title: Ajanta Caves

text: The walls and the ceiling of the side aisles inside the worship hall are covered with paintings. These show the Buddha, flowers, and in the left aisle the "Mother and Child" legend again.


title: Ajanta Caves

text: Cave 20 is a monastery hall (16.2 × 17.91 m) from the 5th century. Its construction, states Spink, was started in the 460s by king Upendragupta, with his expressed desire "to make the great tree of religious merit grow". The work on Cave 20 was pursued in parallel with other caves. Cave 20 has exquisite detailing, states Spink, but it was relatively lower on priority than Caves 17 and 19. The work on Cave 20 was intermittently stopped and then continued in the following decade.


title: Ajanta Caves

text: The vihara consists of a sanctum, four cells for monks and a pillared verandah with two stone cut windows for light. Prior to entering the main hall, on the left of veranda are two Buddhas carved above the window and side cell. The ceiling of the main hall has remnants of painting. The sanctum Buddha is in preaching posture. The cave is known for the sculpture showing seven Buddhas with attendants on its lintel. The cave has a dedicatory Sanskrit inscription in Brahmi script in its verandah, and it calls the cave as a "mandapa".


title: Ajanta Caves

text: Many of the figural and ornamental carvings in Cave 20 are similar to Cave 19, and to a lesser degree to those found in Cave 17. This may be because the same architects and artisans were responsible for the evolution of the three caves. The door frames in Cave 20 are quasi-structural, something unique at the Ajanta site. The decorations are also innovative in Cave 20, such as one showing the Buddha seated against two pillows and "a richly laden mango tree behind him", states Spink.


title: Ajanta Caves

text: Cave 21 is a hall (28.56 × 28.03 m) with twelve rock-cut rooms for monks, a sanctum, twelve pillared and pilastered verandah. The carvings on the pilaster include those of animals and flowers. The pillars feature reliefs of apsaras, Nagaraja and Nagarani, as well as devotees bowing with the namaste mudra. The hall shows evidence that it used to be completely painted. The sanctum Buddha is shown in preaching posture.


title: Ajanta Caves

text: Cave 22 is a small vihara (12.72 × 11.58 m) with a narrow veranda and four unfinished cells. It is excavated at a higher level and has to be reached by a flight of steps. Inside, the Buddha is seated in pralamba-padasana. The painted figures in Cave 22 show Manushi-Buddhas with Maitreya. A pilaster on the left side of the Cave 22 veranda has a Sanskrit prose inscription. It is damaged in parts, and the legible parts state that this is a "meritorious gift of a mandapa by Jayata", calling Jayata's family as "a great Upasaka", and ending the inscription with "may the merit of this be for excellent knowledge to all sentient beings, beginning with father and mother".


title: Ajanta Caves

text: Cave 23 is also unfinished, consisting of a hall (28.32 × 22.52 m) but a design similar to Cave 21. The cave differs in its pillar decorations and the naga doorkeepers.


title: Ajanta Caves

text: Cave 24 is like Cave 21, unfinished but much larger. It features the second largest monastery hall (29.3 × 29.3 m) after Cave 4. The cave 24 monastery has been important to scholarly studies of the site because it shows how multiple crews of workers completed their objectives in parallel. The cell construction began as soon as the aisle had been excavated and while the main hall and sanctum were under construction. The construction of Cave 24 was planned in 467 CE, but likely started in 475 CE, with support from Buddhabhadra, then abruptly ended in 477 with the sponsor king Harisena's death. It is significant in having one of the most complex capitals on a pillar at the Ajanta site, an indication of how the artists excelled and continuously improved their sophistication as they worked with the rock inside the cave. The artists carved fourteen complex miniature figures on the central panel of the right center porch pillar, while working in dim light in a cramped cave space. The medallion reliefs in Cave 24 similarly show loving couples and anthropomorphic arts, rather than flowers of earlier construction. Cave 24's sanctum has a seated Buddha in pralamba-padasana.


title: Ajanta Caves

text: Cave 25 is a monastery. Its hall (11.37 × 12.24 m) is similar to other monasteries, but has no sanctum, includes an enclosed courtyard and is excavated at an upper level.


title: Ajanta Caves

text: Cave 26 is a worship hall (chaityagriha, 25.34 × 11.52 m) similar in plan to Cave 19. It is much larger and with elements of a vihara design. An inscription states that a monk Buddhabhadra and his friend minister serving king of Asmaka gifted this vast cave. The inscription includes a vision statement and the aim to make "a memorial on the mountain that will endure for as long as the moon and the sun continue", translates Walter Spink. It is likely that the builders focussed on sculpture, rather than paintings, in Cave 26 because they believed stone sculpture will far more endure than paintings on the wall.


title: Ajanta Caves

text: The cave drew upon the experiences in building Cave 10, with attached wings similar to the ancient Cave 12 Hinayana-style vihara. The Cave 26 complex has two upper stories and it shows evidence that four wings of the cave were planned, but these were abandoned and only the carved Buddhas on the right and left wall were completed.


title: Ajanta Caves

text: At the center of the apse is a rock-cut stupa. The stupa has an image of the Buddha on its front, 18 panels on its base, 18 panels above these, a three tiered "torana" above him, and apsaras are carved on the "anda" (hemispherical egg) stupa. On top of the dagoba is a nine-tiered "harmika", a symbolism for the nine saṃsāra (Buddhism) heavens in Mahayana cosmology. The walls, pillars, brackets and the triforium are extensively carved with Buddhist themes. Many of the wall reliefs and images in this cave were badly damaged, and have been restored as a part of the site conservation efforts.


title: Ajanta Caves

text: Between cave 26 and its left wing, there is an inscription by a courtier of Rashtrakuta Nanaraj (who is mentioned in the Multai and Sangaloda plates), from late 7th or early 8th century. It is the last inscription in Ajanta.


title: Ajanta Caves

text: Cave 27 is a monastery and may have been planned as an attachment to Cave 26. Its two storeys are damaged, with the upper level partially collapsed. Its plan is similar to other monasteries.


title: Ajanta Caves

text: Cave 28 is an unfinished monastery, partially excavated, at the westernmost end of the Ajanta complex and barely accessible.


title: Ajanta Caves

text: Cave 29 an unfinished monastery at the highest level of the Ajanta complex, apparently unnoticed when the initial numbering system was established, and physically located between Caves 20 and 21.


