that the Emperor Paul had given her as a wedding gift. Marie-Thérèse persuaded Queen Louise of Prussia to give her family refuge on Prussian territory. Though Louise consented,

11000-808: The son of the Count of Artois. Louis XVIII deceived his niece by telling her that her parents' last wishes were for her to marry Louis-Antoine, and she duly agreed to Louis XVIII's wishes. Louis XVIII was forced to abandon Verona when Napoleon Bonaparte invaded the Republic of Venice in 1796. Louis XVIII had been vying for the custody of his niece Marie-Thérèse since her release from the Temple Tower in December 1795. He succeeded when Francis II, Holy Roman Emperor , agreed to relinquish his custody of her in 1796. She had been staying in Vienna with her Habsburg relatives since January 1796. Louis XVIII moved to Blankenburg in

11125-404: The sum is over all the n poles of f ( z ) on and within the contour C . These results of Cauchy's still form the core of complex function theory as it is taught today to physicists and electrical engineers. For quite some time, contemporaries of Cauchy ignored his theory, believing it to be too complicated. Only in the 1840s the theory started to get response, with Pierre Alphonse Laurent being

11250-427: The theorem was given in 1825. In 1826 Cauchy gave a formal definition of a residue of a function. This concept concerns functions that have poles —isolated singularities, i.e., points where a function goes to positive or negative infinity. If the complex-valued function f ( z ) can be expanded in the neighborhood of a singularity a as where φ( z ) is analytic (i.e., well-behaved without singularities), then f

11375-419: The theory of light he worked on Fresnel's wave theory and on the dispersion and polarization of light. He also contributed research in mechanics , substituting the notion of the continuity of geometrical displacements for the principle of the continuity of matter. He wrote on the equilibrium of rods and elastic membranes and on waves in elastic media. He introduced a 3 × 3 symmetric matrix of numbers that

11500-539: The throne of France, behind his father and his two elder brothers: Louis Joseph Xavier, Duke of Burgundy , and Louis Auguste, Duke of Berry . The former died in 1761, leaving Louis Auguste as heir to their father until the Dauphin's own premature death in 1765. The two deaths elevated Louis Stanislas to second in the line of succession, while his brother Louis Auguste acquired the title of Dauphin. Louis Stanislas found comfort in his governess, Madame de Marsan , Governess of

11625-476: The top-rated journals in the field of mathematics education, ESM was focused on publishing research around finding better ways to teach mathematics. Later in his life, Freudenthal focused on elementary mathematics education . In the 1970s, his single-handed intervention prevented the Netherlands from following the worldwide trend of " new math ". He was also a fervent critic of one of the first international school achievement studies. He interpreted mathematics as

11750-405: The usual "epsilontic" definitions or to the notions of non-standard analysis . The consensus is that Cauchy omitted or left implicit the important ideas to make clear the precise meaning of the infinitely small quantities he used. He was the first to prove Taylor's theorem rigorously, establishing his well-known form of the remainder. He wrote a textbook (see the illustration) for his students at

11875-407: The variable always produces an infinitely small increment in the function itself. M. Barany claims that the École mandated the inclusion of infinitesimal methods against Cauchy's better judgement. Gilain notes that when the portion of the curriculum devoted to Analyse Algébrique was reduced in 1825, Cauchy insisted on placing the topic of continuous functions (and therefore also infinitesimals) at

12000-415: The way he thought princes should "know how to withdraw themselves, to like to work," and "to know how to reason correctly". In April 1771, when he was 15, Louis Stanislas's education was formally concluded, and his own independent household was established, which astounded contemporaries with its extravagance: in 1773, the number of his servants reached 390 In the same month his household was founded, Louis

12125-480: The wedding. Furthermore, she was to come without her long-time friend (and rumoured lover) Marguerite de Gourbillon . The Queen refused to leave her friend behind, creating an unpleasant situation that rivalled the wedding in notoriety. Louis XVIII knew that his nephew Louis-Antoine was not compatible with Marie-Thérèse. Despite this, he still pressed for the marriage, which proved to be quite unhappy and produced no children. In 1800, Louis XVIII attempted to strike up

12250-408: The École Polytechnique in which he developed the basic theorems of mathematical analysis as rigorously as possible. In this book he gave the necessary and sufficient condition for the existence of a limit in the form that is still taught. Also Cauchy's well-known test for absolute convergence stems from this book: Cauchy condensation test . In 1829 he defined for the first time a complex function of

12375-595: Was King of France from 1814 to 1824, except for a brief interruption during the Hundred Days in 1815. Before his reign, he spent 23 years in exile from France beginning in 1791, during the French Revolution and the First French Empire . Until his accession to the throne of France, he held the title of Count of Provence as brother of King Louis XVI , the last king of the Ancien Régime . On 21 September 1792,

