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118-496: His research has had major significance for theoretical physics as well as purely mathematical disciplines such as number theory . He was one of the most influential mathematicians of the twentieth century, and an important member of the Institute for Advanced Study during its early years. Weyl contributed to an exceptionally wide range of fields, including works on space , time , matter , philosophy , logic , symmetry and

236-435: A mathematical theory , in the sense that the word "theory" has a different meaning in mathematical terms. R i c = k g {\displaystyle \mathrm {Ric} =kg} The equations for an Einstein manifold , used in general relativity to describe the curvature of spacetime A physical theory involves one or more relationships between various measurable quantities. Archimedes realized that

354-539: A working hypothesis . Oxford Oxford ( / ˈ ɒ k s f ər d / ) is a cathedral city and non-metropolitan district in Oxfordshire , England, of which it is the county town. Founded in the 8th century, it was granted city status in 1542. The city is located at the confluence of the rivers Thames (locally known as the Isis ) and Cherwell . It had a population of 163,257 in 2022. It

472-536: A "revolution." This article was far more influential in propagating intuitionistic views than the original works of Brouwer himself. George Pólya and Weyl, during a mathematicians' gathering in Zürich (9 February 1918), made a bet concerning the future direction of mathematics. Weyl predicted that in the subsequent 20 years, mathematicians would come to realize the total vagueness of notions such as real numbers , sets , and countability , and moreover, that asking about

590-505: A 4th edition in 1922. In 1918, he introduced the notion of gauge , and gave the first example of what is now known as a gauge theory . Weyl's gauge theory was an unsuccessful attempt to model the electromagnetic field and the gravitational field as geometrical properties of spacetime . The Weyl tensor in Riemannian geometry is of major importance in understanding the nature of conformal geometry . His overall approach in physics

708-404: A certain economy and elegance (compare to mathematical beauty ), a notion sometimes called " Occam's razor " after the 13th-century English philosopher William of Occam (or Ockham), in which the simpler of two theories that describe the same matter just as adequately is preferred (but conceptual simplicity may mean mathematical complexity). They are also more likely to be accepted if they connect

826-483: A combined capacity of 1,695 seats. Hybrid buses began to be used in Oxford in 2010, and their usage has been expanded. In 2014 Oxford Bus introduced a fleet of 20 new buses with flywheel energy storage on the services it operates under contract for Oxford Brookes University . Most buses in the city now use a smartcard to pay for journeys and have free WiFi installed. The Oxford to London coach route offers

944-405: A debate between Husserlian phenomenology and Fichtean constructivism. In the 1920s, before the development of quantum mechanics and inspired by the statistical nature of quantum theory, which was becoming increasingly clear at the time, Weyl turned away from the field-theoretical description of matter towards a theory of active (agens) matter, which was achieved by including the spatial environment in

1062-528: A few years, Weyl left Göttingen in 1913 for Zürich to take the chair of mathematics at the ETH Zürich , where he was a colleague of Albert Einstein , who was working out the details of the theory of general relativity . Einstein had a lasting influence on Weyl, who became fascinated by mathematical physics. In 1921, Weyl met Erwin Schrödinger , a theoretical physicist who at the time was a professor at

1180-500: A form of protoscience and others are a form of pseudoscience . The falsification of the original theory sometimes leads to reformulation of the theory. "Thought" experiments are situations created in one's mind, asking a question akin to "suppose you are in this situation, assuming such is true, what would follow?". They are usually created to investigate phenomena that are not readily experienced in every-day situations. Famous examples of such thought experiments are Schrödinger's cat ,

1298-412: A form of crystals known as Weyl semimetals , a type of topological material. Weyl had been interested in philosophy since his youth, when he read Immanuel Kant 's "Critique of Pure Reason" with space and time as a priori concepts of knowledge (even if he later disliked Kant's too close ties to Euclidean geometry). From 1912 onwards he was strongly influenced by Edmund Husserl and his phenomenology, which

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1416-693: A frequent coach service to London. The Oxford Tube is operated by Stagecoach West and the Oxford Bus Company runs the Airline services to Heathrow and Gatwick airports. There is a bus station at Gloucester Green , used mainly by the London and airport buses, National Express coaches and other long-distance buses including route X5 to Milton Keynes and Bedford and Stagecoach Gold route S6. Among cities in England and Wales, Oxford has

1534-766: A good example. For instance: " phenomenologists " might employ ( semi- ) empirical formulas and heuristics to agree with experimental results, often without deep physical understanding . "Modelers" (also called "model-builders") often appear much like phenomenologists, but try to model speculative theories that have certain desirable features (rather than on experimental data), or apply the techniques of mathematical modeling to physics problems. Some attempt to create approximate theories, called effective theories , because fully developed theories may be regarded as unsolvable or too complicated . Other theorists may try to unify , formalise, reinterpret or generalise extant theories, or create completely new ones altogether. Sometimes

1652-607: A group-theoretic basis. This included spinors . Together with the mathematical formulation of quantum mechanics , in large measure due to John von Neumann , this gave the treatment familiar since about 1930. Non-compact groups and their representations, particularly the Heisenberg group , were also streamlined in that specific context, in his 1927 Weyl quantization , the best extant bridge between classical and quantum physics to date. From this time, and certainly much helped by Weyl's expositions, Lie groups and Lie algebras became

1770-438: A mainstream part both of pure mathematics and theoretical physics . His book The Classical Groups reconsidered invariant theory . It covered symmetric groups , general linear groups , orthogonal groups , and symplectic groups and results on their invariants and representations . Weyl also showed how to use exponential sums in diophantine approximation , with his criterion for uniform distribution mod 1 , which

