Paris is the capital and most populous city of France, with an area of 105 square kilometres and an official estimated population of 2,140,526 residents as of 1 January 2019. Since the 17th century, Paris has been one of Europe's major centres of finance, commerce, fashion and the arts; the City of Paris is the centre and seat of government of the Île-de-France, or Paris Region, which has an estimated official 2019 population of 12,213,364, or about 18 percent of the population of France. The Paris Region had a GDP of €681 billion in 2016, accounting for 31 percent of the GDP of France, was the 5th largest region by GDP in the world. According to the Economist Intelligence Unit Worldwide Cost of Living Survey in 2018, Paris was the second most expensive city in the world, after Singapore, ahead of Zurich, Hong Kong and Geneva. Another source ranked Paris as most expensive, on a par with Singapore and Hong-Kong, in 2018; the city is a major rail and air-transport hub served by two international airports: Paris-Charles de Gaulle and Paris-Orly.
Opened in 1900, the city's subway system, the Paris Métro, serves 5.23 million passengers daily, is the second busiest metro system in Europe after Moscow Metro. Gare du Nord is the 24th busiest railway station in the world, the first located outside Japan, with 262 million passengers in 2015. Paris is known for its museums and architectural landmarks: the Louvre was the most visited art museum in the world in 2018, with 10.2 million visitors. The Musée d'Orsay and Musée de l'Orangerie are noted for their collections of French Impressionist art, the Pompidou Centre Musée National d'Art Moderne has the largest collection of modern and contemporary art in Europe; the historical district along the Seine in the city centre is classified as a UNESCO Heritage Site. Popular landmarks in the centre of the city include the Cathedral of Notre Dame de Paris and the Gothic royal chapel of Sainte-Chapelle, both on the Île de la Cité. Paris received 23 million visitors in 2017, measured by hotel stays, with the largest numbers of foreign visitors coming from the United States, the UK, Germany and China.
It was ranked as the third most visited travel destination in the world in 2017, after Bangkok and London. The football club Paris Saint-Germain and the rugby union club Stade Français are based in Paris; the 80,000-seat Stade de France, built for the 1998 FIFA World Cup, is located just north of Paris in the neighbouring commune of Saint-Denis. Paris hosts the annual French Open Grand Slam tennis tournament on the red clay of Roland Garros. Paris will host the 2024 Summer Olympics; the 1938 and 1998 FIFA World Cups, the 2007 Rugby World Cup, the 1960, 1984, 2016 UEFA European Championships were held in the city and, every July, the Tour de France bicycle race finishes there. The name "Paris" is derived from the Celtic Parisii tribe; the city's name is not related to the Paris of Greek mythology. Paris is referred to as the City of Light, both because of its leading role during the Age of Enlightenment and more because Paris was one of the first large European cities to use gas street lighting on a grand scale on its boulevards and monuments.
Gas lights were installed on the Place du Carousel, Rue de Rivoli and Place Vendome in 1829. By 1857, the Grand boulevards were lit. By the 1860s, the boulevards and streets of Paris were illuminated by 56,000 gas lamps. Since the late 19th century, Paris has been known as Panam in French slang. Inhabitants are known in French as Parisiens, they are pejoratively called Parigots. The Parisii, a sub-tribe of the Celtic Senones, inhabited the Paris area from around the middle of the 3rd century BC. One of the area's major north–south trade routes crossed the Seine on the île de la Cité; the Parisii minted their own coins for that purpose. The Romans began their settlement on Paris' Left Bank; the Roman town was called Lutetia. It became a prosperous city with a forum, temples, an amphitheatre. By the end of the Western Roman Empire, the town was known as Parisius, a Latin name that would become Paris in French. Christianity was introduced in the middle of the 3rd century AD by Saint Denis, the first Bishop of Paris: according to legend, when he refused to renounce his faith before the Roman occupiers, he was beheaded on the hill which became known as Mons Martyrum "Montmartre", from where he walked headless to the north of the city.