12500-423: Was "mad and there is nothing that can be done about him", but at the same time praised him as a mathematician. Cauchy's views were widely unpopular among mathematicians and when Guglielmo Libri Carucci dalla Sommaja was made chair in mathematics before him he, and many others, felt his views were the cause. When Libri was accused of stealing books he was replaced by Joseph Liouville rather than Cauchy, which caused

12625-457: Was "the man who taught rigorous analysis to all of Europe". The book is frequently noted as being the first place that inequalities, and δ − ε {\displaystyle \delta -\varepsilon } arguments were introduced into calculus. Here Cauchy defined continuity as follows: The function f(x) is continuous with respect to x between the given limits if, between these limits, an infinitely small increment in

12750-489: Was 28 years old, he was still living with his parents. His father found it time for his son to marry; he found him a suitable bride, Aloïse de Bure, five years his junior. The de Bure family were printers and booksellers, and published most of Cauchy's works. Aloïse and Augustin were married on April 4, 1818, with great Roman Catholic ceremony, in the Church of Saint-Sulpice. In 1819 the couple's first daughter, Marie Françoise Alicia,

12875-658: Was a constitutional monarchy , unlike the absolutist Ancien Régime in France before the Revolution. As a constitutional monarch, Louis XVIII's royal prerogative was reduced substantially by the Charter of 1814 , France's new constitution. His return in 1815 led to a second wave of White Terror headed by the Ultra-royalist faction. The following year, Louis dissolved the unpopular parliament (the Chambre introuvable ), giving rise to

13000-437: Was a highly ranked official in the Parisian police of the Ancien Régime , but lost this position due to the French Revolution (14 July 1789), which broke out one month before Augustin-Louis was born. The Cauchy family survived the revolution and the following Reign of Terror during 1793–94 by escaping to Arcueil , where Cauchy received his first education, from his father. After the execution of Robespierre in 1794, it

13125-638: Was abolished, and the road to an academic appointment was clear for Cauchy. On March 1, 1849, he was reinstated at the Faculté de Sciences, as a professor of mathematical astronomy. After political turmoil all through 1848, France chose to become a Republic, under the Presidency of Napoleon III of France . Early 1852 the President made himself Emperor of France, and took the name Napoleon III . The idea came up in bureaucratic circles that it would be useful to again require

13250-509: Was born in Luckenwalde , Brandenburg , on 17 September 1905, the son of a Jewish teacher. He was interested in both mathematics and literature as a child, and studied mathematics at the University of Berlin beginning in 1923. He met L. E. J. Brouwer in 1927, when Brouwer came to Berlin to give a lecture, and in the same year Freudenthal also visited the University of Paris . He completed his thesis work with Heinz Hopf at Berlin, defended

13375-478: Was born on 17 November 1755 in the Palace of Versailles , a younger son of Louis, Dauphin of France , and his wife Maria Josepha of Saxony . He was the grandson of the reigning King Louis XV . As a son of the Dauphin, he was a Fils de France . He was christened Louis Stanislas Xavier six months after his birth, in accordance with Bourbon family tradition, being nameless before his baptism . By this act, he also became

13500-473: Was born, and in 1823 the second and last daughter, Marie Mathilde. The conservative political climate that lasted until 1830 suited Cauchy perfectly. In 1824 Louis XVIII died, and was succeeded by his even more conservative brother Charles X . During these years Cauchy was highly productive, and published one important mathematical treatise after another. He received cross-appointments at the Collège de France , and

13625-435: Was by then a rising mathematical star. One of his great successes at that time was the proof of Fermat 's polygonal number theorem . He quit his engineering job, and received a one-year contract for teaching mathematics to second-year students of the École Polytechnique. In 1816, this Bonapartist, non-religious school was reorganized, and several liberal professors were fired; Cauchy was promoted to full professor. When Cauchy

13750-455: Was conducted on 14 May at the Palace of Versailles . Marie Joséphine (as she was known in France) was a daughter of Victor Amadeus , Duke of Savoy (later King Victor Amadeus III of Sardinia), and his wife Maria Antonia Ferdinanda of Spain . A luxurious ball followed the wedding on 20 May. Louis Stanislas found his wife repulsive; she was considered ugly, tedious, and ignorant of the customs of

13875-607: Was engineered by local magistrates and nobles, who enticed the people to revolt against the Lit de Justice , which was quite unfavourable to the nobles and magistrates. The clergy also joined the provincial cause, and condemned Brienne's tax reforms. Brienne conceded defeat in July and agreed to a convocation of the Estates-General to meet in 1789. He resigned from his post in August and was replaced by

14000-464: Was forced to retreat with an army in tatters. In 1813, Louis XVIII issued another declaration from Hartwell. The Declaration of Hartwell was even more liberal than his Declaration of 1805, asserting that those who had served Napoleon or the Republic would not suffer repercussions for their acts, and that the original owners of the biens nationaux (lands confiscated from the nobility and clergy during