title: Ajanta Caves

text: In 1956, a landslide covered the footpath leading to Cave 16. In the attempts to clear and restore the walkway, a small aperture and votive stupa were noticed in the debris by the workers, in a location near the stream bed. Further tracing and excavations led to a previously unknown Hinayana monastery cave dated to the 2nd and 1st century BCE. Cave 30 may actually be the oldest cave of the Ajanta complex. It is a 3.66 m × 3.66 m cave with three cells, each with two stone beds and stone pillows on the side of each cell. The cell door lintels show lotus and garland carvings. The cave has two inscriptions in an unknown script. It also has a platform on its veranda with a fine view of the river ravine below and the forest cover. According to Gupte and Mahajan, this cave may have been closed at some point with large carefully carved pieces as it distracted the entrance view of Cave 16.


title: Ajanta Caves

text: Over 80% of the Ajanta caves were "vihara" (temporary traveler residences, monasteries). The designers and artisans who built these caves included facilities for collecting donations and storing grains and food for the visitors and monks. Many of the caves include large repositories cut into the floor. The largest storage spaces are found, states Spink, in the "very commodious recesses in the shrines of both Ajanta Cave Lower 6 and Cave 11". These caves were probably chosen because of their relative convenience and the security they offered due to their higher level. The choice of integrating covered vaults cut into the floor may have been driven by the need to provide sleeping space and logistical ease.


title: Ajanta Caves

text: A burnt-brick vihara monastery facing the caves on the right bank of the river Waghora has been recently excavated. It has a number of cells facing a central courtyard, in which a stupa was established. A coin of the Western Satraps ruler Visvasena (ruled 293–304 CE) as well as a gold coin of the Byzantine Emperor Theodosius II (ruled 402-450 CE) were found in the excavations, giving further numismatic confirmation for the dating of the caves. A terracotta plaque of Mahishasuramardini was also found, which was possibly under worship by the artisans.


title: Ajanta Caves

text: The paintings have deteriorated significantly since they were rediscovered, and a number of 19th-century copies and drawings are important for a complete understanding of the works. A number of attempts to copy the Ajanta paintings began in the 19th century for European and Japanese museums. Some of these works have later been lost in natural and fire disasters. In 1846 for example, Major Robert Gill, an Army officer from Madras Presidency and a painter, was appointed by the Royal Asiatic Society to make copies of the frescos on the cave walls. Gill worked on his painting at the site from 1844 to 1863. He made 27 copies of large sections of murals, but all but four were destroyed in a fire at the Crystal Palace in London in 1866, where they were on display. Gill returned to the site, and recommenced his labours, replicating the murals until his death in 1875.


title: Ajanta Caves

text: Another attempt was made in 1872 when the Bombay Presidency commissioned John Griffiths to work with his students to make copies of Ajanta paintings, again for shipping to England. They worked on this for thirteen years and some 300 canvases were produced, many of which were displayed at the Imperial Institute on Exhibition Road in London, one of the forerunners of the Victoria and Albert Museum. But in 1885 another fire destroyed over a hundred of the paintings in storage in a wing of the museum. The V&A still has 166 paintings surviving from both sets, though none have been on permanent display since 1955. The largest are some . A conservation project was undertaken on about half of them in 2006, also involving the University of Northumbria. Griffith and his students had unfortunately painted many of the paintings with "cheap varnish" in order to make them easier to see, which has added to the deterioration of the originals, as has, according to Spink and others, recent cleaning by the ASI.


title: Ajanta Caves

text: A further set of copies were made between 1909 and 1911 by Christiana Herringham (Lady Herringham) and a group of students from the Calcutta School of Art that included the future Indian Modernist painter Nandalal Bose. The copies were published in full colour as the first publication of London's fledgling India Society. More than the earlier copies, these aimed to fill in holes and damage to recreate the original condition rather than record the state of the paintings as she was seeing them. According to one writer, unlike the paintings created by her predecessors Griffiths and Gill, whose copies were influenced by British Victorian styles of painting, those of the Herringham expedition preferred an 'Indian Renascence' aesthetic of the type pioneered by Abanindranath Tagore.


title: Ajanta Caves

text: Early photographic surveys were made by Robert Gill, whose photos, including some using stereoscopy, were used in books by him and Fergusson (many are available online from the British Library), then Victor Goloubew in 1911 and E.L. Vassey, who took the photos in the four volume study of the caves by Ghulam Yazdani (published 1930–1955).


title: Ajanta Caves

text: Some slightly creative copies of Ajanta frescos, especially the painting of the Adoration of the Buddha from the shrine antechamber of Cave 17, were commissioned by Thomas Holbein Hendley (1847–1917) for the decoration of the walls of the hall of the Albert Hall Museum, Jaipur, India. He had the work painted by a local artist variously named Murli or Murali. The museum was opened to the public in 1887. This work is otherwise presented as characteristic of the end of the 19th century.


title: Ajanta Caves

text: Another attempt to make copies of the murals was made by the Japanese artist Arai Kampō (荒井寛方:1878–1945) after being invited by Rabindranath Tagore to India to teach Japanese painting techniques. He worked on making copies with tracings on Japanese paper from 1916 to 1918 and his work was conserved at Tokyo Imperial University until the materials perished during the 1923 Great Kantō earthquake.


title: Ajanta Caves

text: The Ajanta cave arts are a window into the culture, society and religiosity of the native population of India between the 2nd century BCE and 5th century CE. Different scholars have variously interpreted them from the perspective of gender studies, history, sociology, and the anthropology of South Asia. The dress, the jewelry, the gender relations, the social activities depicted showcase at least a lifestyle of the royalty and elite, and in others definitely the costumes of the common man, monks and rishi depicted therein. They shine "light on life in India" around mid 1st millennium CE.


title: Ajanta Caves

text: The Ajanta artworks provide a contrast between the spiritual life of monks who had given up all materialistic possessions versus the sensual life of those it considered materialistic, luxurious, symbols of wealth, leisurely and high fashion. Many frescos show scenes from shops, festivals, jesters at processions, palaces and performance art pavilions. These friezes share themes and details of those found in Bharhut, Sanchi, Amaravati, Ellora, Bagh, Aihole, Badami and other archaeological sites in India. Ajanta caves contributes to visual and descriptive sense of the ancient and early medieval Indian culture and artistic traditions, particularly those around the Gupta Empire era period.