1888-411: A mathematical framework within which his vision of a true continuum, not “synthesized” from discrete elements, is realized. Although the underlying logic of smooth infinitesimal analysis is intuitionistic — the law of excluded middle not being generally affirmable — mathematics developed within avoids the “unbearable awkwardness” to which Weyl refers above." In 1929, Weyl proposed an equation, known as

2006-546: A mistake. In November 2022, Mogford announced that his hospitality group The Oxford Collection had joined up with Oxford Business Action Group (OBAG), Oxford High Street Association (OHSA), ROX (Backing Oxford Business), Reconnecting Oxford, Jericho Traders, and Summertown traders to launch a legal challenge to the new bus gates. The city is served by the M40 motorway , which connects London to Birmingham . The M40 approached Oxford in 1974, leading from London to Waterstock , where

2124-498: A new branch of mathematics: infinite, orthogonal series . Modern theoretical physics attempts to unify theories and explain phenomena in further attempts to understand the Universe , from the cosmological to the elementary particle scale. Where experimentation cannot be done, theoretical physics still tries to advance through the use of mathematical models. Mainstream theories (sometimes referred to as central theories ) are

2242-494: A new company, Morrells of Oxford. The new owners sold most of the pubs on to Greene King in 2002. The Lion Brewery was converted into luxury apartments in 2002. Oxford's first legal distillery , the Oxford Artisan Distillery , was established in 2017 in historic farm buildings at the top of South Park . The Taylor family of Loughborough had a bell-foundry in Oxford between 1786 and 1854. This

2360-412: A pristine Stradivarius violin, regarded by some as one of the finest examples in existence. The University Museum of Natural History holds the university's zoological , entomological and geological specimens. It is housed in a large neo-Gothic building on Parks Road , in the university's Science Area . Among its collection are the skeletons of a Tyrannosaurus rex and Triceratops , and

2478-498: A ship floats by displacing its mass of water, Pythagoras understood the relation between the length of a vibrating string and the musical tone it produces. Other examples include entropy as a measure of the uncertainty regarding the positions and motions of unseen particles and the quantum mechanical idea that ( action and) energy are not continuously variable. Theoretical physics consists of several different approaches. In this regard, theoretical particle physics forms

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2596-745: A specialist on Johann Gottlieb Fichte. Fichte's Wissenschaftslehre and philosophy, according to which "being" results from the interaction of the "absolute ego" with its material neighbourhood (Umgebung), is also of great influence on Weyl and is reflected in Weyl's use of the neighbourhood concept of topology (continuum). and in Weyl's conception of the general theory of relativity, alongside the influences of Edmund Husserl's phenomenology known directly from Weyl's writings. According to Sieroka, Weyl also finds influences from Gottfried Wilhelm Leibniz's theory of matter (the theory of monads, etc.) and German idealism (Fichte's dialectic) in Weyl's philosophical interpretation of

2714-463: A third route, also to Paddington, running via Thame , High Wycombe and Maidenhead , was provided; this was shortened in 1906 by the opening of a direct route between High Wycombe and London Paddington by way of Denham . The distance from Oxford to London was 78 miles (125.5 km) via Bletchley; 63.5 miles (102.2 km) via Didcot and Reading; 63.25 miles (101.8 km) via Thame and Maidenhead; and 55.75 miles (89.7 km) via Denham. Only

2832-551: A unified treatment of Riemann surfaces . In it Weyl utilized point set topology , in order to make Riemann surface theory more rigorous, a model followed in later work on manifolds . He absorbed L. E. J. Brouwer's early work in topology for this purpose. Weyl, as a major figure in the Göttingen school, was fully apprised of Einstein's work from its early days. He tracked the development of relativity physics in his Raum, Zeit, Materie ( Space, Time, Matter ) from 1918, reaching

2950-469: A wide range of phenomena. Testing the consequences of a theory is part of the scientific method . Physical theories can be grouped into three categories: mainstream theories , proposed theories and fringe theories . Theoretical physics began at least 2,300 years ago, under the Pre-socratic philosophy , and continued by Plato and Aristotle , whose views held sway for a millennium. During

3068-531: A “symbolic construction”). Weyl's involvement with Martin Heidegger was less well known. Although Weyl did not agree with Heidegger's opinion about death, his conception of neighbourhood (Umgebung) was influenced by Heidegger's Existentialism. Theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict natural phenomena . This

3186-500: Is 2014, with an average of 11.8 °C (53 °F) and the coldest is 1879, with a mean temperature of 7.7 °C (46 °F). The sunniest month on record is May 2020, with 331.7 hours and December 1890 is the least sunny, with 5.0 hours. The greatest one-day rainfall occurred on 10 July 1968, with a total of 87.9 mm (3.46 in). The greatest known snow depth was 61.0 cm (24.0 in) in February 1888. The city centre

3304-650: Is 56 miles (90 km) north-west of London , 64 miles (103 km) south-east of Birmingham and 61 miles (98 km) north-east of Bristol . The city is home to the University of Oxford , the oldest university in the English-speaking world ; it has buildings in every style of English architecture since late Anglo-Saxon . Oxford's industries include motor manufacturing, education, publishing, science, and information technologies. The history of Oxford in England dates back to its original settlement in

3422-497: Is a model of physical events. It is judged by the extent to which its predictions agree with empirical observations. The quality of a physical theory is also judged on its ability to make new predictions which can be verified by new observations. A physical theory differs from a mathematical theorem in that while both are based on some form of axioms , judgment of mathematical applicability is not based on agreement with any experimental results. A physical theory similarly differs from

3540-477: Is a small selection of the many notable buildings in Oxford. Oxford is a very green city, with several parks and nature walks within the ring road , as well as several sites just outside the ring road. In total, 28 nature reserves exist within or just outside the ring road, including: In addition to the larger airports in the region, Oxford is served by nearby Oxford Airport , in Kidlington . The airport

