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On 21 December 2011 the bank instituted a programme of making low-interest loans with a term of three years (36 months) and 1% interest to European banks accepting loans from the portfolio of the banks as collateral. Loans totalling €489.2 bn (US$640 bn) were announced. The loans were not offered to European states, but government securities issued by European states would be acceptable collateral as would mortgage-backed securities and other commercial paper that can be demonstrated to be secure. The programme was announced on 8 December 2011 but observers were surprised by the volume of the loans made when it was implemented. Under its LTRO it loaned €489bn to 523 banks for an exceptionally long period of three years at a rate of just one percent. The by far biggest amount of €325bn was tapped by banks in Greece, Ireland, Italy and Spain. This way the ECB tried to make sure that banks have enough cash to pay off €200bn of their own maturing debts in the first three months of 2012, and at the same time keep operating and loaning to businesses so that a credit crunch does not choke off economic growth. It also hoped that banks would use some of the money to buy government bonds, effectively easing the debt crisis.
The ECB's first supplementary longer-term refinancing operation (LTRO) with a six-month maturity was announced March 2008. Previously the longest tender offered was three months. It announced two 3-month and one 6-month full allotment of Long Term Refinancing Operations (LTROs). The first tender was settled 3 April, and was more than four times oversubscribed. The €25 billion auction drew bids amounting to €103.1 billion, from 177 banks. Another six-month tender was allotted on 9 July, again to the amount of €25 billion. The first 12-month LTRO in June 2009 had close to 1100 bidders.
St. John's (/ˌseɪntˈdʒɒnz/, local /ˌseɪntˈdʒɑːnz/) is the capital and largest city in Newfoundland and Labrador, Canada. St. John's was incorporated as a city in 1888, yet is considered by some to be the oldest English-founded city in North America. It is located on the eastern tip of the Avalon Peninsula on the island of Newfoundland. With a population of 214,285 as of July 1, 2015, the St. John's Metropolitan Area is the second largest Census Metropolitan Area (CMA) in Atlantic Canada after Halifax and the 20th largest metropolitan area in Canada. It is one of the world's top ten oceanside destinations, according to National Geographic Magazine. Its name has been attributed to the feast day of John the Baptist, when John Cabot was believed to have sailed into the harbour in 1497, and also to a Basque fishing town with the same name.
St. John's is one of the oldest settlements in North America, with year-round settlement beginning sometime after 1630 and seasonal habitation long before that. It is not, however, the oldest surviving English settlement in North America or Canada, having been preceded by the Cuper's Cove colony at Cupids, founded in 1610, and the Bristol's Hope colony at Harbour Grace, founded in 1618. In fact, although English fishermen had begun setting up seasonal camps in Newfoundland in the 16th Century, they were expressly forbidden by the British government, at the urging of the West Country fishing industry, from establishing permanent settlements along the English controlled coast, hence the town of St. John's was not established as a permanent community until after the 1630s at the earliest. Other permanent English settlements in the Americas that predate St. John's include: St. George's, Bermuda (1612) and Jamestown, Virginia (1607).
Sebastian Cabot declares in a handwritten Latin text in his original 1545 map, that the St. John's earned its name when he and his father, the Venetian explorer John Cabot became the first Europeans to sail into the harbour, in the morning of 24 June 1494 (against British and French historians stating 1497), the feast day of Saint John the Baptist. However, the exact locations of Cabot's landfalls are disputed. A series of expeditions to St. John's by Portuguese from the Azores took place in the early 16th century, and by 1540 French, Spanish and Portuguese ships crossed the Atlantic annually to fish the waters off the Avalon Peninsula. In the Basque Country, it is a common belief that the name of St. John's was given by Basque fishermen because the bay of St. John's is very similar to the Bay of Pasaia in the Basque Country, where one of the fishing towns is also called St. John (in Spanish, San Juan, and in Basque, Donibane).
The earliest record of the location appears as São João on a Portuguese map by Pedro Reinel in 1519. When John Rut visited St. John's in 1527 he found Norman, Breton and Portuguese ships in the harbour. On 3 August 1527, Rut wrote a letter to King Henry on the findings of his voyage to North America; this was the first known letter sent from North America. St. Jehan is shown on Nicholas Desliens' world map of 1541 and San Joham is found in João Freire's Atlas of 1546. It was during this time that Water Street was first developed, making it the oldest street in North America.[dubious – discuss]
By 1620, the fishermen of England's West Country controlled most of Newfoundland's east coast. In 1627, William Payne, called St. John's "the principal prime and chief lot in all the whole country". The population grew slowly in the 17th century and St. John's was the largest settlement in Newfoundland when English naval officers began to take censuses around 1675. The population would grow in the summers with the arrival of migratory fishermen. In 1680, fishing ships (mostly from South Devon) set up fishing rooms at St. John's, bringing hundreds of Irish men into the port to operate inshore fishing boats.
The town's first significant defences were likely erected due to commercial interests, following the temporary seizure of St. John's by the Dutch admiral Michiel de Ruyter in June 1665. The inhabitants were able to fend off a second Dutch attack in 1673, when this time it was defended by Christopher Martin, an English merchant captain. Martin landed six cannons from his vessel, the Elias Andrews, and constructed an earthen breastwork and battery near chain Rock commanding the Narrows leading into the harbour. With only twenty-three men, the valiant Martin beat off an attack by three Dutch warships. The English government planned to expand these fortifications (Fort William) in around 1689, but actual construction didn't begin until after the French admiral Pierre Le Moyne d'Iberville captured and destroyed the town in the Avalon Peninsula Campaign (1696). When 1500 English reinforcements arrived in late 1697 they found nothing but rubble where the town and fortifications had stood.
St. John's was the starting point for the first non-stop transatlantic aircraft flight, by Alcock and Brown in a modified Vickers Vimy IV bomber, in June 1919, departing from Lester's Field in St. John's and ending in a bog near Clifden, Connemara, Ireland. In July 2005, the flight was duplicated by American aviator and adventurer Steve Fossett in a replica Vickers Vimy aircraft, with St. John's International Airport substituting for Lester's Field (now an urban and residential part of the city).
St. John's, and the province as a whole, was gravely affected in the 1990s by the collapse of the Northern cod fishery, which had been the driving force of the provincial economy for hundreds of years. After a decade of high unemployment rates and depopulation, the city's proximity to the Hibernia, Terra Nova and White Rose oil fields has led to an economic boom that has spurred population growth and commercial development. As a result, the St. John's area now accounts for about half of the province's economic output.
St. John's is located along the coast of the Atlantic Ocean, on the northeast of the Avalon Peninsula in southeast Newfoundland. The city covers an area of 446.04 square kilometres (172.22 sq mi) and is the most easterly city in North America, excluding Greenland; it is 295 miles (475 km) closer to London, England than it is to Edmonton, Alberta. The city of St. John's is located at a distance by air of 3,636 kilometres (2,259 mi) from Lorient, France which lies on a nearly precisely identical latitude across the Atlantic on the French western coast. The city is the largest in the province and the second largest in the Atlantic Provinces after Halifax, Nova Scotia. Its downtown area lies to the west and north of St. John's Harbour, and the rest of the city expands from the downtown to the north, south, east and west.
St. John's has a humid continental climate (Köppen Dfb), with lower seasonal variation than normal for the latitude, which is due to Gulf Stream moderation. However, despite this maritime moderation, average January high temperatures are actually slightly colder in St. John's than it is in Kelowna, British Columbia, which is an inland city that is near the more marine air of the Pacific, demonstrating the cold nature of Eastern Canada. Mean temperatures range from −4.9 °C (23.2 °F) in February to 16.1 °C (61.0 °F) in August, showing somewhat of a seasonal lag in the climate. The city is also one of the areas of the country most prone to tropical cyclone activity, as it is bordered by the Atlantic Ocean to the east, where tropical storms (and sometimes hurricanes) travel from the United States. The city is one of the rainiest in Canada outside of coastal British Columbia. This is partly due to its propensity for tropical storm activity as well as moist, Atlantic air frequently blowing ashore and creating precipitation.