title: Ajanta Caves

text: The early colonial era description of Ajanta caves was largely orientalist and critical, inconsistent with the Victorian values and stereotyping. According to William Dalrymple, the themes and arts in the Ajanta caves were puzzling to the 19th-century Orientalists. Lacking the Asian cultural heritage and framework that sees "nothing odd in the juxtaposition of monk and dancing girl", and with no knowledge of Jataka Tales or equivalent Indian fables, they could not comprehend it. They projected their own views and assumptions, calling it something that lacks reason and rationale, something that is meaningless crude representation of royalty and foreigners with mysticism and sensuousness. The 19th-century views and interpretations of the Ajanta Caves were conditioned by ideas and assumptions in the colonial mind, saw what they wanted to see.


title: Ajanta Caves

text: To many who are unaware of the premises of Indian religions in general, and Buddhism in particular, the significance of Ajanta Caves has been like rest of Indian art. According to Richard Cohen, Ajanta Caves to them has been yet another example of "worship this stock, or that stone, or monstrous idol". In contrast, to the Indian mind and the larger Buddhist community, it is everything that art ought to be, the religious and the secular, the spiritual and the social fused to enlightened perfection.


title: Ajanta Caves

text: According to Walter Spink – one of the most respected Art historians on Ajanta, these caves were by 475 CE a much-revered site to the Indians, with throngs of "travelers, pilgrims, monks and traders". The site was vastly transformed into its current form in just 20 years, between early 460 CE to early 480 CE, by regional architects and artisans. This accomplishment, states Spink, makes Ajanta, "one of the most remarkable creative achievements in man's history".


title: Ajanta Caves

text: The Ajanta Caves painting are a significant source of socio-economic information in ancient India, particularly in relation to the interactions of India with foreign cultures at the time most of the paintings were made, in the 5th century CE (Common Era). According to Indian historian Haroon Khan Sherwani: "The paintings at Ajanta clearly demonstrate the cosmopolitan character of Buddhism, which opened its way to men of all races, Greek, Persian, Saka, Pahlava, Kushan and Huna". Depictions of foreigners abound: according to Spink, "Ajanta’s paintings are filled with such foreign types." They have sometimes been a source of misinterpretation as in the so-called "Persian Embassy Scene". These foreigners may reflect the Sassanian merchants, visitors and the flourishing trade routes of the day.


title: Ajanta Caves

text: Cave 1, for example, shows a mural fresco with characters with foreigner faces or dresses, the so-called "Persian Embassy Scene". This scene is located at the right of the entrance door upon entering the hall. According to Spink, James Fergusson, a 19th-century architectural historian, had decided that this scene corresponded to the Persian ambassador in 625 CE to the court of the Hindu Chalukya king Pulakeshin II. An alternate theory has been that the fresco represents a Hindu ambassador visiting the Persian king Khusrau II in 625 CE, a theory that Fergusson disagreed with. These assumptions by colonial British era art historians, state Spink and other scholars, has been responsible for wrongly dating this painting to the 7th century, when in fact this reflects an incomplete Harisena-era painting of a Jataka tale (the Mahasudarsana jataka, in which the enthroned king is actually the Buddha in one of his previous lives as King) with the representation of trade between India and distant lands such as Sassanian near East that was common by the 5th century.


title: Ajanta Caves

text: Cave 1 has several frescos with characters with foreigners' faces or dresses. Similar depictions are found in the paintings of Cave 17. Such murals, states Pia Brancaccio, suggest a prosperous and multicultural society in 5th-century India active in international trade. These also suggest that this trade was economically important enough to the Deccan region that the artists chose to include it with precision.


title: Ajanta Caves

text: Additional evidence of international trade includes the use of the blue lapis lazuli pigment to depict foreigners in the Ajanta paintings, which must have been imported from Afghanistan or Iran. It also suggests, states Branacaccio, that the Buddhist monastic world was closely connected with trading guilds and the court culture in this period. A small number of scenes show foreigners drinking wine in Caves 1 and 2. Some show foreign Near East kings with wine and their retinue which presumably add to the "general regal emphasis" of the cave. According to Brancaccio, the Ajanta paintings show a variety of colorful, delicate textiles and women making cotton. Textile probably was one of the major exports to foreign lands, along with gems. These were exported first through the Red Sea, and later through the Persian Gulf, thereby bringing a period of economic and cultural exchange between the Indians, the Sasanian Empire and the Persian merchants before Islam was founded in the Arabian peninsula.


title: Ajanta Caves

text: While scholars generally agree that these murals confirm trade and cultural connections between India and Sassanian west, their specific significance and interpretation varies. Brancaccio, for example, suggests that the ship and jars in them probably reflect foreign ships carrying wine imported to India. In contrast, Schlinghoff interprets the jars to be holding water, and ships shown as Indian ships used in international trade.


title: Ajanta Caves

text: Similar depictions are found in the paintings of Cave 17, but this time in direct relation to the worship of the Buddha. In Cave 17, a painting of the Buddha descending from the Trayastrimsa Heaven shows he being attended by many foreigners. Many foreigners in this painting are thus shown as listeners to the Buddhist Dharma. The ethnic diversity is depicted in the painting in the clothes (kaftans, Sasanian helmets, round caps), hairdos and skin colors. In the Visvantara Jataka of Cave 17, according to Brancaccio, the scene probably shows a servant from Central Asia holding a foreign metal ewer, while a dark-complexioned servant holds a cup to an amorous couple. In another painting in Cave 17, relating to the conversion of Nanda, a man possibly from northeast Africa appears as a servant. These representations show, states Brancaccio, that the artists were familiar with people of Sogdia, Central Asia, Persia and possibly East Africa. Another hypothesis is offered by Upadhya, who states that the artists who built Ajanta caves "very probably included foreigners".


title: Ajanta Caves

text: The Ajanta paintings, or more likely the general style they come from, influenced painting in Tibet and Sri Lanka. Some influences from Ajanta have also suggested in the Kizil Caves of the Tarim Basin, in particular in early caves such as the "".


title: Ajanta Caves

text: The rediscovery of ancient Indian paintings at Ajanta provided Indian artists with examples from ancient India to follow. Nandalal Bose experimented with techniques to follow the ancient style which allowed him to develop his unique style. Abanindranath Tagore and Syed Thajudeen also used the Ajanta paintings for inspiration.


title: Ajanta Caves

text: Anna Pavlova's ballet "Ajanta's Frescoes" was inspired by her visit to Ajanta, choreographed by Ivan Clustine, with music by Nikolai Tcherepnin (one report says Mikhail Fokine in 1923). and premiered at Covent Garden in 1923.