3658-706: Is also home to CAE Oxford Aviation Academy and Airways Aviation airline pilot flight training centres, and several private jet companies. The airport is also home to Airbus Helicopters UK headquarters. Direct trains run from Oxford station to London Paddington where there is an interchange with the Heathrow Express train links serving Heathrow Airport . Passengers can change at Reading for connecting trains to Gatwick Airport . Some CrossCountry trains run direct services to Birmingham International , as well as to Southampton Airport Parkway further afield. Bus services in Oxford and its suburbs are run by

Hermann Weyl - Misplaced Pages Continue

3776-419: Is in contrast to experimental physics , which uses experimental tools to probe these phenomena. The advancement of science generally depends on the interplay between experimental studies and theory . In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations. For example, while developing special relativity , Albert Einstein

3894-466: Is just outside the city, at the park and ride site near Kidlington . The present railway station opened in 1852. Oxford is the junction for a short branch line to Bicester , a remnant of the former Varsity line to Cambridge . This Oxford–Bicester line was upgraded to 100 mph (161 km/h) running during an 18-month closure in 2014/2015 – and is scheduled to be extended to form the planned East West Rail line to Milton Keynes. East West Rail

4012-553: Is now strongly discouraged, and largely prevented, from using the city centre. The Oxford Ring Road or A4142 (southern part) surrounds the city centre and close suburbs Marston , Iffley , Cowley and Headington ; it consists of the A34 to the west, a 330-yard section of the A44 , the A40 north and north-east, A4142/ A423 to the east. It is a dual carriageway , except for a 330-yard section of

4130-508: Is proposed to continue through Bletchley (for Milton Keynes Central ) to Bedford , Cambridge, and ultimately Ipswich and Norwich , thus providing alternative route to East Anglia without needing to travel via, and connect between, the London mainline terminals. Chiltern Railways operates from Oxford to London Marylebone via Bicester Village , having sponsored the building of about 400 metres of new track between Bicester Village and

4248-519: Is relatively small and is centred on Carfax , a crossroads which forms the junction of Cornmarket Street (pedestrianised), Queen Street (mainly pedestrianised ), St Aldate's and the High Street ("the High"; blocked for through traffic). Cornmarket Street and Queen Street are home to Oxford's chain stores, as well as a small number of independent retailers, one of the longest established of which

4366-1093: The Castle Mill Stream . The rapid expansion of Oxford and the development of its railway links after the 1840s facilitated expansion of the brewing trade. As well as expanding the market for Oxford's brewers, railways enabled brewers further from the city to compete for a share of its market. By 1874 there were nine breweries in Oxford and 13 brewers' agents in Oxford shipping beer in from elsewhere. The nine breweries were: Flowers & Co in Cowley Road , Hall's St Giles Brewery, Hall's Swan Brewery (see below), Hanley's City Brewery in Queen Street , Le Mills's Brewery in St. Ebbes , Morrell's Lion Brewery in St Thomas Street (see below), Simonds's Brewery in Queen Street, Weaving's Eagle Brewery (by 1869

4484-557: The Chiltern Main Line southwards in 2014. The route serves High Wycombe and London Marylebone, avoiding London Paddington and Didcot Parkway . In 1844, the Great Western Railway linked Oxford with London Paddington via Didcot and Reading ; in 1851, the London & North Western Railway opened its own route from Oxford to London Euston , via Bicester , Bletchley and Watford ; and in 1864

4602-539: The EPR thought experiment , simple illustrations of time dilation , and so on. These usually lead to real experiments designed to verify that the conclusion (and therefore the assumptions) of the thought experiments are correct. The EPR thought experiment led to the Bell inequalities , which were then tested to various degrees of rigor , leading to the acceptance of the current formulation of quantum mechanics and probabilism as

4720-493: The Oxford Bus Company and Stagecoach West as well as other operators including Arriva Shires & Essex and Thames Travel . Oxford has one of the largest urban park and ride networks in the United Kingdom. Its five sites, at Pear Tree, Redbridge , Seacourt , Thornhill, Water Eaton and Oxford Parkway have a combined capacity of 4,930 car parking spaces, served by 20 Oxford Bus Company double decker buses with

4838-461: The Oxford Star (tabloid; free and delivered), and Oxford Journal (tabloid; weekly free pick-up). Oxford is also home to several advertising agencies . Daily Information (known locally as "Daily Info") is an event information and advertising news sheet which has been published since 1964 and now provides a connected website. Nightshift is a monthly local free magazine that has covered

Hermann Weyl - Misplaced Pages Continue

4956-541: The Princeton Cemetery . The remains of Hermann's son Michael Weyl (1917–2011) are interred right next to Hermann's ashes in the same columbarium vault. Weyl was a pantheist . In 1911 Weyl published Über die asymptotische Verteilung der Eigenwerte ( On the asymptotic distribution of eigenvalues ) in which he proved that the eigenvalues of the Laplacian in the compact domain are distributed according to

5074-818: The Saxon period . Originally of strategic significance due to its controlling location on the upper reaches of the River Thames at its confluence with the River Cherwell , the town grew in national importance during the early Norman period , and in the late 12th century became home to the fledgling University of Oxford . The city was besieged during The Anarchy in 1142. During the Middle Ages Oxford had an important Jewish community, of which David of Oxford and his wife Licoricia of Winchester were prominent members. The university rose to dominate

5192-572: The Scientific Revolution gathered pace, the concepts of matter , energy, space, time and causality slowly began to acquire the form we know today, and other sciences spun off from the rubric of natural philosophy . Thus began the modern era of theory with the Copernican paradigm shift in astronomy, soon followed by Johannes Kepler 's expressions for planetary orbits, which summarized the meticulous observations of Tycho Brahe ;