Clovis the Frank, the first king of the Merovingian dynasty, made the city his capital from 508. As the Frankish domination of Gaul began, there was a gradual immigration by the Franks to Paris and the Parisian Francien dialects were born. Fortification of the Île-de-la-Citie failed to avert sacking by Vikings in 845, but Paris' strategic importance—with its bridges prevent
The French Revolution was a period of far-reaching social and political upheaval in France and its colonies beginning in 1789. The Revolution overthrew the monarchy, established a republic, catalyzed violent periods of political turmoil, culminated in a dictatorship under Napoleon who brought many of its principles to areas he conquered in Western Europe and beyond. Inspired by liberal and radical ideas, the Revolution profoundly altered the course of modern history, triggering the global decline of absolute monarchies while replacing them with republics and liberal democracies. Through the Revolutionary Wars, it unleashed a wave of global conflicts that extended from the Caribbean to the Middle East. Historians regard the Revolution as one of the most important events in human history; the causes of the French Revolution are still debated among historians. Following the Seven Years' War and the American Revolution, the French government was in debt, it attempted to restore its financial status through unpopular taxation schemes, which were regressive.
Leading up to the Revolution, years of bad harvests worsened by deregulation of the grain industry and environmental problems inflamed popular resentment of the privileges enjoyed by the aristocracy and the Catholic clergy of the established church. Some historians hold something similar to what Thomas Jefferson proclaimed: that France had "been awakened by our Revolution." Demands for change were formulated in terms of Enlightenment ideals and contributed to the convocation of the Estates General in May 1789. During the first year of the Revolution, members of the Third Estate took control, the Bastille was attacked in July, the Declaration of the Rights of Man and of the Citizen was passed in August, the Women's March on Versailles forced the royal court back to Paris in October. A central event of the first stage, in August 1789, was the abolition of feudalism and the old rules and privileges left over from the Ancien Régime; the next few years featured political struggles between various liberal assemblies and right-wing supporters of the monarchy intent on thwarting major reforms.
The Republic was proclaimed in September 1792 after the French victory at Valmy. In a momentous event that led to international condemnation, Louis XVI was executed in January 1793. External threats shaped the course of the Revolution; the Revolutionary Wars beginning in 1792 featured French victories that facilitated the conquest of the Italian Peninsula, the Low Countries and most territories west of the Rhine – achievements that had eluded previous French governments for centuries. Internally, popular agitation radicalised the Revolution culminating in the rise of Maximilien Robespierre and the Jacobins; the dictatorship imposed by the Committee of Public Safety during the Reign of Terror, from 1793 until 1794, established price controls on food and other items, abolished slavery in French colonies abroad, de-established the Catholic church and created a secular Republican calendar, religious leaders were expelled, the borders of the new republic were secured from its enemies. After the Thermidorian Reaction, an executive council known as the Directory assumed control of the French state in 1795.
They suspended elections, repudiated debts, persecuted the Catholic clergy, made significant military conquests abroad. Dogged by charges of corruption, the Directory collapsed in a coup led by Napoleon Bonaparte in 1799. Napoleon, who became the hero of the Revolution through his popular military campaigns, established the Consulate and the First Empire, setting the stage for a wider array of global conflicts in the Napoleonic Wars; the modern era has unfolded in the shadow of the French Revolution. All future revolutionary movements looked back to the Revolution as their predecessor, its central phrases and cultural symbols, such as La Marseillaise and Liberté, fraternité, égalité, ou la mort, became the clarion call for other major upheavals in modern history, including the Russian Revolution over a century later. The values and institutions of the Revolution dominate French politics to this day; the Revolution resulted in the suppression of the feudal system, emancipation of the individual, a greater division of landed property, abolition of the privileges of noble birth, nominal establishment of equality among men.
The French Revolution differed from other revolutions in being not only national, for it intended to benefit all humanity. Globally, the Revolution accelerated the rise of democracies, it became the focal point for the development of most modern political ideologies, leading to the spread of liberalism, radicalism and secularism, among many others. The Revolution witnessed the birth of total war by organising the resources of France and the lives of its citizens towards the objective of military conquest; some of its central documents, such as the Declaration of the Rights of Man and of the Citizen, continued to inspire movements for abolitionism and universal suffrage in the next century. Historians have pointed to many events and factors within the Ancien Régime that led to the Revolution. Rising social and economic inequality, new political ideas emerging from the Enlightenment, economic mismanagement, environmental factors leading to agricultural failure, unmanageable national debt, political mismanagement on the part of King Louis XVI have all been cited as laying the groundwork for the Revolution.