title: Ajanta Caves

text: Jewish American poet Muriel Rukeyser wrote about the caves in "Ajanta," the opening poem of her third collection "Beast in View" (1944). Rukeyser was inspired in part by writings on the caves by artist Mukul Dey in 1925 and art historian Stella Kramrisch in 1937.


title: Terence Tao

text: Terence Chi-Shen Tao (; born 17 July 1975) is an Australian mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory.


title: Terence Tao

text: Tao was born to ethnic Chinese immigrant parents and raised in Adelaide. Tao won the Fields Medal in 2006 and won the Royal Medal and Breakthrough Prize in Mathematics in 2014. He is also a 2006 MacArthur Fellow. Tao has been the author or co-author of over three hundred research papers. He is widely regarded as one of the greatest living mathematicians and has been referred to as the "Mozart of mathematics".


title: Terence Tao

text: Tao's parents are first-generation immigrants from Hong Kong to Australia. Tao's father, Billy Tao (), was a Chinese paediatrician who was born in Shanghai and earned his medical degree (MBBS) from the University of Hong Kong in 1969. Tao's mother, Grace Leong (), was born in Hong Kong; she received a first-class honours degree in astrophysics and mathematics at the University of Hong Kong. She was a secondary school teacher of mathematics and physics in Hong Kong. Billy and Grace met as students at the University of Hong Kong. They then emigrated from Hong Kong to Australia in 1972.


title: Terence Tao

text: Tao also has two brothers, who are living in Australia. Both formerly represented the country at the International Mathematical Olympiad. Tao speaks Cantonese but cannot write Chinese. Tao is married to Laura Tao, a Chinese-American woman who is an electrical engineer at NASA's Jet Propulsion Laboratory. They live with their son and daughter in Los Angeles, California.


title: Terence Tao

text: A child prodigy, Tao exhibited extraordinary mathematical abilities from an early age, attending university-level mathematics courses at the age of 9. He is one of only three children in the history of the Johns Hopkins' Study of Exceptional Talent program to have achieved a score of 700 or greater on the SAT math section while just eight years old; Tao scored a 760. Julian Stanley, Director of the Study of Mathematically Precocious Youth, stated that Tao had the greatest mathematical reasoning ability he had found in years of intensive searching.


title: Terence Tao

text: Tao was the youngest participant to date in the International Mathematical Olympiad, first competing at the age of ten; in 1986, 1987, and 1988, he won a bronze, silver, and gold medal, respectively. Tao remains the youngest winner of each of the three medals in the Olympiad's history, having won the gold medal at the age of 13 in 1988.


title: Terence Tao

text: At age 14, Tao attended the Research Science Institute, a summer program for secondary students. In 1991, he received his bachelor's and master's degrees at the age of 16 from Flinders University under the direction of Garth Gaudry. In 1992, he won a Postgraduate Fulbright Scholarship to undertake research in mathematics at Princeton University in the United States. From 1992 to 1996, Tao was a graduate student at Princeton University under the direction of Elias Stein, receiving his PhD at the age of 21. In 1996, he joined the faculty of the University of California, Los Angeles. In 1999, when he was 24, he was promoted to full professor at UCLA and remains the youngest person ever appointed to that rank by the institution.


title: Terence Tao

text: He is known for his collaborative mindset; by 2006, Tao had worked with over 30 others in his discoveries, reaching 68 co-authors by October 2015.


title: Terence Tao

text: Tao has had a particularly extensive collaboration with British mathematician Ben J. Green; together they proved the Green–Tao theorem, which is well-known among both amateur and professional mathematicians. This theorem states that there are arbitrarily long arithmetic progressions of prime numbers. "The New York Times" described it this way:


title: Terence Tao

text: Tao has also resolved or made progress on a number of conjectures. In 2012, Green and Tao announced proofs of the conjectured "orchard-planting problem," which asks for the maximum number of lines through exactly 3 points in a set of n points in the plane, not all on a line. In 2018, with Brad Rodgers, Tao showed that the de Bruijn–Newman constant, the nonpositivity of which is equivalent to the Riemann hypothesis, is nonnegative. In 2020, Tao proved Sendov's conjecture, concerning the locations of the roots and critical points of a complex polynomial, in the special case of polynomials with sufficiently high degree.


title: Terence Tao

text: Tao has won numerous mathematician honours and awards over the years. He is a Fellow of the Royal Society, the Australian Academy of Science (Corresponding Member), the National Academy of Sciences (Foreign member), the American Academy of Arts and Sciences, the American Philosophical Society, and the American Mathematical Society. In 2006 he received the Fields Medal; he was the first Australian, the first UCLA faculty member, and one of the youngest mathematicians to receive the award. He was also awarded the MacArthur Fellowship. He has been featured in "The New York Times", CNN, "USA Today", "Popular Science", and many other media outlets. In 2014, Tao received a CTY Distinguished Alumni Honor from Johns Hopkins Center for Gifted and Talented Youth in front of 979 attendees in 8th and 9th grade that are in the same program from which Tao graduated. In 2021, President Joe Biden announced Tao had been selected as one of 30 members of his President's Council of Advisors on Science and Technology, a body bringing together America's most distinguished leaders in science and technology. In 2021, Tao was awarded the Riemann Prize Week as recipient of the inaugural Riemann Prize 2019 by the Riemann International School of Mathematics at the University of Insubria. Tao was a finalist to become Australian of the Year in 2007.


title: Terence Tao

text: As of 2022, Tao has published over three hundred articles, along with sixteen books. He has an Erdős number of 2. He is a highly cited researcher.


title: Terence Tao

text: From 2001 to 2010, Tao was part of a well-known collaboration with James Colliander, Markus Keel, Gigliola Staffilani, and Hideo Takaoka. They found a number of novel results, many to do with the well-posedness of weak solutions, for Schrödinger equations, KdV equations, and KdV-type equations.


title: Terence Tao

text: Michael Christ, Colliander, and Tao developed methods of Carlos Kenig, Gustavo Ponce, and Luis Vega to establish ill-posedness of certain Schrödinger and KdV equations for Sobolev data of sufficiently low exponents. In many cases these results were sharp enough to perfectly complement well-posedness results for sufficiently large exponents as due to Bourgain, Colliander−Keel−Staffilani−Takaoka−Tao, and others. Further such notable results for Schrödinger equations were found by Tao in collaboration with Ioan Bejenaru.