5310-599: The University of Zürich . They were to become close friends over time. Weyl had some sort of childless love affair with Schrödinger's wife Annemarie (Anny) Schrödinger (née Bertel), while at the same time Anny was helping raise an illegitimate daughter of Erwin's named Ruth Georgie Erica March, who was born in 1934 in Oxford , England. Weyl was a Plenary Speaker of the International Congress of Mathematicians (ICM) in 1928 at Bologna and an Invited Speaker of

5428-529: The Westgate Oxford . The Westgate Centre is named for the original West Gate in the city wall, and is at the west end of Queen Street . A major redevelopment and expansion to 750,000 sq ft (70,000 m ), with a new 230,000 sq ft (21,000 m ) John Lewis department store and a number of new homes, was completed in October 2017. Blackwell's Bookshop is a bookshop which claims

5546-534: The Weyl equation , for use in a replacement to the Dirac equation . This equation describes massless fermions . A normal Dirac fermion could be split into two Weyl fermions or formed from two Weyl fermions. Neutrinos were once thought to be Weyl fermions, but they are now known to have mass. Weyl fermions are sought after for electronics applications. Quasiparticles that behave as Weyl fermions were discovered in 2015, in

5664-437: The history of mathematics . He was one of the first to conceive of combining general relativity with the laws of electromagnetism . Freeman Dyson wrote that Weyl alone bore comparison with the "last great universal mathematicians of the nineteenth century", Poincaré and Hilbert . Michael Atiyah , in particular, has commented that whenever he examined a mathematical topic, he found that Weyl had preceded him. Hermann Weyl

5782-516: The truth or falsity of the least upper bound property of the real numbers was as meaningful as asking about truth of the basic assertions of Hegel on the philosophy of nature. Any answer to such a question would be unverifiable, unrelated to experience, and therefore senseless. However, within a few years Weyl decided that Brouwer's intuitionism did put too great restrictions on mathematics, as critics had always said. The "Crisis" article had disturbed Weyl's formalist teacher Hilbert, but later in

5900-461: The two-fluid theory of electricity are two cases in this point. However, an exception to all the above is the wave–particle duality , a theory combining aspects of different, opposing models via the Bohr complementarity principle . Physical theories become accepted if they are able to make correct predictions and no (or few) incorrect ones. The theory should have, at least as a secondary objective,

6018-576: The 1920s Weyl partially reconciled his position with that of Hilbert. After about 1928 Weyl had apparently decided that mathematical intuitionism was not compatible with his enthusiasm for the phenomenological philosophy of Husserl , as he had apparently earlier thought. In the last decades of his life Weyl emphasized mathematics as "symbolic construction" and moved to a position closer not only to Hilbert but to that of Ernst Cassirer . Weyl however rarely refers to Cassirer, and wrote only brief articles and passages articulating this position. By 1949, Weyl

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6136-815: The 1970s and 1980s, leaving behind a city which had developed far beyond the university town of the past. Oxford's latitude and longitude are 51°45′07″N 1°15′28″W  /  51.75194°N 1.25778°W  / 51.75194; -1.25778 , with Ordnance Survey grid reference SP513061 (at Carfax Tower , which is usually considered the centre). Oxford is 24 miles (39 km) north-west of Reading , 26 miles (42 km) north-east of Swindon , 36 miles (58 km) east of Cheltenham , 43 miles (69 km) east of Gloucester , 29 miles (47 km) south-west of Milton Keynes , 38 miles (61 km) south-east of Evesham , 43 miles (69 km) south of Rugby and 51 miles (82 km) west-north-west of London . The rivers Cherwell and Thames (also sometimes known as

6254-429: The 19th century. Another important event in the 19th century was the discovery of electromagnetic theory , unifying the previously separate phenomena of electricity, magnetism and light. The pillars of modern physics , and perhaps the most revolutionary theories in the history of physics, have been relativity theory and quantum mechanics . Newtonian mechanics was subsumed under special relativity and Newton's gravity

6372-597: The A40 continued to Oxford. When the M40 extension to Birmingham was completed in January 1991, it curved sharply north, and a mile of the old motorway became a spur. The M40 comes no closer than 6 miles (10 km) away from the city centre, curving to pass to the east of Otmoor . The M40 meets the A34 to the north of Oxford. There are two universities in Oxford, the University of Oxford and Oxford Brookes University , as well as

6490-421: The A40 where two residential service roads adjoin, and was completed in 1966. The main roads to/from Oxford are: On 28 February 2022 a zero-emission pilot area became operational in Oxford city centre. Zero-emission vehicles can be used without incurring a charge but all petrol and diesel vehicles (including hybrids) incur a daily charge if they are driven in the zone between 7am and 7pm. A consultation on

6608-476: The Dutchmen Snell and Huygens. In the 18th and 19th centuries Joseph-Louis Lagrange , Leonhard Euler and William Rowan Hamilton would extend the theory of classical mechanics considerably. They picked up the interactive intertwining of mathematics and physics begun two millennia earlier by Pythagoras. Among the great conceptual achievements of the 19th and 20th centuries were the consolidation of

6726-724: The Eagle Steam Brewery) in Park End Street and Wootten and Cole's St. Clement's Brewery. The Swan's Nest Brewery, later the Swan Brewery, was established by the early 18th century in Paradise Street , and in 1795 was acquired by William Hall. The brewery became known as Hall's Oxford Brewery, which acquired other local breweries. Hall's Brewery was acquired by Samuel Allsopp & Sons in 1926, after which it ceased brewing in Oxford. Morrell's