Of major Canadian cities, St. John's is the foggiest (124 days), windiest (24.3 km/h (15.1 mph) average speed), and cloudiest (1,497 hours of sunshine). St. John's experiences milder temperatures during the winter season in comparison to other Canadian cities, and has the mildest winter for any Canadian city outside of British Columbia. Precipitation is frequent and often heavy, falling year round. On average, summer is the driest season, with only occasional thunderstorm activity, and the wettest months are from October to January, with December the wettest single month, with nearly 165 millimetres of precipitation on average. This winter precipitation maximum is quite unusual for humid continental climates, which most commonly have a late spring or early summer precipitation maximum (for example, most of the Midwestern U.S.). Most heavy precipitation events in St. John's are the product of intense mid-latitude storms migrating from the Northeastern U.S. and New England states, and these are most common and intense from October to March, bringing heavy precipitation (commonly 4 to 8 centimetres of rainfall equivalent in a single storm), and strong winds. In winter, two or more types of precipitation (rain, freezing rain, sleet and snow) can fall from passage of a single storm. Snowfall is heavy, averaging nearly 335 centimetres per winter season. However, winter storms can bring changing precipitation types. Heavy snow can transition to heavy rain, melting the snow cover, and possibly back to snow or ice (perhaps briefly) all in the same storm, resulting in little or no net snow accumulation. Snow cover in St. John's is variable, and especially early in the winter season, may be slow to develop, but can extend deeply into the spring months (March, April). The St. John's area is subject to freezing rain (called "silver thaws"), the worst of which paralyzed the city over a three-day period in April 1984.
Starting as a fishing outpost for European fishermen, St. John's consisted mostly of the homes of fishermen, sheds, storage shacks, and wharves constructed out of wood. Like many other cities of the time, as the Industrial Revolution took hold and new methods and materials for construction were introduced, the landscape changed as the city grew in width and height. The Great Fire of 1892 destroyed most of the downtown core, and most residential and other wood-frame buildings date from this period.
Often compared to San Francisco due to the hilly terrain and steep maze of residential streets, housing in St. John's is typically painted in bright colours. The city council has implemented strict heritage regulations in the downtown area, including restrictions on the height of buildings. These regulations have caused much controversy over the years. With the city experiencing an economic boom a lack of hotel rooms and office space has seen proposals put forward that do not meet the current height regulations. Heritage advocates argue that the current regulations should be enforced while others believe the regulations should be relaxed to encourage economic development.
To meet the need for more office space downtown without compromising the city's heritage, the city council amended heritage regulations, which originally restricted height to 15 metres in the area of land on Water Street between Bishop's Cove and Steer's Cove, to create the "Commercial Central Retail – West Zone". The new zone will allow for buildings of greater height. A 47-metre, 12-storey office building, which includes retail space and a parking garage, was the first building to be approved in this area.
As of the 2006 Census, there were 100,646 inhabitants in St. John's itself, 151,322 in the urban area and 181,113 in the St. John's Census Metropolitan Area (CMA). Thus, St. John's is Newfoundland and Labrador's largest city and Canada's 20th largest CMA. Apart from St. John's, the CMA includes 12 other communities: the city of Mount Pearl and the towns of Conception Bay South, Paradise, Portugal Cove-St. Philip's, Torbay, Logy Bay-Middle Cove-Outer Cove, Pouch Cove, Flatrock, Bay Bulls, Witless Bay, Petty Harbour-Maddox Cove and Bauline. The population of the CMA was 192,326 as of 1 July 2010.
Predominantly Christian, the population of St. John's was once divided along sectarian (Catholic/Protestant) lines. In recent years, this sectarianism has declined significantly, and is no longer a commonly acknowledged facet of life in St. John's. St. John's is the seat of the Roman Catholic Archbishop of St. John's, and the Anglican Bishop of Eastern Newfoundland and Labrador. All major Christian sects showed a decline from 2001–2011 with a large increase in those with no religion from 3.9% to 11.1%.
St. John's economy is connected to both its role as the provincial capital of Newfoundland and Labrador and to the ocean. The civil service which is supported by the federal, provincial and municipal governments has been the key to the expansion of the city's labour force and to the stability of its economy, which supports a sizable retail, service and business sector. The provincial government is the largest employer in the city, followed by Memorial University. With the collapse of the fishing industry in Newfoundland and Labrador in the 1990s, the role of the ocean is now tied to what lies beneath it – oil and gas – as opposed to what swims in or travels across it. The city is the centre of the oil and gas industry in Eastern Canada and is one of 19 World Energy Cities. ExxonMobil Canada is headquartered in St. John's and companies such as Chevron, Husky Energy, Suncor Energy and Statoil have major regional operations in the city. Three major offshore oil developments, Hibernia, Terra Nova and White Rose, are in production off the coast of the city and a fourth development, Hebron, is expected to be producing oil by 2017.
The economy has been growing quickly in recent years. In both 2010 and 2011, the metro area's gross domestic product (GDP) led 27 other metropolitan areas in the country, according to the Conference Board of Canada, recording growth of 6.6 per cent and 5.8 per cent respectively. At $52,000 the city's per capita GDP is the second highest out of all major Canadian cities. Economic forecasts suggest that the city will continue its strong economic growth in the coming years not only in the "oceanic" industries mentioned above, but also in tourism and new home construction as the population continues to grow. In May 2011, the city's unemployment rate fell to 5.6 per cent, the second lowest unemployment rate for a major city in Canada.
The LSPU Hall is home to the Resource Centre for the Arts. The "Hall" hosts a vibrant and diverse arts community and is regarded as the backbone of artistic infrastructure and development in the downtown. The careers of many well-known Newfoundland artists were launched there including Rick Mercer, Mary Walsh, Cathy Jones, Andy Jones and Greg Thomey. The St. John's Arts and Culture Centre houses an art gallery, libraries and a 1000-seat theatre, which is the city's major venue for entertainment productions.
Pippy Park is an urban park located in the east end of the city; with over 3,400 acres (14 km2) of land, it is one of Canada's largest urban parks. The park contains a range of recreational facilities including two golf courses, Newfoundland and Labrador's largest serviced campground, walking and skiing trails as well as protected habitat for many plants and animals. Pippy Park is also home to the Fluvarium, an environmental education centre which offers a cross section view of Nagle's Hill Brook.
Bannerman Park is a Victorian-style park located near the downtown. The park was officially opened in 1891 by Sir Alexander Bannerman, Governor of the Colony of Newfoundland who donated the land to create the park. Today the park contains a public swimming pool, playground, a baseball diamond and many large open grassy areas. Bannerman Park plays host to many festivals and sporting events, most notably the Newfoundland and Labrador Folk Festival and St. John's Peace-a-chord. The park is also the finishing location for the annual Tely 10 Mile Road Race.
Signal Hill is a hill which overlooks the city of St. John's. It is the location of Cabot Tower which was built in 1897 to commemorate the 400th anniversary of John Cabot's discovery of Newfoundland, and Queen Victoria's Diamond Jubilee. The first transatlantic wireless transmission was received here by Guglielmo Marconi on 12 December 1901. Today, Signal Hill is a National Historic Site of Canada and remains incredibly popular amongst tourists and locals alike; 97% of all tourists to St. John's visit Signal Hill. Amongst its popular attractions are the Signal Hill Tattoo, showcasing the Royal Newfoundland Regiment of foot, c. 1795, and the North Head Trail which grants an impressive view of the Atlantic Ocean and the surrounding coast.