title: Terence Tao

text: A particularly notable result of the Colliander−Keel−Staffilani−Takaoka−Tao collaboration established the long-time existence and scattering theory of a power-law Schrödinger equation in three dimensions. Their methods, which made use of the scale-invariance of the simple power law, were extended by Tao in collaboration with Monica Vișan and Xiaoyi Zhang to deal with nonlinearities in which the scale-invariance is broken. Rowan Killip, Tao, and Vișan later made notable progress on the two-dimensional problem in radial symmetry.


title: Terence Tao

text: A technical tour de force by Tao in 2001 considered the wave maps equation with two-dimensional domain and spherical range. He built upon earlier innovations of Daniel Tataru, who considered wave maps valued in Minkowski space. Tao proved the global well-posedness of solutions with sufficiently small initial data. The fundamental difficulty is that Tao considers smallness relative to the critical Sobolev norm, which typically requires sophisticated techniques. Tao later adapted some of his work on wave maps to the setting of the Benjamin–Ono equation; Alexandru Ionescu and Kenig later obtained improved results with Tao's methods.


title: Terence Tao

text: In 2016, Tao constructed a variant of the Navier–Stokes equations which possess solutions exhibiting irregular behavior in finite time. Due to structural similarities between Tao's system and the Navier–Stokes equations themselves, it follows that any positive resolution of the Navier–Stokes existence and smoothness problem must take into account the specific nonlinear structure of the equations. In particular, certain previously-proposed resolutions of the problem could not be legitimate. Tao speculated that the Navier–Stokes equations might be able to simulate a Turing complete system, and that as a consequence it might be possible to (negatively) resolve the existence and smoothness problem using a modification of his results. However, such results remain (as of 2022) conjectural.


title: Terence Tao

text: Bent Fuglede introduced the Fuglede conjecture in the 1970s, positing a tile-based characterisation of those Euclidean domains for which a Fourier ensemble provides a basis of Tao resolved the conjecture in the negative for dimensions larger than 5, based upon the construction of an elementary counterexample to an analogous problem in the setting of finite groups.


title: Terence Tao

text: With Camil Muscalu and Christoph Thiele, Tao considered certain multilinear singular integral operators with the multiplier allowed to degenerate on a hyperplane, identifying conditions which ensure operator continuity relative to spaces. This unified and extended earlier notable results of Ronald Coifman, Carlos Kenig, Michael Lacey, Yves Meyer, Elias Stein, and Thiele, among others. Similar problems were analyzed by Tao in 2001 in the context of Bourgain spaces, rather than the usual spaces. Such estimates are used in establishing well-posedness results for dispersive partial differential equations, following famous earlier work of Jean Bourgain, Kenig, Gustavo Ponce, and Luis Vega, among others.


title: Terence Tao

text: A number of Tao's results deal with "restriction" phenomena in Fourier analysis, which have been widely studied since seminal articles of Charles Fefferman, Robert Strichartz, and Peter Tomas in the 1970s. Here one studies the operation which restricts input functions on Euclidean space to a submanifold and outputs the product of the Fourier transforms of the corresponding measures. It is of major interest to identify exponents such that this operation is continuous relative to spaces. Such multilinear problems originated in the 1990s, including in notable work of Jean Bourgain, Sergiu Klainerman, and Matei Machedon. In collaboration with Ana Vargas and Luis Vega, Tao made some foundational contributions to the study of the bilinear restriction problem, establishing new exponents and drawing connections to the linear restriction problem. They also found analogous results for the bilinear Kakeya problem which is based upon the X-ray transform instead of the Fourier transform. In 2003, Tao adapted ideas developed by Thomas Wolff for bilinear restriction to conical sets into the setting of restriction to quadratic hypersurfaces. The multilinear setting for these problems was further developed by Tao in collaboration with Jonathan Bennett and Anthony Carbery; their work was extensively used by Bourgain and Larry Guth in deriving estimates for general oscillatory integral operators.


title: Terence Tao

text: In collaboration with Emmanuel Candes and Justin Romberg, Tao has made notable contributions to the field of compressed sensing. In mathematical terms, most of their results identify settings in which a convex optimisation problem correctly computes the solution of an optimisation problem which seems to lack a computationally tractable structure. These problems are of the nature of finding the solution of an underdetermined linear system with the minimal possible number of nonzero entries, referred to as "sparsity". Around the same time, David Donoho considered similar problems from the alternative perspective of high-dimensional geometry.


title: Terence Tao

text: Motivated by striking numerical experiments, Candes, Romberg, and Tao first studied the case where the matrix is given by the discrete Fourier transform. Candes and Tao abstracted the problem and introduced the notion of a "restricted linear isometry," which is a matrix that is quantitatively close to an isometry when restricted to certain subspaces. They showed that it is sufficient for either exact or optimally approximate recovery of sufficiently sparse solutions. Their proofs, which involved the theory of convex duality, were markedly simplified in collaboration with Romberg, to use only linear algebra and elementary ideas of harmonic analysis. These ideas and results were later improved by Candes. Candes and Tao also considered relaxations of the sparsity condition, such as power-law decay of coefficients. They complemented these results by drawing on a large corpus of past results in random matrix theory to show that, according to the Gaussian ensemble, a large number of matrices satisfy the restricted isometry property.


title: Terence Tao

text: In 2009, Candes and Benjamin Recht considered an analogous problem for recovering a matrix from knowledge of only a few of its entries and the information that the matrix is of low rank. They formulated the problem in terms of convex optimisation, studying minimisation of the nuclear norm. Candes and Tao, in 2010, developed further results and techniques for the same problem. Improved results were later found by Recht. Similar problems and results have also been considered by a number of other authors.


title: Terence Tao

text: In 2007, Candes and Tao introduced a novel statistical estimator for linear regression, which they called the "Dantzig selector." They proved a number of results on its success as an estimator and model selector, roughly in parallel to their earlier work on compressed sensing. A number of other authors have since studied the Dantzig selector, comparing it to similar objects such as the statistical lasso introduced in the 1990s. Trevor Hastie, Robert Tibshirani, and Jerome H. Friedman conclude that it is "somewhat unsatisfactory" in a number of cases. Nonetheless it remains of significant interest in the statistical literature.


title: Terence Tao

text: In the 1950s, Eugene Wigner initiated the study of random matrices and their eigenvalues. Wigner studied the case of hermitian and symmetric matrices, proving a "semicircle law" for their eigenvalues. In 2010, Tao and Van Vu made a major contribution to the study of non-symmetric random matrices. They showed that if is large and the entries of a matrix are selected randomly according to any fixed probability distribution of average 0 and standard deviation 1, then the eigenvalues of will tend to be uniformly scattered across the disk of radius around the origin; this can be made precise using the language of measure theory. This gave a proof of the long-conjectured circular law, which had previously been proved in weaker formulations by many other authors. In Tao and Vu's formulation, the circular law becomes an immediate consequence of a "universality principle" stating that the distribution of the eigenvalues can depend only on the average and standard deviation of the given component-by-component probability distribution, thereby providing a reduction of the general circular law to a calculation for specially-chosen probability distributions.