6844-587: The Earth ) or may be an alternative model that provides answers that are more accurate or that can be more widely applied. In the latter case, a correspondence principle will be required to recover the previously known result . Sometimes though, advances may proceed along different paths. For example, an essentially correct theory may need some conceptual or factual revisions; atomic theory , first postulated millennia ago (by several thinkers in Greece and India ) and

6962-749: The ICM in 1936 at Oslo . He was elected a fellow of the American Physical Society in 1928, a member of the American Academy of Arts and Sciences in 1929, a member of the American Philosophical Society in 1935, and a member of the National Academy of Sciences in 1940. For the academic year 1928–1929, he was a visiting professor at Princeton University , where he wrote a paper, "On a problem in

7080-555: The Isis locally, supposedly from the Latinised name Thamesis ) run through Oxford and meet south of the city centre. These rivers and their flood plains constrain the size of the city centre. Oxford has a maritime temperate climate ( Köppen : Cfb ). Precipitation is uniformly distributed throughout the year and is provided mostly by weather systems that arrive from the Atlantic . The lowest temperature ever recorded in Oxford

7198-514: The Oxford music scene since 1991. Oxford is home to many museums , galleries , and collections, most of which are free of admission charges and are major tourist attractions . The majority are departments of the University of Oxford . The first of these to be established was the Ashmolean Museum , the world's first university museum , and the oldest museum in the UK. Its first building

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7316-809: The United Kingdom, after the British Library . The Bodleian Library is a legal deposit library, which means that it is entitled to request a free copy of every book published in the United Kingdom. As such, its collection is growing at a rate of over three miles (five kilometres) of shelving every year. As well as the BBC national radio stations , Oxford and the surrounding area has several local stations, including BBC Radio Oxford , Heart South , Destiny 105 , Greatest Hits Radio and Hits Radio Oxfordshire , along with Oxide: Oxford Student Radio (which went on terrestrial radio at 87.7 MHz FM in late May 2005). A local TV station , Six TV : The Oxford Channel,

7434-419: The applications of relativity to problems in astronomy and cosmology respectively . All of these achievements depended on the theoretical physics as a moving force both to suggest experiments and to consolidate results — often by ingenious application of existing mathematics, or, as in the case of Descartes and Newton (with Leibniz ), by inventing new mathematics. Fourier's studies of heat conduction led to

7552-528: The area is often used by film and TV crews. Aside from the city centre, there are several suburbs and neighbourhoods within the borders of the city of Oxford, including: Oxford is at the centre of the Oxford Green Belt , which is an environmental and planning policy that regulates the rural space in Oxfordshire surrounding the city, aiming to prevent urban sprawl and minimize convergence with nearby settlements. The policy has been blamed for

7670-514: The body of knowledge of both factual and scientific views and possess a usual scientific quality of the tests of repeatability, consistency with existing well-established science and experimentation. There do exist mainstream theories that are generally accepted theories based solely upon their effects explaining a wide variety of data, although the detection, explanation, and possible composition are subjects of debate. The proposed theories of physics are usually relatively new theories which deal with

7788-795: The city of Oxford was a county borough , independent from the county council. Oxford City Council meets at the Town Hall on the street called St Aldate's in the city centre. The current building was completed in 1897, on a site which had been occupied by Oxford's guildhall since the 13th century. Most of Oxford is an unparished area , but there are four civil parishes within the city's boundaries: Blackbird Leys , Littlemore , Old Marston , and Risinghurst and Sandhills . Oxford's economy includes manufacturing, publishing and science-based industries as well as education, sports, entertainment, breweries, research and tourism. Oxford has been an important centre of motor manufacturing since Morris Motors

7906-452: The field theoretical description expressed. He had previously described the general theory of relativity and his own extensions of it, which led to the origin of today's concept of gauge field theories, using differential geometric methods. Under the influence of quantum theory, he turned away from this “geometric field theory”. According to Sieroka, Fichte and Ernst Cassirer were also an important influence in Weyl's late philosophy (science as

8024-416: The highest order, writing Principia Mathematica . In it contained a grand synthesis of the work of Copernicus, Galileo and Kepler; as well as Newton's theories of mechanics and gravitation, which held sway as worldviews until the early 20th century. Simultaneously, progress was also made in optics (in particular colour theory and the ancient science of geometrical optics ), courtesy of Newton, Descartes and

8142-455: The idea of energy (as well as its global conservation) by the inclusion of heat , electricity and magnetism , and then light . The laws of thermodynamics , and most importantly the introduction of the singular concept of entropy began to provide a macroscopic explanation for the properties of matter. Statistical mechanics (followed by statistical physics and Quantum statistical mechanics ) emerged as an offshoot of thermodynamics late in

8260-400: The introduction of a wider zero-emission zone is expected in the future, at a date to be confirmed. Oxford has eight bus gates, short sections of road where only buses and other authorised vehicles can pass. Six further bus gates are currently proposed. A council-led consultation on the traffic filters ended on 13 October 2022. On 29 November 2022, Oxfordshire County Council cabinet approved

8378-494: The introduction on a trial basis, for a minimum period of six months. The trial will begin after improvement works to Oxford railway station are complete, which is expected to be by October 2024. The additional bus gates have been controversial; Oxford University and Oxford Bus Company support the proposals but more than 3,700 people have signed an online petition opposing the new traffic filters for Marston Ferry Road and Hollow Way, and hotelier Jeremy Mogford has argued they would be

8496-493: The large rise in house prices in Oxford, making it the least affordable city in the United Kingdom outside of London, with estate agents calling for brownfield land inside the green belt to be released for new housing. The vast majority of the area covered is outside of the city, but there are some green spaces within that which are covered by the designation, such as much of the Thames and river Cherwell flood-meadows , and