The rugby union team The Rock is the Eastern Canadian entry in the Americas Rugby Championship. The Rock play their home games at Swilers Rugby Park, as did the Rugby Canada Super League champions for 2005 and 2006, the Newfoundland Rock. The city hosted a Rugby World Cup qualifying match between Canada and the USA on 12 August 2006, where the Canadians heavily defeated the USA 56–7 to qualify for the 2007 Rugby World Cup finals in France. The 2007 age-grade Rugby Canada National Championship Festival was held in the city.
St. John's served as the capital city of the Colony of Newfoundland and the Dominion of Newfoundland before Newfoundland became Canada's tenth province in 1949. The city now serves as the capital of Newfoundland and Labrador, therefore the provincial legislature is located in the city. The Confederation Building, located on Confederation Hill, is home to the House of Assembly along with the offices for the Members of the House of Assembly (MHAs) and Ministers. The city is represented by ten MHAs, four who are members of the governing Progressive Conservative Party, three that belong to the New Democratic Party (NDP), and three that belong to the Liberal Party. Lorraine Michael, leader of the NDP since 2006, represents the district of Signal Hill-Quidi Vidi.
St. John's has traditionally been one of the safest cities in Canada to live; however, in recent years crime in the city has steadily increased. While nationally crime decreased by 4% in 2009, the total crime rate in St. John's saw an increase of 4%. During this same time violent crime in the city decreased 6%, compared to a 1% decrease nationally. In 2010 the total crime severity index for the city was 101.9, an increase of 10% from 2009 and 19.2% above the national average. The violent crime severity index was 90.1, an increase of 29% from 2009 and 1.2% above the national average. St. John's had the seventh-highest metropolitan crime index and twelfth-highest metropolitan violent crime index in the country in 2010.
St. John's is served by St. John's International Airport (YYT), located 10 minutes northwest of the downtown core. In 2011, roughly 1,400,000 passengers travelled through the airport making it the second busiest airport in Atlantic Canada in passenger volume. Regular destinations include Halifax, Montreal, Ottawa, Toronto, as well as destinations throughout the province. International locations include Dublin, London, New York City, Saint Pierre and Miquelon, Glasgow and Varadero. Scheduled service providers include Air Canada, Air Canada Jazz, Air Saint-Pierre, Air Transat, United Airlines, Porter Airlines, Provincial Airlines, Sunwing Airlines and Westjet.
St. John's is the eastern terminus of the Trans-Canada Highway, one of the longest national highways in the world. The divided highway, also known as "Outer Ring Road" in the city, runs just outside the main part of the city, with exits to Pitts Memorial Drive, Topsail Road, Team Gushue Highway, Thorburn Road, Allandale Road, Portugal Cove Road and Torbay Road, providing relatively easy access to neighbourhoods served by those streets. Pitts Memorial Drive runs from Conception Bay South, through the city of Mount Pearl and into downtown St. John's, with interchanges for Goulds, Water Street and Hamilton Avenue-New Gower Street.
Metrobus Transit is responsible for public transit in the region. Metrobus has a total of 19 routes, 53 buses and an annual ridership of 3,014,073. Destinations include the Avalon Mall, The Village Shopping Centre, Memorial University, Academy Canada, the College of the North Atlantic, the Marine Institute, the Confederation Building, downtown, Stavanger Drive Business Park, Kelsey Drive, Goulds, Kilbride, Shea Heights, the four hospitals in the city as well as other important areas in St. John's and Mount Pearl.
St. John's is served by the Eastern School District, the largest school district in Newfoundland and Labrador by student population. There are currently 36 primary, elementary and secondary schools in the city of St. John's, including three private schools. St. John's also includes one school that is part of the province-wide Conseil Scolaire Francophone (CSF), the Francophone public school district. It also contains two private schools, St. Bonaventure's College and Lakecrest Independent. Atlantic Canada's largest university, Memorial University of Newfoundland (MUN), is located in St. John's. MUN provides comprehensive education and grants degrees in several fields and its historical strengths in engineering, business, geology, and medicine, make MUN one of the top comprehensive universities in Canada. The Fisheries and Marine Institute of Memorial University of Newfoundland (MI) or simply Marine Institute, is a post-secondary ocean and marine polytechnic located in St. John's and is affiliated with Memorial University of Newfoundland. MUN also offers the lowest tuition in Canada ($2,644, per Academic Year)
CJON-DT, known on air as "NTV", is an independent station. The station sublicenses entertainment programming from Global and news programming from CTV and Global, rather than purchasing primary broadcast rights. Rogers Cable has its provincial headquarters in St. John's, and their community channel Rogers TV airs local shows such as Out of the Fog and One Chef One Critic. CBC has its Newfoundland and Labrador headquarters in the city and their television station CBNT-DT broadcasts from University Avenue.
The city is home to 15 am and FM radio stations, two of which are French-language stations. St. John's is the only Canadian city served by radio stations whose call letters do not all begin with the letter C. The ITU prefix VO was assigned to the Dominion of Newfoundland before the province joined Canadian Confederation in 1949, and three AM stations kept their existing call letters. However, other commercial radio stations in St. John's which went to air after 1949 use the same range of prefixes (CF–CK) currently in use elsewhere in Canada, with the exception of VOCM-FM, which was permitted to adopt the VOCM callsign because of its corporate association with the AM station that already bore that callsign. VO also remains in use in amateur radio.
John von Neumann (/vɒn ˈnɔɪmən/; Hungarian: Neumann János Lajos, pronounced [ˈnɒjmɒn ˈjaːnoʃ ˈlɒjoʃ]; December 28, 1903 – February 8, 1957) was a Hungarian-American pure and applied mathematician, physicist, inventor, computer scientist, and polymath. He made major contributions to a number of fields, including mathematics (foundations of mathematics, functional analysis, ergodic theory, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, fluid dynamics and quantum statistical mechanics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics.
He was a pioneer of the application of operator theory to quantum mechanics, in the development of functional analysis, a principal member of the Manhattan Project and the Institute for Advanced Study in Princeton (as one of the few originally appointed), and a key figure in the development of game theory and the concepts of cellular automata, the universal constructor and the digital computer. He published 150 papers in his life; 60 in pure mathematics, 20 in physics, and 60 in applied mathematics. His last work, an unfinished manuscript written while in the hospital, was later published in book form as The Computer and the Brain.
Von Neumann's mathematical analysis of the structure of self-replication preceded the discovery of the structure of DNA. In a short list of facts about his life he submitted to the National Academy of Sciences, he stated "The part of my work I consider most essential is that on quantum mechanics, which developed in Göttingen in 1926, and subsequently in Berlin in 1927–1929. Also, my work on various forms of operator theory, Berlin 1930 and Princeton 1935–1939; on the ergodic theorem, Princeton, 1931–1932."
During World War II he worked on the Manhattan Project with J. Robert Oppenheimer and Edward Teller, developing the mathematical models behind the explosive lenses used in the implosion-type nuclear weapon. After the war, he served on the General Advisory Committee of the United States Atomic Energy Commission, and later as one of its commissioners. He was a consultant to a number of organizations, including the United States Air Force, the Armed Forces Special Weapons Project, and the Lawrence Livermore National Laboratory. Along with theoretical physicist Edward Teller, mathematician Stanislaw Ulam, and others, he worked out key steps in the nuclear physics involved in thermonuclear reactions and the hydrogen bomb.