title: Terence Tao

text: In 2011, Tao and Vu established a "four moment theorem", which applies to random hermitian matrices whose components are independently distributed, each with average 0 and standard deviation 1, and which are exponentially unlikely to be large (as for a Gaussian distribution). If one considers two such random matrices which agree on the average value of any quadratic polynomial in the diagonal entries and on the average value of any quartic polynomial in the off-diagonal entries, then Tao and Vu show that the expected value of a large number of functions of the eigenvalues will also coincide, up to an error which is uniformly controllable by the size of the matrix and which becomes arbitrarily small as the size of the matrix increases. Similar results were obtained around the same time by László Erdös, Horng-Tzer Yau, and Jun Yin.


title: Terence Tao

text: In 2004, Tao, together with Jean Bourgain and Nets Katz, studied the additive and multiplicative structure of subsets of finite fields of prime order. It is well known that there are no nontrivial subrings of such a field. Bourgain, Katz, and Tao provided a quantitative formulation of this fact, showing that for any subset of such a field, the number of sums and products of elements of the subset must be quantitatively large, as compared to the size of the field and the size of the subset itself. Improvements of their result were later given by Bourgain, Alexey Glibichuk, and Sergei Konyagin.


title: Terence Tao

text: Tao and Ben Green proved the existence of arbitrarily long arithmetic progressions in the prime numbers; this result is generally referred to as the Green–Tao theorem, and is among Tao's most well-known results. The source of Green and Tao's arithmetic progressions is Endre Szemerédi's seminal 1975 theorem on existence of arithmetic progressions in certain sets of integers. Green and Tao showed that one can use a "transference principle" to extend the validity of Szemerédi's theorem to further sets of integers. The Green–Tao theorem then arises as a special case, although it is not trivial to show that the prime numbers satisfy the conditions of Green and Tao's extension of the Szemerédi theorem.


title: Terence Tao

text: In 2010, Green and Tao gave a multilinear extension of Dirichlet's celebrated theorem on arithmetic progressions. Given a matrix and a matrix whose components are all integers, Green and Tao give conditions on when there exist infinitely many matrices such that all components of are prime numbers. The proof of Green and Tao was incomplete, as it was conditioned upon unproven conjectures. Those conjectures were proved in later work of Green, Tao, and Tamar Ziegler.


title: Terence Tao

text: Research articles. Tao is the author of over 300 articles. The following, among the most cited, are surveyed above.


title: 7 July 2005 London bombings

text: The 7 July 2005 London bombings, often referred to as 7/7, were a series of four coordinated suicide attacks carried out by Islamic terrorists in London that targeted commuters travelling on the city's public transport system during the morning rush hour.


title: 7 July 2005 London bombings

text: Three terrorists separately detonated three homemade bombs in quick succession aboard London Underground trains across the city and, later, a fourth terrorist detonated another bomb on a double-decker bus in Tavistock Square. The train bombings occurred on the Circle line near and at Edgware Road, and on the Piccadilly line near .


title: 7 July 2005 London bombings

text: Apart from the bombers, 52 UK residents of 18 different nationalities were killed and more than 700 were injured in the attacks, making it the UK's deadliest terrorist incident since the 1988 bombing of Pan Am Flight 103 near Lockerbie, as well as the country's first Islamist suicide attack.


title: 7 July 2005 London bombings

text: The explosions were caused by improvised explosive devices made from triacetone triperoxide, packed into backpacks. The bombings were followed two weeks later by a series of attempted attacks that failed to cause injury or damage.


title: 7 July 2005 London bombings

text: At 8:49a.m. on Thursday 7 July 2005, three bombs were detonated onboard London Underground trains within 50 seconds of each other:


title: 7 July 2005 London bombings

text: It was originally thought that there had been six, rather than three, explosions on the Underground network. The bus bombing brought the reported total to seven; this was clarified later in the day. The erroneous reporting can be attributed to the fact that the blasts occurred on trains that were between stations, causing wounded passengers to emerge from both stations, giving the impression that there was an incident at each. Police also revised the timings of the tube blasts: initial reports had indicated that they occurred during a period of almost half an hour. This was due to initial confusion at London Underground (LU), where the explosions were originally believed to have been caused by power surges. An early report, made in the minutes after the explosions, involved a person under a train, while another described a derailment (both of which did occur, but only as a result of the explosions). A code amber alert was declared by LU at 9:19am, and LU began to cease the network's operations, ordering trains to continue only to the next station and suspending all services.


title: 7 July 2005 London bombings

text: The effects of the explosions varied due to the differing characteristics of the tunnels in which each occurred:


title: 7 July 2005 London bombings

text: Almost one hour after the attacks on the London Underground, a fourth bomb exploded on the top deck of a number 30 double-decker bus, travelling its route from Marble Arch to Hackney Wick.


title: 7 July 2005 London bombings

text: The bus left Marble Arch at 9:00a.m. and arrived at Euston bus station at 9:35a.m., where crowds of people had been evacuated from the tube and boarded buses as an alternative method of transport.


title: 7 July 2005 London bombings

text: The explosion at 9:47am in Tavistock Square ripped off the roof and destroyed the rear portion of the bus. The blast took place near BMA House, the headquarters of the British Medical Association, on Upper Woburn Place. A number of doctors and medical staff in or near that building were able to provide immediate emergency assistance.


title: 7 July 2005 London bombings

text: Witnesses reported seeing "papers and half a bus flying through the air". Two injured bus passengers said that they saw a man exploding in the bus.


title: 7 July 2005 London bombings

text: The location of the bomb inside the bus meant the front of the vehicle remained mostly intact. Most of the passengers at the front of the top deck survived, as did those near the front of the lower deck, including the driver, but those at the rear of the bus suffered more serious injuries, with several individuals being blown from the bus. The extent of the damage caused to the victims' bodies resulted in a lengthy delay in announcing the death toll from the bombing while the police determined how many bodies were present and whether the bomber was one of them. Several passers-by were also injured by the explosion and surrounding buildings were damaged by debris.