Over the course of the 18th century, there emerged what the philosopher Jürgen Habermas called the idea of the "public sphere" in France and elsewhere
Nice is the seventh most populous urban area in France and the capital of the Alpes-Maritimes département. The metropolitan area of Nice extends beyond the administrative city limits, with a population of about 1 million on an area of 721 km2. Located in the French Riviera, on the south east coast of France on the Mediterranean Sea, at the foot of the Alps, Nice is the second-largest French city on the Mediterranean coast and the second-largest city in the Provence-Alpes-Côte d'Azur region after Marseille. Nice is 13 kilometres from the principality of Monaco and 30 kilometres from the French-Italian border. Nice's airport serves as a gateway to the region; the city is nicknamed Nice la Belle, which means Nice the Beautiful, the title of the unofficial anthem of Nice, written by Menica Rondelly in 1912. The area of today's Nice contains Terra Amata, an archaeological site which displays evidence of a early use of fire. Around 350 BC, Greeks of Marseille founded a permanent settlement and called it Nikaia, after Nike, the goddess of victory.
Through the ages, the town has changed hands many times. Its strategic location and port contributed to its maritime strength. For centuries it was a dominion of Savoy, was part of France between 1792 and 1815, when it was returned to the Kingdom of Piedmont-Sardinia until its re-annexation by France in 1860; the natural environment of the Nice area and its mild Mediterranean climate came to the attention of the English upper classes in the second half of the 18th century, when an increasing number of aristocratic families took to spending their winters there. The city's main seaside promenade, the Promenade des Anglais owes its name to visitors to the resort; the clear air and soft light have appealed to notable painters, such as Marc Chagall, Henri Matisse, Niki de Saint Phalle and Arman. Their work is commemorated in many of the city's museums, including Musée Marc Chagall, Musée Matisse and Musée des Beaux-Arts. Nice has the second largest hotel capacity in the country and it is one of its most visited cities, receiving 4 million tourists every year.
It has the third busiest airport in France, after the two main Parisian ones. It is the historical capital city of the County of Nice; the first known hominid settlements in the Nice area date back about 400,000 years. Nice was founded around 350 BC by the Greeks Phoceans of Massalia, was given the name of Nikaia in honour of a victory over the neighbouring Ligurians; the city soon became one of the busiest trading ports on the Ligurian coast. The ruins of Cemenelum are in Cimiez, now a district of Nice. In the 7th century, Nice joined. In 729 the city repulsed the Saracens. During the Middle Ages, Nice participated in the wars and history of Italy; as an ally of Pisa it was the enemy of Genoa, both the King of France and the Holy Roman Emperor endeavoured to subjugate it. During the 13th and 14th centuries the city fell more than once into the hands of the Counts of Provence, but it regained its independence though related to Genoa; the medieval city walls surrounded the Old Town. The landward side was protected by the River Paillon, covered over and is now the tram route towards the Acropolis.
The east side of the town was protected by fortifications on Castle Hill. Another river flowed into the port on the east side of Castle Hill. Engravings suggest that the port area was defended by walls. Under Monoprix in Place de Garibaldi are excavated remains of a well-defended city gate on the main road from Turin. In 1388 the commune placed itself under the protection of the Counts of Savoy. Nice participated – directly or indirectly – in the history of Savoy until 1860; the maritime strength of Nice now increased until it was able to cope with the Barbary pirates. In 1561 Emmanuel Philibert, Duke of Savoy abolished the use of Latin as an administrative language and established the Italian language as the official language of government affairs in Nice. During the struggle between Francis I and Charles V great damage was caused by the passage of the armies invading Provence. In 1538, in the nearby town of Villeneuve-Loubet, through the mediation of Pope Paul III, the two monarchs concluded a ten years' truce.
In 1543, Nice was attacked by the united Franco-Ottoman forces of Francis I and Barbarossa Hayreddin Pasha, in the Siege of Nice. Pestilence appeared again in 1550 and 1580. In 1600, Nice was taken by the Duke of Guise. By opening the ports of the county to all nations, proclaiming full freedom of trade, the commerce of the city was given great stimulu
Louis XVI of France
Louis XVI, born Louis-Auguste, was the last King of France before the fall of the monarchy during the French Revolution. He was referred to as Citizen Louis Capet during the four months. In 1765, at the death of his father, Louis and heir apparent of Louis XV, Louis-Auguste became the new Dauphin of France. Upon his grandfather's death on 10 May 1774, he assumed the title "King of France and Navarre", which he used until 4 September 1791, when he received the title of "King of the French" until the monarchy was abolished on 21 September 1792; the first part of his reign was marked by attempts to reform the French government in accordance with Enlightenment ideas. These included efforts to abolish serfdom, remove the taille, increase tolerance toward non-Catholics; the French nobility reacted to the proposed reforms with hostility, opposed their implementation. Louis implemented deregulation of the grain market, advocated by his economic liberal minister Turgot, but it resulted in an increase in bread prices.