Von Neumann was born Neumann János Lajos (in Hungarian the family name comes first), Hebrew name Yonah, in Budapest, Kingdom of Hungary, which was then part of the Austro-Hungarian Empire, to wealthy Jewish parents of the Haskalah. He was the eldest of three children. He had two younger brothers: Michael, born in 1907, and Nicholas, who was born in 1911. His father, Neumann Miksa (Max Neumann) was a banker, who held a doctorate in law. He had moved to Budapest from Pécs at the end of the 1880s. Miksa's father and grandfather were both born in Ond (now part of the town of Szerencs), Zemplén County, northern Hungary. John's mother was Kann Margit (Margaret Kann); her parents were Jakab Kann and Katalin Meisels. Three generations of the Kann family lived in spacious apartments above the Kann-Heller offices in Budapest; von Neumann's family occupied an 18-room apartment on the top floor.
In 1913, his father was elevated to the nobility for his service to the Austro-Hungarian Empire by Emperor Franz Joseph. The Neumann family thus acquired the hereditary appellation Margittai, meaning of Marghita. The family had no connection with the town; the appellation was chosen in reference to Margaret, as was those chosen coat of arms depicting three marguerites. Neumann János became Margittai Neumann János (John Neumann of Marghita), which he later changed to the German Johann von Neumann.
Formal schooling did not start in Hungary until the age of ten. Instead, governesses taught von Neumann, his brothers and his cousins. Max believed that knowledge of languages other than Hungarian was essential, so the children were tutored in English, French, German and Italian. By the age of 8, von Neumann was familiar with differential and integral calculus, but he was particularly interested in history, reading his way through Wilhelm Oncken's Allgemeine Geschichte in Einzeldarstellungen. A copy was contained in a private library Max purchased. One of the rooms in the apartment was converted into a library and reading room, with bookshelves from ceiling to floor.
Von Neumann entered the Lutheran Fasori Evangelikus Gimnázium in 1911. This was one of the best schools in Budapest, part of a brilliant education system designed for the elite. Under the Hungarian system, children received all their education at the one gymnasium. Despite being run by the Lutheran Church, the majority of its pupils were Jewish. The school system produced a generation noted for intellectual achievement, that included Theodore von Kármán (b. 1881), George de Hevesy (b. 1885), Leó Szilárd (b. 1898), Eugene Wigner (b. 1902), Edward Teller (b. 1908), and Paul Erdős (b. 1913). Collectively, they were sometimes known as Martians. Wigner was a year ahead of von Neumann at the Lutheran School. When asked why the Hungary of his generation had produced so many geniuses, Wigner, who won the Nobel Prize in Physics in 1963, replied that von Neumann was the only genius.
Although Max insisted von Neumann attend school at the grade level appropriate to his age, he agreed to hire private tutors to give him advanced instruction in those areas in which he had displayed an aptitude. At the age of 15, he began to study advanced calculus under the renowned analyst Gábor Szegő. On their first meeting, Szegő was so astounded with the boy's mathematical talent that he was brought to tears. Some of von Neumann's instant solutions to the problems in calculus posed by Szegő, sketched out on his father's stationery, are still on display at the von Neumann archive in Budapest. By the age of 19, von Neumann had published two major mathematical papers, the second of which gave the modern definition of ordinal numbers, which superseded Georg Cantor's definition. At the conclusion of his education at the gymnasium, von Neumann sat for and won the Eötvös Prize, a national prize for mathematics.
Since there were few posts in Hungary for mathematicians, and those were not well-paid, his father wanted von Neumann to follow him into industry and therefore invest his time in a more financially useful endeavor than mathematics. So it was decided that the best career path was to become a chemical engineer. This was not something that von Neumann had much knowledge of, so it was arranged for him to take a two-year non-degree course in chemistry at the University of Berlin, after which he sat the entrance exam to the prestigious ETH Zurich, which he passed in September 1923. At the same time, von Neumann also entered Pázmány Péter University in Budapest, as a Ph.D. candidate in mathematics. For his thesis, he chose to produce an axiomatization of Cantor's set theory. He passed his final examinations for his Ph.D. soon after graduating from ETH Zurich in 1926. He then went to the University of Göttingen on a grant from the Rockefeller Foundation to study mathematics under David Hilbert.
Von Neumann's habilitation was completed on December 13, 1927, and he started his lectures as a privatdozent at the University of Berlin in 1928. By the end of 1927, von Neumann had published twelve major papers in mathematics, and by the end of 1929, thirty-two papers, at a rate of nearly one major paper per month. His reputed powers of speedy, massive memorization and recall allowed him to recite volumes of information, and even entire directories, with ease. In 1929, he briefly became a privatdozent at the University of Hamburg, where the prospects of becoming a tenured professor were better, but in October of that year a better offer presented itself when he was invited to Princeton University in Princeton, New Jersey.
On New Year's Day in 1930, von Neumann married Mariette Kövesi, who had studied economics at the Budapest University. Before his marriage he was baptized a Catholic. Max had died in 1929. None of the family had converted to Christianity while he was alive, but afterwards they all did. They had one child, a daughter, Marina, who is now a distinguished professor of business administration and public policy at the University of Michigan. The couple divorced in 1937. In October 1938, von Neumann married Klara Dan, whom he had met during his last trips back to Budapest prior to the outbreak of World War II.
In 1933, von Neumann was offered a lifetime professorship on the faculty of the Institute for Advanced Study when the institute's plan to appoint Hermann Weyl fell through. He remained a mathematics professor there until his death, although he announced that shortly before his intention to resign and become a professor at large at the University of California. His mother, brothers and in-laws followed John to the United States in 1939. Von Neumann anglicized his first name to John, keeping the German-aristocratic surname of von Neumann. His brothers changed theirs to "Neumann" and "Vonneumann". Von Neumann became a naturalized citizen of the United States in 1937, and immediately tried to become a lieutenant in the United States Army's Officers Reserve Corps. He passed the exams easily, but was ultimately rejected because of his age. His prewar analysis is often quoted. Asked about how France would stand up to Germany he said "Oh, France won't matter."
Von Neumann liked to eat and drink; his wife, Klara, said that he could count everything except calories. He enjoyed Yiddish and "off-color" humor (especially limericks). He was a non-smoker. At Princeton he received complaints for regularly playing extremely loud German march music on his gramophone, which distracted those in neighbouring offices, including Albert Einstein, from their work. Von Neumann did some of his best work blazingly fast in noisy, chaotic environments, and once admonished his wife for preparing a quiet study for him to work in. He never used it, preferring the couple's living room with its television playing loudly.
Von Neumann's closest friend in the United States was mathematician Stanislaw Ulam. A later friend of Ulam's, Gian-Carlo Rota writes: "They would spend hours on end gossiping and giggling, swapping Jewish jokes, and drifting in and out of mathematical talk." When von Neumann was dying in hospital, every time Ulam would visit he would come prepared with a new collection of jokes to cheer up his friend. He believed that much of his mathematical thought occurred intuitively, and he would often go to sleep with a problem unsolved, and know the answer immediately upon waking up.
The axiomatization of mathematics, on the model of Euclid's Elements, had reached new levels of rigour and breadth at the end of the 19th century, particularly in arithmetic, thanks to the axiom schema of Richard Dedekind and Charles Sanders Peirce, and geometry, thanks to David Hilbert. At the beginning of the 20th century, efforts to base mathematics on naive set theory suffered a setback due to Russell's paradox (on the set of all sets that do not belong to themselves). The problem of an adequate axiomatization of set theory was resolved implicitly about twenty years later by Ernst Zermelo and Abraham Fraenkel. Zermelo–Fraenkel set theory provided a series of principles that allowed for the construction of the sets used in the everyday practice of mathematics. But they did not explicitly exclude the possibility of the existence of a set that belongs to itself. In his doctoral thesis of 1925, von Neumann demonstrated two techniques to exclude such sets—the axiom of foundation and the notion of class.