title: 7 July 2005 London bombings

text: The bombed bus was subsequently covered with tarpaulin and removed for forensic examination at a secure Ministry of Defence site. A replacement bus was named "Spirit of London".


title: 7 July 2005 London bombings

text: The 52 victims were of diverse backgrounds. All were UK residents, including exchange students. The majority lived in or near London. Their ages ranged from 20 to 60 years old, with an average age of 34.


title: 7 July 2005 London bombings

text: Thirty two victims were British, while one victim each came from Afghanistan, France, Ghana, Grenada, India, Iran, Israel, Italy, Kenya, Mauritius, New Zealand, Nigeria, Romania, Sri Lanka and Turkey. Three victims were Polish nationals, while one victim was a Vietnamese born Australian and one held dual American-Vietnamese citizenship.


title: 7 July 2005 London bombings

text: Seven of the victims were killed at Aldgate, six at Edgware Road, 26 at King's Cross and 13 at Tavistock Square.


title: 7 July 2005 London bombings

text: Three of the bombers were British-born sons of Pakistani immigrants; Lindsay was a convert born in Jamaica.


title: 7 July 2005 London bombings

text: Charles Clarke, Home Secretary when the attacks occurred, described the bombers as "cleanskins", a term describing them as previously unknown to authorities until they carried out their attacks. On the day of the attacks, all four had travelled to Luton, Bedfordshire, by car, then to London by train. They were filmed on CCTV arriving at King's Cross station at about 8:30a.m.


title: 7 July 2005 London bombings

text: Two of the bombers made videotapes describing their reasons for becoming what they called "soldiers". In a videotape broadcast by Al Jazeera on 1 September 2005, Mohammad Sidique Khan described his motivation. The tape had been edited and mentioned al-Qaeda members Osama Bin Laden, Ayman al-Zawahiri and Abu Musab al-Zarqawi, describing them as "today's heroes". Khan's tape said:


title: 7 July 2005 London bombings

text: On 6 July 2006, a videotaped statement by Shehzad Tanweer was broadcast by Al-Jazeera. In the video, which may have been edited to include remarks by al-Zawahiri, Tanweer said:


title: 7 July 2005 London bombings

text: Tanweer argued that the non-Muslims of Britain deserve such attacks because they voted for a government which "continues to oppress our mothers, children, brothers and sisters in Palestine, Afghanistan, Iraq and Chechnya."


title: 7 July 2005 London bombings

text: Initial reports suggested that a power surge on the Underground power grid had caused explosions in power circuits. This was later ruled out by power suppliers National Grid. Commentators suggested that the explanation had been made because of bomb damage to power lines along the tracks; the rapid series of power failures caused by the explosions (or power being ended by means of switches at the locations to permit evacuation) looked similar, from the point of view of a control room operator, to a cascading series of circuit breaker operations that would result from a major power surge. A couple of hours after the bombings, Home Secretary Charles Clarke confirmed the incidents were terrorist attacks.


title: 7 July 2005 London bombings

text: Although there were security alerts at many locations throughout the United Kingdom, no terrorist incidents occurred outside central London. Suspicious packages were destroyed in controlled explosions in Edinburgh, Brighton, Coventry, Southampton, Portsmouth, Darlington and Nottingham. Security across the country was increased to the highest alert level.


title: 7 July 2005 London bombings

text: "The Times" reported on 17 July 2005 that police sniper units were following as many as a dozen al-Qaeda suspects in Britain. The covert armed teams were ordered to shoot to kill if surveillance suggested that a terror suspect was carrying a bomb and he refused to surrender if challenged. A member of the Metropolitan Police's Specialist Firearms Command said: "These units are trained to deal with any eventuality. Since the London bombs, they have been deployed to look at certain people."


title: 7 July 2005 London bombings

text: Vodafone reported that its mobile telephone network reached capacity at about 10a.m. on the day of the bombings, and it was forced to initiate emergency procedures to prioritise emergency calls (ACCOLC, the 'access overload control'). Other mobile phone networks also reported failures. The BBC speculated that the telephone system was shut down by security services to prevent the possibility of mobile phones being used to trigger bombs. Although this option was considered, it became clear later that the intermittent unavailability of both mobile and landline telephone systems was due only to excessive usage. ACCOLC was activated only in a radius around Aldgate Tube Station because key emergency personnel did not have ACCOLC-enabled mobile phones. The communications failures during the emergency sparked discussions to improve London's emergency communications system.


title: 7 July 2005 London bombings

text: For most of the day, central London's public transport system was largely out of service following the complete closure of the Underground, the closure of the Zone 1 bus network, and the evacuation of incident sites such as Russell Square. Bus services restarted at 4:00p.m. on 7 July, and most mainline railway stations resumed service soon afterward. River vessels were pressed into service to provide a free alternative to overcrowded trains and buses. Local lifeboats were required to act as safety boats, including the Sheerness lifeboat from the Isle of Sheppey in Kent. Thousands of people chose to walk home or to the nearest Zone 2 bus or railway station. Most of the Underground, apart from the stations affected by the bombs, resumed service the next morning, though some commuters chose to stay at home. Affected stretches were also closed for police investigations.


title: 7 July 2005 London bombings

text: Much of the King's Cross railway station was also closed, with the ticket hall and waiting area being used as a makeshift hospital to treat casualties. Although the station reopened later during the day, only suburban rail services were able to use it, with Great North Eastern Railway trains terminating at Peterborough (the service was fully restored on 9 July). King's Cross St Pancras tube station remained available only to Metropolitan line services to facilitate the ongoing recovery and investigation for a week, though Victoria line services were restored on 15 July and the Northern line on 18 July. All of the damaged trains were removed in stages. St Pancras station, located next to King's Cross, was shut on the afternoon of the attacks, with all Midland Mainline trains terminating at Leicester, causing disruption to services to Sheffield, Nottingham and Derby.


title: 7 July 2005 London bombings

text: On 25 July, the Hammersmith & City line was reopened from Baker Street to Barking after the affected train was cleared at Aldgate, together with the stretch from Moorgate to Aldgate of the Metropolitan Line. The Hammersmith to Paddington part of the Hammersmith & City line was a shuttle service after the bombings. On 29 July, the District line was reopened from High Street Kensington to Edgware Road, after the affected train was cleared.


title: 7 July 2005 London bombings

text: On 2 August, the Hammersmith & City line resumed normal service; the Circle line was still suspended, though all Circle line stations are also served by other lines. The Piccadilly line service resumed on 4 August after the affected train was cleared on 16 July, and enhanced maintenance work was done. On 4 August, the Circle line was reopened again.