8614-548: The largest single room devoted to book sales in the whole of Europe, the Norrington Room (10,000 sq ft). There is a long history of brewing in Oxford. Several of the colleges had private breweries, one of which, at Brasenose , survived until 1889. In the 16th century brewing and malting appear to have been the most popular trades in the city. There were breweries in Brewer Street and Paradise Street , near

8732-675: The late 1920s. In the aftermath of World War 2, more progress brought much renewed interest in QFT, which had since the early efforts, stagnated. The same period also saw fresh attacks on the problems of superconductivity and phase transitions, as well as the first applications of QFT in the area of theoretical condensed matter. The 1960s and 70s saw the formulation of the Standard model of particle physics using QFT and progress in condensed matter physics (theoretical foundations of superconductivity and critical phenomena , among others ), in parallel to

8850-678: The most complete remains of a dodo found anywhere in the world. It also hosts the Simonyi Professorship of the Public Understanding of Science , currently held by Marcus du Sautoy . Adjoining the Museum of Natural History is the Pitt Rivers Museum , founded in 1884, which displays the university's archaeological and anthropological collections, currently holding over 500,000 items. It recently built

8968-484: The name Helene (nickname "Hella"). Helene was a daughter of Dr. Bruno Joseph (December 13, 1861 – June 10, 1934), a physician who held the position of Sanitätsrat in Ribnitz-Damgarten , Germany. Helene was a philosopher (she was a disciple of phenomenologist Edmund Husserl ) and a translator of Spanish literature into German and English (especially the works of Spanish philosopher José Ortega y Gasset ). It

9086-416: The original ( Didcot ) route is still in use for its full length, portions of the others remain. There were also routes to the north and west. The line to Banbury was opened in 1850, and was extended to Birmingham Snow Hill in 1852; a route to Worcester opened in 1853. A branch to Witney was opened in 1862, which was extended to Fairford in 1873. The line to Witney and Fairford closed in 1962, but

9204-695: The others remain open. Oxford was historically an important port on the River Thames , with this section of the river being called the Isis ; the Oxford-Burcot Commission in the 17th century attempted to improve navigation to Oxford. Iffley Lock and Osney Lock lie within the bounds of the city. In the 18th century the Oxford Canal was built to connect Oxford with the Midlands . Commercial traffic has given way to recreational use of

9322-450: The philosophy of arithmetic and was investigating the sense of mathematical and other structures, which Frege had distinguished from empirical reference. From 1923 to 1938, Weyl developed the theory of compact groups , in terms of matrix representations . In the compact Lie group case he proved a fundamental character formula . These results are foundational in understanding the symmetry structure of quantum mechanics , which he put on

9440-400: The physical concept of matter in the context of quantum theory and general relativity and with regard to interaction of a symbol with its surroundings in a mathematical theory structure also in Weyl's philosophy of mathematics (debate between formalism and intuitionism under the influence of Brouwer). He understands the intra-mathematical debate about intuitionism and formalism along the lines of

9558-594: The political situation in Germany grew worse, he changed his mind and accepted when offered the position again. He remained there until his retirement in 1951. Together with his second wife Ellen, he spent his time in Princeton and Zürich, and died from a heart attack on December 8, 1955, while living in Zürich. Weyl was cremated in Zürich on December 12, 1955. His ashes remained in private hands until 1999, at which time they were interred in an outdoor columbarium vault in

9676-519: The pool of Oxford University students and graduates, and, especially for EFL education , use their Oxford location as a selling point. Oxford has numerous major tourist attractions, many belonging to the university and colleges. As well as several famous institutions, the town centre is home to Carfax Tower and the University Church of St Mary the Virgin, both of which offer views over

9794-419: The process of becoming established and some proposed theories. It can include speculative sciences. This includes physics fields and physical theories presented in accordance with known evidence, and a body of associated predictions have been made according to that theory. Some fringe theories go on to become a widely accepted part of physics. Other fringe theories end up being disproven. Some fringe theories are

9912-469: The radical constructivism of the German romantic, subjective idealist Fichte . Shortly after publishing The Continuum Weyl briefly shifted his position wholly to the intuitionism of Brouwer. In The Continuum , the constructible points exist as discrete entities. Weyl wanted a continuum that was not an aggregate of points. He wrote a controversial article proclaiming, for himself and L. E. J. Brouwer,

10030-607: The rise of medieval universities , the only acknowledged intellectual disciplines were the seven liberal arts of the Trivium like grammar , logic , and rhetoric and of the Quadrivium like arithmetic , geometry , music and astronomy . During the Middle Ages and Renaissance , the concept of experimental science, the counterpoint to theory, began with scholars such as Ibn al-Haytham and Francis Bacon . As

10148-518: The river and canal. Oxford was the original base of Salters Steamers (founded in 1858), which was a leading racing-boatbuilder that played an important role in popularising pleasure boating on the Upper Thames. The firm runs a regular service from Folly Bridge downstream to Abingdon and beyond. Oxford's central location on several transport routes means that it has long been a crossroads city with many coaching inns , although road traffic

10266-458: The second highest percentage of people cycling to work. Oxford railway station is half a mile (about 1 km) west of the city centre. The station is served by CrossCountry services to Bournemouth and Manchester Piccadilly ; Great Western Railway (who manage the station) services to London Paddington , Banbury and Hereford ; and Chiltern Railways services to London Marylebone . Oxford has had three main railway stations. The first

10384-403: The simple laws of classical logic eventually results in an almost unbearable awkwardness. And the mathematician watches with pain the greater part of his towering edifice which he believed to be built of concrete blocks dissolve into mist before his eyes." As John L Bell puts it: "It seems to me a great pity that Weyl did not live to see the emergence in the 1970s of smooth infinitesimal analysis,