The axiom of foundation established that every set can be constructed from the bottom up in an ordered succession of steps by way of the principles of Zermelo and Fraenkel, in such a manner that if one set belongs to another then the first must necessarily come before the second in the succession, hence excluding the possibility of a set belonging to itself. To demonstrate that the addition of this new axiom to the others did not produce contradictions, von Neumann introduced a method of demonstration, called the method of inner models, which later became an essential instrument in set theory.
The second approach to the problem took as its base the notion of class, and defines a set as a class which belongs to other classes, while a proper class is defined as a class which does not belong to other classes. Under the Zermelo–Fraenkel approach, the axioms impede the construction of a set of all sets which do not belong to themselves. In contrast, under the von Neumann approach, the class of all sets which do not belong to themselves can be constructed, but it is a proper class and not a set.
With this contribution of von Neumann, the axiomatic system of the theory of sets became fully satisfactory, and the next question was whether or not it was also definitive, and not subject to improvement. A strongly negative answer arrived in September 1930 at the historic mathematical Congress of Königsberg, in which Kurt Gödel announced his first theorem of incompleteness: the usual axiomatic systems are incomplete, in the sense that they cannot prove every truth which is expressible in their language. This result was sufficiently innovative as to confound the majority of mathematicians of the time.
But von Neumann, who had participated at the Congress, confirmed his fame as an instantaneous thinker, and in less than a month was able to communicate to Gödel himself an interesting consequence of his theorem: namely that the usual axiomatic systems are unable to demonstrate their own consistency. However, Gödel had already discovered this consequence, now known as his second incompleteness theorem and sent von Neumann a preprint of his article containing both incompleteness theorems. Von Neumann acknowledged Gödel's priority in his next letter. He never thought much of "the American system of claiming personal priority for everything."
Von Neumann founded the field of continuous geometry. It followed his path-breaking work on rings of operators. In mathematics, continuous geometry is an analogue of complex projective geometry, where instead of the dimension of a subspace being in a discrete set 0, 1, ..., n, it can be an element of the unit interval [0,1]. Von Neumann was motivated by his discovery of von Neumann algebras with a dimension function taking a continuous range of dimensions, and the first example of a continuous geometry other than projective space was the projections of the hyperfinite type II factor.
In a series of famous papers, von Neumann made spectacular contributions to measure theory. The work of Banach had implied that the problem of measure has a positive solution if n = 1 or n = 2 and a negative solution in all other cases. Von Neumann's work argued that the "problem is essentially group-theoretic in character, and that, in particular, for the solvability of the problem of measure the ordinary algebraic concept of solvability of a group is relevant. Thus, according to von Neumann, it is the change of group that makes a difference, not the change of space."
In a number of von Neumann's papers, the methods of argument he employed are considered even more significant than the results. In anticipation of his later study of dimension theory in algebras of operators, von Neumann used results on equivalence by finite decomposition, and reformulated the problem of measure in terms of functions. In his 1936 paper on analytic measure theory, he used the Haar theorem in the solution of Hilbert's fifth problem in the case of compact groups. In 1938, he was awarded the Bôcher Memorial Prize for his work in analysis.
Von Neumann introduced the study of rings of operators, through the von Neumann algebras. A von Neumann algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. The von Neumann bicommutant theorem shows that the analytic definition is equivalent to a purely algebraic definition as an algebra of symmetries. The direct integral was introduced in 1949 by John von Neumann. One of von Neumann's analyses was to reduce the classification of von Neumann algebras on separable Hilbert spaces to the classification of factors.
Von Neumann worked on lattice theory between 1937 and 1939. Von Neumann provided an abstract exploration of dimension in completed complemented modular topological lattices: "Dimension is determined, up to a positive linear transformation, by the following two properties. It is conserved by perspective mappings ("perspectivities") and ordered by inclusion. The deepest part of the proof concerns the equivalence of perspectivity with "projectivity by decomposition"—of which a corollary is the transitivity of perspectivity." Garrett Birkhoff writes: "John von Neumann's brilliant mind blazed over lattice theory like a meteor".
Additionally, "[I]n the general case, von Neumann proved the following basic representation theorem. Any complemented modular lattice L having a "basis" of n≥4 pairwise perspective elements, is isomorphic with the lattice ℛ(R) of all principal right-ideals of a suitable regular ring R. This conclusion is the culmination of 140 pages of brilliant and incisive algebra involving entirely novel axioms. Anyone wishing to get an unforgettable impression of the razor edge of von Neumann's mind, need merely try to pursue this chain of exact reasoning for himself—realizing that often five pages of it were written down before breakfast, seated at a living room writing-table in a bathrobe."
Von Neumann was the first to establish a rigorous mathematical framework for quantum mechanics, known as the Dirac–von Neumann axioms, with his 1932 work Mathematical Foundations of Quantum Mechanics. After having completed the axiomatization of set theory, he began to confront the axiomatization of quantum mechanics. He realized, in 1926, that a state of a quantum system could be represented by a point in a (complex) Hilbert space that, in general, could be infinite-dimensional even for a single particle. In this formalism of quantum mechanics, observable quantities such as position or momentum are represented as linear operators acting on the Hilbert space associated with the quantum system.
The physics of quantum mechanics was thereby reduced to the mathematics of Hilbert spaces and linear operators acting on them. For example, the uncertainty principle, according to which the determination of the position of a particle prevents the determination of its momentum and vice versa, is translated into the non-commutativity of the two corresponding operators. This new mathematical formulation included as special cases the formulations of both Heisenberg and Schrödinger. When Heisenberg was informed von Neumann had clarified the difference between an unbounded operator that was a Self-adjoint operator and one that was merely symmetric, Heisenberg replied "Eh? What is the difference?"
Von Neumann's abstract treatment permitted him also to confront the foundational issue of determinism versus non-determinism, and in the book he presented a proof that the statistical results of quantum mechanics could not possibly be averages of an underlying set of determined "hidden variables," as in classical statistical mechanics. In 1966, John S. Bell published a paper arguing that the proof contained a conceptual error and was therefore invalid. However, in 2010, Jeffrey Bub argued that Bell had misconstrued von Neumann's proof, and pointed out that the proof, though not valid for all hidden variable theories, does rule out a well-defined and important subset. Bub also suggests that von Neumann was aware of this limitation, and that von Neumann did not claim that his proof completely ruled out hidden variable theories.
In a chapter of The Mathematical Foundations of Quantum Mechanics, von Neumann deeply analyzed the so-called measurement problem. He concluded that the entire physical universe could be made subject to the universal wave function. Since something "outside the calculation" was needed to collapse the wave function, von Neumann concluded that the collapse was caused by the consciousness of the experimenter (although this view was accepted by Eugene Wigner, the Von Neumann–Wigner interpretation never gained acceptance amongst the majority of physicists).
In a famous paper of 1936 with Garrett Birkhoff, the first work ever to introduce quantum logics, von Neumann and Birkhoff first proved that quantum mechanics requires a propositional calculus substantially different from all classical logics and rigorously isolated a new algebraic structure for quantum logics. The concept of creating a propositional calculus for quantum logic was first outlined in a short section in von Neumann's 1932 work, but in 1936, the need for the new propositional calculus was demonstrated through several proofs. For example, photons cannot pass through two successive filters that are polarized perpendicularly (e.g., one horizontally and the other vertically), and therefore, a fortiori, it cannot pass if a third filter polarized diagonally is added to the other two, either before or after them in the succession, but if the third filter is added in between the other two, the photons will, indeed, pass through. This experimental fact is translatable into logic as the non-commutativity of conjunction . It was also demonstrated that the laws of distribution of classical logic, and , are not valid for quantum theory.