In periods of bad harvests, it would lead to food scarcity. From 1776, Louis XVI supported the North American colonists, who were seeking their independence from Great Britain, realised in the 1783 Treaty of Paris; the ensuing debt and financial crisis contributed to the unpopularity of the Ancien Régime. This led to the convening of the Estates-General of 1789. Discontent among the members of France's middle and lower classes resulted in strengthened opposition to the French aristocracy and to the absolute monarchy, of which Louis and his wife, Queen Marie Antoinette, were viewed as representatives. Increasing tensions and violence were marked by events such as the storming of the Bastille, during which riots in Paris forced Louis to definitively recognize the legislative authority of the National Assembly. Louis XVI was initiated into masonic lodge Trois-Frères à l'Orient de la Cour. Louis's indecisiveness and conservatism led some elements of the people of France to view him as a symbol of the perceived tyranny of the Ancien Régime, his popularity deteriorated progressively.
His disastrous flight to Varennes in June 1791, four months before the constitutional monarchy was declared, seemed to justify the rumors that the king tied his hopes of political salvation to the prospects of foreign intervention. The credibility of the king was undermined, the abolition of the monarchy and the establishment of a republic became an ever-increasing possibility. Despite his lack of popular approbation, Louis XVI did abolish the death penalty for deserters, as well as the labor tax, which had compelled the French lower classes to spend two weeks out of the year working on buildings and roads. In a context of civil and international war, Louis XVI was suspended and arrested at the time of the Insurrection of 10 August 1792, he was tried by the National Convention, found guilty of high treason, executed by guillotine on 21 January 1793, as a desacralized French citizen under the name of "Citizen Louis Capet," in reference to Hugh Capet, the founder of the Capetian dynasty – which the revolutionaries interpreted as Louis's family name.
Louis XVI was the only King of France to be executed, his death brought an end to more than a thousand years of continuous French monarchy. Both of his sons died before the Bourbon Restoration. Louis-Auguste de France, given the title Duc de Berry at birth, was born in the Palace of Versailles. One of seven children, he was the second surviving son of Louis, the Dauphin of France, thus the grandson of Louis XV of France and of his consort, Maria Leszczyńska, his mother was Marie-Josèphe of Saxony, the daughter of Frederick Augustus II of Saxony, Prince-Elector of Saxony and King of Poland. Louis-Auguste was overlooked by his parents who favored his older brother, duc de Bourgogne, regarded as bright and handsome but who died at the age of nine in 1761. Louis-Auguste, a strong and healthy boy but shy, excelled in his studies and had a strong taste for Latin, history and astronomy and became fluent in Italian and English, he enjoyed physical activities such as hunting with his grandfather and rough play with his younger brothers, Louis-Stanislas, comte de Provence, Charles-Philippe, comte d'Artois.
From an early age, Louis-Auguste was encouraged in another of his interests, seen as a useful pursuit for a child. Upon the death of his father, who died of tuberculosis on 20 December 1765, the eleven-year-old Louis-Auguste became the new Dauphin, his mother never recovered from the loss of her husband and died on 13 March 1767 from tuberculosis. The strict and conservative education he received from the Duc de La Vauguyon, "gouverneur des Enfants de France", from 1760 until his marriage in 1770, did not prepare him for the throne that he was to inherit in 1774 after the death of his grandfather, Louis XV. Throughout his education, Louis-Auguste received a mixture of studies particular to religion and humanities, his instructors may have had a good hand in shaping Louis-Auguste into the indecisive king that he became. Abbé Berthier, his instructor, taught him that timidity was a value in strong monarchs, Abbé Soldini, his confessor, instructed him not to let people read his mind. On 16 May 1770, at the ag
Jardin du Luxembourg
The Jardin du Luxembourg known in English as the Luxembourg Gardens, is located in the 6th arrondissement of Paris, France. It was created beginning in 1612 by Marie de' Medici, the widow of King Henry IV of France, for a new residence she constructed, the Luxembourg Palace; the garden today is owned by the French Senate. It covers 23 hectares and is known for its lawns, tree-lined promenades, model sailboats on its circular basin, picturesque Medici Fountain, built in 1620.. The name Luxembourg comes from the Latin Mons Lucotitius, the name of the hill where the garden is located. In 1611, Marie de' Medici, the widow of Henry IV and the regent for the King Louis XIII decided to build a palace in imitation of the Pitti Palace in her native Florence, she began construction of the new palace. She commissioned Salomon de Brosse to build a fountain, which still exists. In 1612 she planted 2,000 elm trees, directed a series of gardeners, most notably Tommaso Francini, to build a park in the style she had known as a child in Florence.