10502-413: The so-called Weyl law . In 1912 he suggested a new proof, based on variational principles. Weyl returned to this topic several times, considered elasticity system and formulated the Weyl conjecture . These works started an important domain— asymptotic distribution of eigenvalues—of modern analysis. In 1913, Weyl published Die Idee der Riemannschen Fläche ( The Concept of a Riemann Surface ), which gave

10620-623: The specialist further and higher education institution Ruskin College that is part of the University of West London in Oxford. The Islamic Azad University also has a campus near Oxford. The University of Oxford is the oldest university in the English-speaking world, and one of the most prestigious higher education institutions of the world, averaging nine applications to every available place, and attracting 40% of its academic staff and 17% of undergraduates from overseas. In September 2016, it

10738-532: The spires of the city. Many tourists shop at the historic Covered Market . In the summer, punting on the Thames / Isis and the Cherwell is a common practice. As well as being a major draw for tourists (9.1 million in 2008, similar in 2009) , Oxford city centre has many shops, several theatres and an ice rink. There are two small shopping malls in the city centre: the Clarendon Centre and

10856-484: The study of physics which include scientific approaches, means for determining the validity of models and new types of reasoning used to arrive at the theory. However, some proposed theories include theories that have been around for decades and have eluded methods of discovery and testing. Proposed theories can include fringe theories in the process of becoming established (and, sometimes, gaining wider acceptance). Proposed theories usually have not been tested. In addition to

10974-472: The theories like those listed below, there are also different interpretations of quantum mechanics , which may or may not be considered different theories since it is debatable whether they yield different predictions for physical experiments, even in principle. For example, AdS/CFT correspondence , Chern–Simons theory , graviton , magnetic monopole , string theory , theory of everything . Fringe theories include any new area of scientific endeavor in

11092-559: The theory of groups arising in the foundations of infinitesimal geometry," with Howard P. Robertson . Weyl left Zürich in 1930 to become Hilbert's successor at Göttingen, leaving when the Nazis assumed power in 1933, particularly as his wife was Jewish. He had been offered one of the first faculty positions at the new Institute for Advanced Study in Princeton, New Jersey , but had declined because he did not desire to leave his homeland. As

11210-660: The town. A heavily ecclesiastical town, Oxford was greatly affected by the changes of the English Reformation , emerging as the seat of a bishopric and a full-fledged city. During the English Civil War , Oxford housed the court of Charles I and stood at the heart of national affairs. The city began to grow industrially during the 19th century, and had an industrial boom in the early 20th century, with major printing and car-manufacturing industries. These declined, along with other British heavy industry, in

11328-591: The village of Binsey , along with several smaller portions on the fringes. Other landscape features and places of interest covered include Cutteslowe Park and the mini railway attraction, the University Parks , Hogacre Common Eco Park, numerous sports grounds, Aston's Eyot , St Margaret 's Church and well, and Wolvercote Common and community orchard. There are two tiers of local government covering Oxford, at district and county level: Oxford City Council and Oxfordshire County Council . From 1889 to 1974

11446-539: The vision provided by pure mathematical systems can provide clues to how a physical system might be modeled; e.g., the notion, due to Riemann and others, that space itself might be curved. Theoretical problems that need computational investigation are often the concern of computational physics . Theoretical advances may consist in setting aside old, incorrect paradigms (e.g., aether theory of light propagation, caloric theory of heat, burning consisting of evolving phlogiston , or astronomical bodies revolving around

11564-530: The works of these men (alongside Galileo's) can perhaps be considered to constitute the Scientific Revolution. The great push toward the modern concept of explanation started with Galileo , one of the few physicists who was both a consummate theoretician and a great experimentalist . The analytic geometry and mechanics of Descartes were incorporated into the calculus and mechanics of Isaac Newton , another theoretician/experimentalist of

11682-426: Was Boswell's , founded in 1738. The store closed in 2020. St Aldate's has few shops but several local government buildings, including the town hall , the city police station and local council offices. The High (the word street is traditionally omitted) is the longest of the four streets and has a number of independent and high-end chain stores, but mostly university and college buildings. The historic buildings mean

11800-412: Was 1788, with 336.7 mm (13.26 in) of rainfall. The wettest year was 2012, with 979.5 mm (38.56 in). The wettest month on record was September 1774, with a total fall of 223.9 mm (8.81 in). The warmest month on record is July 1983, with an average of 21.1 °C (70 °F) and the coldest is January 1963, with an average of −3.0 °C (27 °F). The warmest year on record

11918-576: Was a fundamental step in analytic number theory . This work applied to the Riemann zeta function , as well as additive number theory . It was developed by many others. In The Continuum Weyl developed the logic of predicative analysis using the lower levels of Bertrand Russell 's ramified theory of types . He was able to develop most of classical calculus , while using neither the axiom of choice nor proof by contradiction , and avoiding Georg Cantor 's infinite sets . Weyl appealed in this period to

12036-607: Was also available but closed in April 2009; a service operated by That's TV , originally called That's Oxford (now That's Oxfordshire), took to the airwaves in 2015. The city is home to a BBC Television newsroom which produces an opt-out from the main South Today programme broadcast from Southampton . Local papers include The Oxford Times (compact; weekly), its sister papers the Oxford Mail ( tabloid ; daily) and

12154-578: Was also reflected in some passages in his book “Space, Time, Matter”. In 1927 his contribution Philosophy of Mathematics and Natural Sciences to the Handbook of Philosophy was published by Oldenbourg Verlag, which was later published separately and revised as a book. In an attempt to reconstruct the origins of Hermann Weyl's philosophy and to integrate them into the main currents of philosophy, Norman Sieroka pointed to intensive, long-term discussions between Weyl and his Zurich philosopher colleague Fritz Medicus,