Von Neumann founded the field of game theory as a mathematical discipline. Von Neumann proved his minimax theorem in 1928. This theorem establishes that in zero-sum games with perfect information (i.e. in which players know at each time all moves that have taken place so far), there exists a pair of strategies for both players that allows each to minimize his maximum losses, hence the name minimax. When examining every possible strategy, a player must consider all the possible responses of his adversary. The player then plays out the strategy that will result in the minimization of his maximum loss.
The reason for this is that a quantum disjunction, unlike the case for classical disjunction, can be true even when both of the disjuncts are false and this is, in turn, attributable to the fact that it is frequently the case, in quantum mechanics, that a pair of alternatives are semantically determinate, while each of its members are necessarily indeterminate. This latter property can be illustrated by a simple example. Suppose we are dealing with particles (such as electrons) of semi-integral spin (angular momentum) for which there are only two possible values: positive or negative. Then, a principle of indetermination establishes that the spin, relative to two different directions (e.g., x and y) results in a pair of incompatible quantities. Suppose that the state ɸ of a certain electron verifies the proposition "the spin of the electron in the x direction is positive." By the principle of indeterminacy, the value of the spin in the direction y will be completely indeterminate for ɸ. Hence, ɸ can verify neither the proposition "the spin in the direction of y is positive" nor the proposition "the spin in the direction of y is negative." Nevertheless, the disjunction of the propositions "the spin in the direction of y is positive or the spin in the direction of y is negative" must be true for ɸ. In the case of distribution, it is therefore possible to have a situation in which , while .
Such strategies, which minimize the maximum loss for each player, are called optimal. Von Neumann showed that their minimaxes are equal (in absolute value) and contrary (in sign). Von Neumann improved and extended the minimax theorem to include games involving imperfect information and games with more than two players, publishing this result in his 1944 Theory of Games and Economic Behavior (written with Oskar Morgenstern). Morgenstern wrote a paper on game theory and thought he would show it to von Neumann because of his interest in the subject. He read it and said to Morgenstern that he should put more in it. This was repeated a couple of times, and then von Neumann became a coauthor and the paper became 100 pages long. Then it became a book. The public interest in this work was such that The New York Times ran a front-page story. In this book, von Neumann declared that economic theory needed to use functional analytic methods, especially convex sets and topological fixed-point theorem, rather than the traditional differential calculus, because the maximum-operator did not preserve differentiable functions.
Von Neumann raised the intellectual and mathematical level of economics in several stunning publications. For his model of an expanding economy, von Neumann proved the existence and uniqueness of an equilibrium using his generalization of the Brouwer fixed-point theorem. Von Neumann's model of an expanding economy considered the matrix pencil A − λB with nonnegative matrices A and B; von Neumann sought probability vectors p and q and a positive number λ that would solve the complementarity equation
along with two inequality systems expressing economic efficiency. In this model, the (transposed) probability vector p represents the prices of the goods while the probability vector q represents the "intensity" at which the production process would run. The unique solution λ represents the growth factor which is 1 plus the rate of growth of the economy; the rate of growth equals the interest rate. Proving the existence of a positive growth rate and proving that the growth rate equals the interest rate were remarkable achievements, even for von Neumann.
Von Neumann's results have been viewed as a special case of linear programming, where von Neumann's model uses only nonnegative matrices. The study of von Neumann's model of an expanding economy continues to interest mathematical economists with interests in computational economics. This paper has been called the greatest paper in mathematical economics by several authors, who recognized its introduction of fixed-point theorems, linear inequalities, complementary slackness, and saddlepoint duality. In the proceedings of a conference on von Neumann's growth model, Paul Samuelson said that many mathematicians had developed methods useful to economists, but that von Neumann was unique in having made significant contributions to economic theory itself.
Von Neumann's famous 9-page paper started life as a talk at Princeton and then became a paper in Germany, which was eventually translated into English. His interest in economics that led to that paper began as follows: When lecturing at Berlin in 1928 and 1929 he spent his summers back home in Budapest, and so did the economist Nicholas Kaldor, and they hit it off. Kaldor recommended that von Neumann read a book by the mathematical economist Léon Walras. Von Neumann found some faults in that book and corrected them, for example, replacing equations by inequalities. He noticed that Walras's General Equilibrium Theory and Walras' Law, which led to systems of simultaneous linear equations, could produce the absurd result that the profit could be maximized by producing and selling a negative quantity of a product. He replaced the equations by inequalities, introduced dynamic equilibria, among other things, and eventually produced the paper.
Later, von Neumann suggested a new method of linear programming, using the homogeneous linear system of Gordan (1873), which was later popularized by Karmarkar's algorithm. Von Neumann's method used a pivoting algorithm between simplices, with the pivoting decision determined by a nonnegative least squares subproblem with a convexity constraint (projecting the zero-vector onto the convex hull of the active simplex). Von Neumann's algorithm was the first interior point method of linear programming.
Von Neumann made fundamental contributions to mathematical statistics. In 1941, he derived the exact distribution of the ratio of the mean square of successive differences to the sample variance for independent and identically normally distributed variables. This ratio was applied to the residuals from regression models and is commonly known as the Durbin–Watson statistic for testing the null hypothesis that the errors are serially independent against the alternative that they follow a stationary first order autoregression.
Von Neumann made fundamental contributions in exploration of problems in numerical hydrodynamics. For example, with Robert D. Richtmyer he developed an algorithm defining artificial viscosity that improved the understanding of shock waves. A problem was that when computers solved hydrodynamic or aerodynamic problems, they tried to put too many computational grid points at regions of sharp discontinuity (shock waves). The mathematics of artificial viscosity smoothed the shock transition without sacrificing basic physics. Other well known contributions to fluid dynamics included the classic flow solution to blast waves, and the co-discovery of the ZND detonation model of explosives.
Von Neumann's principal contribution to the atomic bomb was in the concept and design of the explosive lenses needed to compress the plutonium core of the Fat Man weapon that was later dropped on Nagasaki. While von Neumann did not originate the "implosion" concept, he was one of its most persistent proponents, encouraging its continued development against the instincts of many of his colleagues, who felt such a design to be unworkable. He also eventually came up with the idea of using more powerful shaped charges and less fissionable material to greatly increase the speed of "assembly".
When it turned out that there would not be enough uranium-235 to make more than one bomb, the implosive lens project was greatly expanded and von Neumann's idea was implemented. Implosion was the only method that could be used with the plutonium-239 that was available from the Hanford Site. He established the design of the explosive lenses required, but there remained concerns about "edge effects" and imperfections in the explosives. His calculations showed that implosion would work if it did not depart by more than 5% from spherical symmetry. After a series of failed attempts with models, this was achieved by George Kistiakowsky, and the construction of the Trinity bomb was completed in July 1945.
Along with four other scientists and various military personnel, von Neumann was included in the target selection committee responsible for choosing the Japanese cities of Hiroshima and Nagasaki as the first targets of the atomic bomb. Von Neumann oversaw computations related to the expected size of the bomb blasts, estimated death tolls, and the distance above the ground at which the bombs should be detonated for optimum shock wave propagation and thus maximum effect. The cultural capital Kyoto, which had been spared the bombing inflicted upon militarily significant cities, was von Neumann's first choice, a selection seconded by Manhattan Project leader General Leslie Groves. However, this target was dismissed by Secretary of War Henry L. Stimson.