Francini planned two terraces with balustrades and parterres laid out along the axis of the chateau, aligned around a circular basin. He built the Medici Fountain to the east of the palace as a nympheum, an artificial grotto and fountain, without its present pond and statuary; the original garden was just eight hectares in size. In 1630 she bought additional land and enlarged the garden to thirty hectares, entrusted the work to Jacques Boyceau de la Barauderie, the indendant of the royal gardens of Tuileries and the early garden of Versailles, he was one of the early theorists of the new and more formal garden à la française, he laid out a series of squares along an east-west alley closed at the east end by the Medici Fountain, a rectangle of parterres with broderies of flowers and hedges in front of the palace. In the center he placed an octagonal basin with a fountain, with a perspective toward what is now the Paris observatory. Monarchs neglected the garden. In 1780, the Comte de Provence, the future Louis XVIII, sold the eastern part of the garden for real estate development.
Following the French Revolution, the leaders of the French Directory expanded the garden to forty hectares by confiscating the land of the neighboring religious order of the Carthusian monks. The architect Jean Chalgrin, the architect of the Arc de Triomphe, took on the task of restoring the garden, he laid out a long perspective from the palace to the observatory. He preserved the famous pepiniere, or nursery garden of the Carthusian order, the old vineyards, kept the garden in a formal French style. During and after the July Monarchy of 1848, the park became the home of a large population of statues. In 1865, during the reconstruction of Paris by Louis Napoleon, the rue de l'Abbé de l'Épée, was extended into the park, cutting off about seven hectares, including a large part of the old nursery garden; the building of new streets next to the park required moving and rebuilding the Medici Fountain to its present location. The long basin of the fountain was added at this time, along with the statues at the foot of the fountain.
During this reconstruction, the director of parks and promenades of Paris, Gabriel Davioud, built new ornamental gates and fences around the park, polychrome brick garden houses. He transformed what remained of the old Chartreux nursery garden, at the south end of the park, into an English garden with winding paths, planted a fruit garden in the southwest corner, he kept the regular geometric pattern of the paths and alleys, but did create one diagonal alley near the Medici fountain which opened a view of the Pantheon. The garden in the late nineteenth century contained a marionette theater, a music kiosk, greenhouses, an apiary or bee-house; the garden is devoted to a green parterre of gravel and lawn populated with statues and centred on a large octagonal basin of water, with a central jet of water. The garden is famed for its calm atmosphere. Surrounding the bassin on the raised balustraded terraces are a series of statues of former French queens and copies after the Antique. In the southwest corner, there is an orchard of apple and pear trees and the théâtre des marionnettes.
The gardens include a large fenced-in playground for young children and their parents and a vintage carousel. In addition, free musical performances are presented in a gazebo on the grounds and there is a small cafe restaurant nearby, under the trees, with both indoor and outdoor seating from which many people enjoy the music over a glass of wine; the orangerie displays art and sculptures. The École nationale supérieure des Mines de Paris and the Odéon theatre stand next to the Luxembourg Garden; the central axis of the garden is extended, beyond its wrought iron grill and gates opening to rue Auguste Comte, by the central esplanade of the rue de l'Observatoire the Jardin Marco Polo, where sculptures of the four Times of Day alternate with columns and culminate at the southern end with the 1874 "Fountain of the Observatory" known as the "Fontaine des Quatre-Parties-du-Monde
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university in Cambridge, Massachusetts. Founded in 1861 in response to the increasing industrialization of the United States, MIT adopted a European polytechnic university model and stressed laboratory instruction in applied science and engineering; the Institute is a land-grant, sea-grant, space-grant university, with a campus that extends more than a mile alongside the Charles River. Its influence in the physical sciences and architecture, more in biology, linguistics and social science and art, has made it one of the most prestigious universities in the world. MIT is ranked among the world's top universities; as of March 2019, 93 Nobel laureates, 26 Turing Award winners, 8 Fields Medalists have been affiliated with MIT as alumni, faculty members, or researchers. In addition, 58 National Medal of Science recipients, 29 National Medals of Technology and Innovation recipients, 50 MacArthur Fellows, 73 Marshall Scholars, 45 Rhodes Scholars, 41 astronauts, 16 Chief Scientists of the US Air Force have been affiliated with MIT.