14125-505: Was given a chair in pure and applied mathematics and foundations of mathematics at Utrecht University , where he remained for the rest of his career. He served as the 8th president of the International Commission on Mathematical Instruction from 1967 to 1970. In 1971 he founded the Institute for the Development of Mathematical Education (IOWO) at Utrecht University, which after his death

14250-427: Was granted several titles by his grandfather, Louis XV: Duke of Anjou, Count of Maine, Count of Perche, and Count of Senoches. During this period of his life he was often known by the title Count of Provence. On 17 December 1773, he was inaugurated as a Grand Master of the Order of St. Lazarus . On 16 April 1771, Louis Stanislas was married by proxy to Princess Maria Giuseppina of Savoy . The in-person ceremony

14375-408: Was named a baron , a title by which Cauchy set great store. In 1834, his wife and two daughters moved to Prague, and Cauchy was reunited with his family after four years in exile. Cauchy returned to Paris and his position at the Academy of Sciences late in 1838. He could not regain his teaching positions, because he still refused to swear an oath of allegiance. In August 1839 a vacancy appeared in

14500-490: Was not only being spied on by Napoleonic agents but was also being forced to make significant economies, financed as it was mainly from interest owed by the Emperor Francis II on valuables his aunt, Marie Antoinette, had removed from France. In 1803, Napoleon tried to force Louis XVIII to renounce his right to the throne of France, but Louis refused. In May the following year, 1804, Napoleon declared himself Emperor of

14625-558: Was not required. In 1831 Cauchy went to the Italian city of Turin , and after some time there, he accepted an offer from the King of Sardinia (who ruled Turin and the surrounding Piedmont region) for a chair of theoretical physics, which was created especially for him. He taught in Turin during 1832–1833. In 1831, he was elected a foreign member of the Royal Swedish Academy of Sciences , and

14750-519: Was obese and waddled instead of walked. He never exercised and continued to eat enormous amounts of food. Despite the fact that Louis Stanislas was not infatuated with his wife, he boasted that the two enjoyed vigorous conjugal relations – but such declarations were held in low esteem by courtiers at Versailles. He also proclaimed his wife to be pregnant merely to spite Louis Auguste and his wife Marie Antoinette , who had not yet consummated their marriage. The Dauphin and Louis Stanislas did not enjoy

14875-522: Was placed in what he, and the French royalists, considered his rightful position. However, Napoleon escaped from his exile in Elba and restored his French Empire. Louis XVIII fled, and a Seventh Coalition declared war on the French Empire, defeated Napoleon again, and again restored Louis XVIII to the French throne. Louis XVIII ruled as king for slightly less than a decade. His Bourbon Restoration government

15000-534: Was renamed the Freudenthal Institute . In 1972 he founded and became editor-in-chief of the journal Geometriae Dedicata . He retired from his professorship in 1975 and from his journal editorship in 1981. He died in Utrecht in 1990, sitting on a bench in a park where he always took a morning walk. In his thesis work, published as a journal article in 1931, Freudenthal introduced the concept of an end of

15125-450: Was safe for the family to return to Paris. There, Louis-François Cauchy found a bureaucratic job in 1800, and quickly advanced his career. When Napoleon came to power in 1799, Louis-François Cauchy was further promoted, and became Secretary-General of the Senate, working directly under Laplace (who is now better known for his work on mathematical physics). The mathematician Lagrange was also

15250-622: Was the Archbishop-Elector . The activities of the émigrés bore fruit when the rulers of Prussia and the Holy Roman Empire gathered at Dresden . They released the Declaration of Pillnitz in August 1791, which urged Europe to intervene in France if Louis XVI or his family were threatened. Provence's endorsement of the declaration was not well received in France, either by the ordinary citizens or by Louis XVI himself. In January 1792,

15375-494: Was the following: where f ( z ) is a complex-valued function holomorphic on and within the non-self-intersecting closed curve C (contour) lying in the complex plane . The contour integral is taken along the contour C . The rudiments of this theorem can already be found in a paper that the 24-year-old Cauchy presented to the Académie des Sciences (then still called "First Class of the Institute") on August 11, 1814. In full form

15500-492: Was too young to be head of the House of Bourbon. Louis XVII, still a minor, died in prison in June 1795. His only surviving sibling was his sister Marie-Thérèse , who was not considered a candidate for the throne because of France's traditional adherence to Salic law . Thus on 16 June, the princes-in-exile declared the Count of Provence "King Louis XVIII". The new king accepted their declaration soon after and busied himself drafting

15625-443: Was very productive, in number of papers second only to Leonhard Euler . It took almost a century to collect all his writings into 27 large volumes: His greatest contributions to mathematical science are enveloped in the rigorous methods which he introduced; these are mainly embodied in his three great treatises: His other works include: Augustin-Louis Cauchy grew up in the house of a staunch royalist. This made his father flee with

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