On July 16, 1945, with numerous other Manhattan Project personnel, von Neumann was an eyewitness to the first atomic bomb blast, code named Trinity, conducted as a test of the implosion method device, at the bombing range near Alamogordo Army Airfield, 35 miles (56 km) southeast of Socorro, New Mexico. Based on his observation alone, von Neumann estimated the test had resulted in a blast equivalent to 5 kilotons of TNT (21 TJ) but Enrico Fermi produced a more accurate estimate of 10 kilotons by dropping scraps of torn-up paper as the shock wave passed his location and watching how far they scattered. The actual power of the explosion had been between 20 and 22 kilotons. It was in von Neumann's 1944 papers that the expression "kilotons" appeared for the first time. After the war, Robert Oppenheimer remarked that the physicists involved in the Manhattan project had "known sin". Von Neumann's response was that "sometimes someone confesses a sin in order to take credit for it."
Von Neumann continued unperturbed in his work and became, along with Edward Teller, one of those who sustained the hydrogen bomb project. He then collaborated with Klaus Fuchs on further development of the bomb, and in 1946 the two filed a secret patent on "Improvement in Methods and Means for Utilizing Nuclear Energy", which outlined a scheme for using a fission bomb to compress fusion fuel to initiate nuclear fusion. The Fuchs–von Neumann patent used radiation implosion, but not in the same way as is used in what became the final hydrogen bomb design, the Teller–Ulam design. Their work was, however, incorporated into the "George" shot of Operation Greenhouse, which was instructive in testing out concepts that went into the final design. The Fuchs–von Neumann work was passed on, by Fuchs, to the Soviet Union as part of his nuclear espionage, but it was not used in the Soviets' own, independent development of the Teller–Ulam design. The historian Jeremy Bernstein has pointed out that ironically, "John von Neumann and Klaus Fuchs, produced a brilliant invention in 1946 that could have changed the whole course of the development of the hydrogen bomb, but was not fully understood until after the bomb had been successfully made."
In 1950, von Neumann became a consultant to the Weapons Systems Evaluation Group (WSEG), whose function was to advise the Joint Chiefs of Staff and the United States Secretary of Defense on the development and use of new technologies. He also became an adviser to the Armed Forces Special Weapons Project (AFSWP), which was responsible for the military aspects on nuclear weapons.Over the following two years, he also became a consultant to the Central Intelligence Agency (CIA), a member of the influential General Advisory Committee of the Atomic Energy Commission, a consultant to the newly established Lawrence Livermore National Laboratory, and a member of the Scientific Advisory Group of the United States Air Force.
In 1955, von Neumann became a commissioner of the AEC. He accepted this position and used it to further the production of compact hydrogen bombs suitable for Intercontinental ballistic missile delivery. He involved himself in correcting the severe shortage of tritium and lithium 6 needed for these compact weapons, and he argued against settling for the intermediate range missiles that the Army wanted. He was adamant that H-bombs delivered into the heart of enemy territory by an ICBM would be the most effective weapon possible, and that the relative inaccuracy of the missile wouldn't be a problem with an H-bomb. He said the Russians would probably be building a similar weapon system, which turned out to be the case. Despite his disagreement with Oppenheimer over the need for a crash program to develop the hydrogen bomb, he testified on the latter's behalf at the 1954 Oppenheimer security hearing, at which he asserted that Oppenheimer was loyal, and praised him for his helpfulness once the program went ahead.
Shortly before his death, when he was already quite ill, von Neumann headed the United States government's top secret ICBM committee, and it would sometimes meet in his home. Its purpose was to decide on the feasibility of building an ICBM large enough to carry a thermonuclear weapon. Von Neumann had long argued that while the technical obstacles were sizable, they could be overcome in time. The SM-65 Atlas passed its first fully functional test in 1959, two years after his death. The feasibility of an ICBM owed as much to improved, smaller warheads as it did to developments in rocketry, and his understanding of the former made his advice invaluable.
Von Neumann is credited with the equilibrium strategy of mutual assured destruction, providing the deliberately humorous acronym, MAD. (Other humorous acronyms coined by von Neumann include his computer, the Mathematical Analyzer, Numerical Integrator, and Computer—or MANIAC). He also "moved heaven and earth" to bring MAD about. His goal was to quickly develop ICBMs and the compact hydrogen bombs that they could deliver to the USSR, and he knew the Soviets were doing similar work because the CIA interviewed German rocket scientists who were allowed to return to Germany, and von Neumann had planted a dozen technical people in the CIA. The Russians believed that bombers would soon be vulnerable, and they shared von Neumann's view that an H-bomb in an ICBM was the ne plus ultra of weapons, and they believed that whoever had superiority in these weapons would take over the world, without necessarily using them. He was afraid of a "missile gap" and took several more steps to achieve his goal of keeping up with the Soviets:
Von Neumann entered government service (Manhattan Project) primarily because he felt that, if freedom and civilization were to survive, it would have to be because the US would triumph over totalitarianism from Nazism, Fascism and Soviet Communism. During a Senate committee hearing he described his political ideology as "violently anti-communist, and much more militaristic than the norm". He was quoted in 1950 remarking, "If you say why not bomb [the Soviets] tomorrow, I say, why not today? If you say today at five o'clock, I say why not one o'clock?"
Von Neumann was a founding figure in computing. Donald Knuth cites von Neumann as the inventor, in 1945, of the merge sort algorithm, in which the first and second halves of an array are each sorted recursively and then merged. Von Neumann wrote the sorting program for the EDVAC in ink, being 23 pages long; traces can still be seen on the first page of the phrase "TOP SECRET", which was written in pencil and later erased. He also worked on the philosophy of artificial intelligence with Alan Turing when the latter visited Princeton in the 1930s.
Von Neumann's hydrogen bomb work was played out in the realm of computing, where he and Stanislaw Ulam developed simulations on von Neumann's digital computers for the hydrodynamic computations. During this time he contributed to the development of the Monte Carlo method, which allowed solutions to complicated problems to be approximated using random numbers. His algorithm for simulating a fair coin with a biased coin is used in the "software whitening" stage of some hardware random number generators. Because using lists of "truly" random numbers was extremely slow, von Neumann developed a form of making pseudorandom numbers, using the middle-square method. Though this method has been criticized as crude, von Neumann was aware of this: he justified it as being faster than any other method at his disposal, and also noted that when it went awry it did so obviously, unlike methods which could be subtly incorrect. "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin."
While consulting for the Moore School of Electrical Engineering at the University of Pennsylvania on the EDVAC project, von Neumann wrote an incomplete First Draft of a Report on the EDVAC. The paper, whose premature distribution nullified the patent claims of EDVAC designers J. Presper Eckert and John Mauchly, described a computer architecture in which the data and the program are both stored in the computer's memory in the same address space. This architecture is to this day the basis of modern computer design, unlike the earliest computers that were "programmed" using a separate memory device such as a paper tape or plugboard. Although the single-memory, stored program architecture is commonly called von Neumann architecture as a result of von Neumann's paper, the architecture's description was based on the work of J. Presper Eckert and John William Mauchly, inventors of the ENIAC computer at the University of Pennsylvania.
John von Neumann also consulted for the ENIAC project. The electronics of the new ENIAC ran at one-sixth the speed, but this in no way degraded the ENIAC's performance, since it was still entirely I/O bound. Complicated programs could be developed and debugged in days rather than the weeks required for plugboarding the old ENIAC. Some of von Neumann's early computer programs have been preserved. The next computer that von Neumann designed was the IAS machine at the Institute for Advanced Study in Princeton, New Jersey. He arranged its financing, and the components were designed and built at the RCA Research Laboratory nearby. John von Neumann recommended that the IBM 701, nicknamed the defense computer include a magnetic drum. It was a faster version of the IAS machine and formed the basis for the commercially successful IBM 704.