The school has a strong entrepreneurial culture, the aggregated annual revenues of companies founded by MIT alumni would rank as the tenth-largest economy in the world. MIT is a member of the Association of American Universities. In 1859, a proposal was submitted to the Massachusetts General Court to use newly filled lands in Back Bay, Boston for a "Conservatory of Art and Science", but the proposal failed. A charter for the incorporation of the Massachusetts Institute of Technology, proposed by William Barton Rogers, was signed by the governor of Massachusetts on April 10, 1861. Rogers, a professor from the University of Virginia, wanted to establish an institution to address rapid scientific and technological advances, he did not wish to found a professional school, but a combination with elements of both professional and liberal education, proposing that: The true and only practicable object of a polytechnic school is, as I conceive, the teaching, not of the minute details and manipulations of the arts, which can be done only in the workshop, but the inculcation of those scientific principles which form the basis and explanation of them, along with this, a full and methodical review of all their leading processes and operations in connection with physical laws.
The Rogers Plan reflected the German research university model, emphasizing an independent faculty engaged in research, as well as instruction oriented around seminars and laboratories. Two days after MIT was chartered, the first battle of the Civil War broke out. After a long delay through the war years, MIT's first classes were held in the Mercantile Building in Boston in 1865; the new institute was founded as part of the Morrill Land-Grant Colleges Act to fund institutions "to promote the liberal and practical education of the industrial classes" and was a land-grant school. In 1863 under the same act, the Commonwealth of Massachusetts founded the Massachusetts Agricultural College, which developed as the University of Massachusetts Amherst. In 1866, the proceeds from land sales went toward new buildings in the Back Bay. MIT was informally called "Boston Tech"; the institute adopted the European polytechnic university model and emphasized laboratory instruction from an early date. Despite chronic financial problems, the institute saw growth in the last two decades of the 19th century under President Francis Amasa Walker.
Programs in electrical, chemical and sanitary engineering were introduced, new buildings were built, the size of the student body increased to more than one thousand. The curriculum drifted with less focus on theoretical science; the fledgling school still suffered from chronic financial shortages which diverted the attention of the MIT leadership. During these "Boston Tech" years, MIT faculty and alumni rebuffed Harvard University president Charles W. Eliot's repeated attempts to merge MIT with Harvard College's Lawrence Scientific School. There would be at least six attempts to absorb MIT into Harvard. In its cramped Back Bay location, MIT could not afford to expand its overcrowded facilities, driving a desperate search for a new campus and funding; the MIT Corporation approved a formal agreement to merge with Harvard, over the vehement objections of MIT faculty and alumni. However, a 1917 decision by the Massachusetts Supreme Judicial Court put an end to the merger scheme. In 1916, the MIT administration and the MIT charter crossed the Charles River on the ceremonial barge Bucentaur built for the occasion, to signify MIT's move to a spacious new campus consisting of filled land on a mile-long tract along the Cambridge side of the Charles River.
The neoclassical "New Technology" campus was designed by William W. Bosworth and had been funded by anonymous donations from a mysterious "Mr. Smith", starting in 1912. In January 1920, the donor was revealed to be the industrialist George Eastman of Rochester, New York, who had invented methods of film production and processing, founded Eastman Kodak. Between 1912 and 1920, Eastman donated $20 million in cash and Kodak stock to MIT. In the 1930s, President Karl Taylor Compton and Vice-President Vannevar Bush emphasized the importance of pure sciences like physics and chemistry and reduced the vocational practice required in shops and drafting studios; the Compton reforms "renewed confidence in the ability of the Institute to develop leadership in science as well as in engineering". Unlike Ivy League schools, MIT catered more to middle-class families, depended more on tuition than on endow
Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to