12272-414: Was based on the phenomenological philosophy of Edmund Husserl , specifically Husserl's 1913 Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie. Erstes Buch: Allgemeine Einführung in die reine Phänomenologie (Ideas of a Pure Phenomenology and Phenomenological Philosophy. First Book: General Introduction). Husserl had reacted strongly to Gottlob Frege 's criticism of his first work on

12390-815: Was born in Elmshorn , a small town near Hamburg , in Germany , and attended the Gymnasium Christianeum in Altona . His father, Ludwig Weyl, was a banker; whereas his mother, Anna Weyl (née Dieck), came from a wealthy family. From 1904 to 1908, he studied mathematics and physics in both Göttingen and Munich . His doctorate was awarded at the University of Göttingen under the supervision of David Hilbert , whom he greatly admired. In September 1913, in Göttingen, Weyl married Friederike Bertha Helene Joseph (March 30, 1893 – September 5, 1948) who went by

12508-569: Was concerned with the Lorentz transformation which left Maxwell's equations invariant, but was apparently uninterested in the Michelson–Morley experiment on Earth 's drift through a luminiferous aether . Conversely, Einstein was awarded the Nobel Prize for explaining the photoelectric effect , previously an experimental result lacking a theoretical formulation. A physical theory

12626-619: Was erected in 1678–1683 to house a cabinet of curiosities given to the University of Oxford in 1677. The museum reopened in 2009 after a major redevelopment. It holds significant collections of art and archaeology, including works by Michelangelo , Leonardo da Vinci , Turner , and Picasso , as well as treasures such as the Scorpion Macehead , the Parian Marble and the Alfred Jewel . It also contains " The Messiah ",

12744-529: Was established in 1990, and the Begbroke Science Park , owned by the university, lies north of the city. Oxford increasingly has a reputation for being a centre of digital innovation, as epitomized by Digital Oxford. Several startups including Passle, Brainomix, Labstep, and more, are based in Oxford. The presence of the university has also led to Oxford becoming a centre for the education industry. Companies often draw their teaching staff from

12862-527: Was established in the city in 1910. The principal production site for Mini cars, owned by BMW since 2000, is in the Oxford suburb of Cowley . The plant, which survived the turbulent years of British Leyland in the 1970s and was threatened with closure in the early 1990s, also produced cars under the Austin and Rover brands following the demise of the Morris brand in 1984, although the last Morris-badged car

12980-592: Was founded in 1743 by Richard Tawney. He formed a partnership in 1782 with Mark and James Morrell, who eventually became the owners. After an acrimonious family dispute the brewery was closed in 1998. The beer brand names were taken over by the Thomas Hardy Burtonwood brewery, while the 132 tied pubs were bought by Michael Cannon, owner of the American hamburger chain Fuddruckers , through

13098-422: Was given a kinematic explanation by general relativity . Quantum mechanics led to an understanding of blackbody radiation (which indeed, was an original motivation for the theory) and of anomalies in the specific heats of solids — and finally to an understanding of the internal structures of atoms and molecules . Quantum mechanics soon gave way to the formulation of quantum field theory (QFT), begun in

13216-404: Was held in Princeton on September 9, 1948. Speakers at her memorial service included her son Fritz Joachim Weyl and mathematicians Oswald Veblen and Richard Courant . In 1950. Hermann married sculptor Ellen Bär (née Lohnstein) (April 17, 1902 – July 14, 1988), who was the widow of professor Richard Josef Bär (September 11, 1892 – December 15, 1940) of Zürich. After taking a teaching post for

13334-565: Was opened at Grandpont in 1844, but this was a terminus, inconvenient for routes to the north; it was replaced by the present station on Park End Street in 1852 with the opening of the Birmingham route. Another terminus, at Rewley Road , was opened in 1851 to serve the Bletchley route; this station closed in 1951. There have also been a number of local railway stations, all of which are now closed. A fourth station, Oxford Parkway ,

13452-581: Was produced there in 1982. Oxford University Press , a department of the University of Oxford , is based in the city, although it no longer operates its own paper mill and printing house. The city is also home to the UK operations of Wiley-Blackwell , Elsevier and several smaller publishing houses. The presence of the university has given rise to many science and technology based businesses, including Oxford Instruments , Research Machines and Sophos . The university established Isis Innovation in 1987 to promote technology transfer. The Oxford Science Park

13570-586: Was ranked as the world's number one university, according to the Times Higher Education World University Rankings . Oxford is renowned for its tutorial -based method of teaching. The University of Oxford maintains the largest university library system in the United Kingdom, and, with over 11 million volumes housed on 120 miles (190 km) of shelving, the Bodleian group is the second-largest library in

13688-420: Was thoroughly disillusioned with the ultimate value of intuitionism, and wrote: "Mathematics with Brouwer gains its highest intuitive clarity. He succeeds in developing the beginnings of analysis in a natural manner, all the time preserving the contact with intuition much more closely than had been done before. It cannot be denied, however, that in advancing to higher and more general theories the inapplicability of

13806-418: Was through Helene's close connection with Husserl that Hermann became familiar with (and greatly influenced by) Husserl's thought. Hermann and Helene had two sons, Fritz Joachim Weyl (February 19, 1915 – July 20, 1977) and Michael Weyl (September 15, 1917 – March 19, 2011), both of whom were born in Zürich, Switzerland. Helene died in Princeton, New Jersey, on September 5, 1948. A memorial service in her honor

13924-617: Was −17.8 °C (0.0 °F) on 24 December 1860. The highest temperature ever recorded in Oxford is 38.1 °C (101 °F) on 19 July 2022. The average conditions below are from the Radcliffe Meteorological Station . It has the longest series of temperature and rainfall records for one site in Britain . These records are continuous from January 1815. Irregular observations of rainfall, cloud cover, and temperature exist since 1767. The driest year on record

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