Stochastic computing was first introduced in a pioneering paper by von Neumann in 1953. However, the theory could not be implemented until advances in computing of the 1960s. He also created the field of cellular automata without the aid of computers, constructing the first self-replicating automata with pencil and graph paper. The concept of a universal constructor was fleshed out in his posthumous work Theory of Self Reproducing Automata. Von Neumann proved that the most effective way of performing large-scale mining operations such as mining an entire moon or asteroid belt would be by using self-replicating spacecraft, taking advantage of their exponential growth. His rigorous mathematical analysis of the structure of self-replication (of the semiotic relationship between constructor, description and that which is constructed), preceded the discovery of the structure of DNA. Beginning in 1949, von Neumann's design for a self-reproducing computer program is considered the world's first computer virus, and he is considered to be the theoretical father of computer virology.
Von Neumann's team performed the world's first numerical weather forecasts on the ENIAC computer; von Neumann published the paper Numerical Integration of the Barotropic Vorticity Equation in 1950. Von Neumann's interest in weather systems and meteorological prediction led him to propose manipulating the environment by spreading colorants on the polar ice caps to enhance absorption of solar radiation (by reducing the albedo). thereby inducing global warming. Noting that the Earth was only 6 °F (3.3 °C) colder during the last glacial period, he noted that the burning of coal and oil "a general warming of the Earth by about one degree Fahrenheit."
Von Neumann's ability to instantaneously perform complex operations in his head stunned other mathematicians. Eugene Wigner wrote that, seeing von Neumann's mind at work, "one had the impression of a perfect instrument whose gears were machined to mesh accurately to a thousandth of an inch." Paul Halmos states that "von Neumann's speed was awe-inspiring." Israel Halperin said: "Keeping up with him was ... impossible. The feeling was you were on a tricycle chasing a racing car." Edward Teller wrote that von Neumann effortlessly outdid anybody he ever met, and said "I never could keep up with him". Teller also said "von Neumann would carry on a conversation with my 3-year-old son, and the two of them would talk as equals, and I sometimes wondered if he used the same principle when he talked to the rest of us. Most people avoid thinking if they can, some of us are addicted to thinking, but von Neumann actually enjoyed thinking, maybe even to the exclusion of everything else."
Lothar Wolfgang Nordheim described von Neumann as the "fastest mind I ever met", and Jacob Bronowski wrote "He was the cleverest man I ever knew, without exception. He was a genius." George Pólya, whose lectures at ETH Zürich von Neumann attended as a student, said "Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper." Halmos recounts a story told by Nicholas Metropolis, concerning the speed of von Neumann's calculations, when somebody asked von Neumann to solve the famous fly puzzle:
Herman Goldstine wrote: "One of his remarkable abilities was his power of absolute recall. As far as I could tell, von Neumann was able on once reading a book or article to quote it back verbatim; moreover, he could do it years later without hesitation. He could also translate it at no diminution in speed from its original language into English. On one occasion I tested his ability by asking him to tell me how A Tale of Two Cities started. Whereupon, without any pause, he immediately began to recite the first chapter and continued until asked to stop after about ten or fifteen minutes." Ulam noted that von Neumann's way of thinking might not be visual, but more of an aural one.
"I have sometimes wondered whether a brain like von Neumann's does not indicate a species superior to that of man", said Nobel Laureate Hans Bethe of Cornell University. "It seems fair to say that if the influence of a scientist is interpreted broadly enough to include impact on fields beyond science proper, then John von Neumann was probably the most influential mathematician who ever lived," wrote Miklós Rédei in "Selected Letters." James Glimm wrote: "he is regarded as one of the giants of modern mathematics". The mathematician Jean Dieudonné called von Neumann "the last of the great mathematicians", while Peter Lax described him as possessing the "most scintillating intellect of this century".
In 1955, von Neumann was diagnosed with what was either bone or pancreatic cancer. His mother, Margaret von Neumann, was diagnosed with cancer in 1956 and died within two weeks. John had eighteen months from diagnosis till death. In this period von Neumann returned to the Roman Catholic faith that had also been significant to his mother after the family's conversion in 1929–1930. John had earlier said to his mother, "There is probably a God. Many things are easier to explain if there is than if there isn't." Von Neumann held on to his exemplary knowledge of Latin and quoted to a deathbed visitor the declamation "Judex ergo cum sedebit," and ends "Quid sum miser tunc dicturus? Quem patronum rogaturus, Cum vix iustus sit securus?" (When the judge His seat hath taken ... What shall wretched I then plead? Who for me shall intercede when the righteous scarce is freed?)
He invited a Roman Catholic priest, Father Anselm Strittmatter, O.S.B., to visit him for consultation. Von Neumann reportedly said in explanation that Pascal had a point, referring to Pascal's Wager. Father Strittmatter administered the last sacraments to him. Some of von Neumann's friends (such as Abraham Pais and Oskar Morgenstern) said they had always believed him to be "completely agnostic." "Of this deathbed conversion, Morgenstern told Heims, "He was of course completely agnostic all his life, and then he suddenly turned Catholic—it doesn't agree with anything whatsoever in his attitude, outlook and thinking when he was healthy." Father Strittmatter recalled that von Neumann did not receive much peace or comfort from it, as he still remained terrified of death.
The console was first officially announced at E3 2005, and was released at the end of 2006. It was the first console to use Blu-ray Disc as its primary storage medium. The console was the first PlayStation to integrate social gaming services, included it being the first to introduce Sony's social gaming service, PlayStation Network, and its remote connectivity with PlayStation Portable and PlayStation Vita, being able to remote control the console from the devices. In September 2009, the Slim model of the PlayStation 3 was released, being lighter and thinner than the original version, which notably featured a redesigned logo and marketing design, as well as a minor start-up change in software. A Super Slim variation was then released in late 2012, further refining and redesigning the console. As of March 2016, PlayStation 3 has sold 85 million units worldwide. Its successor, the PlayStation 4, was released later in November 2013.
Sony officially unveiled PlayStation 3 (then marketed as PLAYSTATION 3) to the public on May 16, 2005, at E3 2005, along with a 'boomerang' shaped prototype design of the Sixaxis controller. A functional version of the system was not present there, nor at the Tokyo Game Show in September 2005, although demonstrations (such as Metal Gear Solid 4: Guns of the Patriots) were held at both events on software development kits and comparable personal computer hardware. Video footage based on the predicted PlayStation 3 specifications was also shown (notably a Final Fantasy VII tech demo).
The initial prototype shown in May 2005 featured two HDMI ports, three Ethernet ports and six USB ports; however, when the system was shown again a year later at E3 2006, these were reduced to one HDMI port, one Ethernet port and four USB ports, presumably to cut costs. Two hardware configurations were also announced for the console: a 20 GB model and a 60 GB model, priced at US$499 (€499) and US$599 (€599), respectively. The 60 GB model was to be the only configuration to feature an HDMI port, Wi-Fi internet, flash card readers and a chrome trim with the logo in silver. Both models were announced for a simultaneous worldwide release: November 11, 2006, for Japan and November 17, 2006, for North America and Europe.
On September 6, 2006, Sony announced that PAL region PlayStation 3 launch would be delayed until March 2007, because of a shortage of materials used in the Blu-ray drive. At the Tokyo Game Show on September 22, 2006, Sony announced that it would include an HDMI port on the 20 GB system, but a chrome trim, flash card readers, silver logo and Wi-Fi would not be included. Also, the launch price of the Japanese 20 GB model was reduced by over 20%, and the 60 GB model was announced for an open pricing scheme in Japan. During the event, Sony showed 27 playable PS3 games running on final hardware.

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