title: 7 July 2005 London bombings

text: The list below is of the emergency services, police forces and voluntary aid societies that responded to the bombings to assist with rescue, recovery, security and scene control:


title: 7 July 2005 London bombings

text: There were limited reactions to the attack in the world economy as measured by financial market and exchange rate activity. The value of the British pound decreased 0.89cents to a 19-month low against the US dollar. The FTSE 100 Index fell by about 200 points during the two hours after the first attack. This was its greatest decrease since the invasion of Iraq, and it triggered the London Stock Exchange's 'Special Measures', restricting panic selling and aimed at ensuring market stability. By the time the market closed, it had recovered to only 71.3 points (1.36%) down on the previous day's three-year closing high. Markets in France, Germany, the Netherlands and Spain also closed about 1% down on the day.


title: 7 July 2005 London bombings

text: US market indexes increased slightly, partly because the dollar index increased sharply against the pound and the euro. The Dow Jones Industrial Average gained 31.61 to 10,302.29. The NASDAQ Composite Index increased 7.01 to 2,075.66. The S&P 500 increased 2.93 points to 1,197.87 after decreasing as much as 1%. Every benchmark value gained 0.3%.


title: 7 July 2005 London bombings

text: The market values increased again on 8 July as it became clear that the damage caused by the bombings was not as great as thought initially. By end of trading the market had recovered fully to above its level at start of trading on 7 July. Insurers in the UK tend to reinsure their terrorist liabilities in excess of the first £75,000,000 with Pool Re, a mutual insurer established by the government with major insurers. Pool Re has substantial reserves and newspaper reports indicated that claims would easily be funded.


title: 7 July 2005 London bombings

text: On 9 July, the Bank of England, HM Treasury and the Financial Services Authority revealed that they had instigated contingency plans immediately after the attacks to ensure that the UK financial markets could keep trading. This involved the activation of a "secret chatroom" on the British government's Financial Sector Continuity website, which allowed the institutions to communicate with the country's banks and market dealers.


title: 7 July 2005 London bombings

text: Continuous news coverage of the attacks was broadcast throughout 7 July, by both BBC One and ITV, uninterrupted until 7:00p.m., although the BBC stuck with initial reports of a power surge on the London Underground until actual events could be corroborated. Sky News did not broadcast any advertisements for 24 hours. ITN confirmed later that its coverage on ITV was its longest uninterrupted on-air news broadcast of its 50-year history. Television coverage was notable for the use of mobile telephone footage sent in by members of the public and live pictures from traffic CCTV cameras.


title: 7 July 2005 London bombings

text: The BBC Online website recorded an all-time bandwidth peak of 11Gb/s at midday on 7 July. BBC News received some 1billion total accesses throughout the course of the day (including all images, text and HTML), serving some 5.5terabytes of data. At peak times during the day there were 40,000-page requests per second for the BBC News website. The previous day's announcement of the 2012 Summer Olympics being awarded to London resulted in up to 5Gb/s. The previous all-time maximum for the website followed the announcement of the Michael Jackson verdict, which used 7.2Gb/s.


title: 7 July 2005 London bombings

text: On 12 July, it was reported that the British National Party released leaflets showing images of the 'No. 30 bus' after it was destroyed. The slogan, "Maybe now it's time to start listening to the BNP" was printed beside the photo. Home Secretary Charles Clarke described it as an attempt by the BNP to "cynically exploit the current tragic events in London to further their spread of hatred".


title: 7 July 2005 London bombings

text: Some media outside the UK complained that successive British governments had been unduly tolerant towards radical Islamist militants, so long as they were involved in activities outside the UK. Britain's alleged reluctance to extradite or prosecute terrorist suspects resulted in London being dubbed "Londonistan" by the columnist Melanie Phillips.


title: 7 July 2005 London bombings

text: Even before the identity of the bombers became known, former Metropolitan Police commissioner Lord Stevens said he believed they were almost certainly born or based in Britain, and would not "fit the caricature al-Qaeda fanatic from some backward village in Algeria or Afghanistan". The attacks would have required extensive preparation and prior reconnaissance efforts, and a familiarity with bomb-making and the London transport network as well as access to significant amounts of bomb-making equipment and chemicals.


title: 7 July 2005 London bombings

text: Some newspaper editorials in Iran blamed the bombing on British or American authorities seeking to further justify the War on Terror, and claimed that the plan that included the bombings also involved increasing harassment of Muslims in Europe.


title: 7 July 2005 London bombings

text: On 13 August, quoting police and MI5 sources, "The Independent" reported that the bombers acted independently of an al-Qaeda terror mastermind some place abroad.


title: 7 July 2005 London bombings

text: On 1 September, it was reported that al-Qaeda officially claimed responsibility for the attacks in a videotape broadcast by the Arab television network Al Jazeera. However, an official inquiry by the British government reported that the tape claiming responsibility had been edited after the attacks, and that the bombers did not have direct assistance from al-Qaeda. Zabi uk-Taifi, an al-Qaeda commander arrested in Pakistan in January 2009, may have had connections to the bombings, according to Pakistani intelligence sources. More recently, documents found by German authorities on a terrorist suspect arrested in Berlin in May 2011 have suggested that Rashid Rauf, a British al Qaeda operative, played a key role in planning the attacks.


title: 7 July 2005 London bombings

text: A second claim of responsibility was posted on the Internet by another al-Qaeda-linked group, Abu Hafs al-Masri Brigades. The group had, however, previously falsely claimed responsibility for events that were the result of technical problems, such as the 2003 London blackout and the US Northeast blackout of 2003.


title: 7 July 2005 London bombings

text: A survey of 500 British Muslims undertaken by Channel 4 News in 2007 found that 24% believed the four bombers blamed for the attacks did not perform them.


title: 7 July 2005 London bombings

text: There have been various conspiracy theories proposed about the bombings, including the suggestion that the bombers were 'patsies', based on claims about timings of the trains and the train from Luton, supposed explosions underneath the carriages, and allegations of the faking of the one time-stamped and dated photograph of the bombers at Luton station. Claims made by one theorist in the Internet video "7/7 Ripple Effect" were examined by the BBC documentary series "The Conspiracy Files", in an episode titled "7/7" first broadcast on 30 June 2009, which debunked many of the video's claims.


title: 7 July 2005 London bombings

text: On the day of the bombings, Peter Power of Visor Consultants gave interviews on BBC Radio 5 Live and ITV saying that he was working on a crisis management simulation drill, in the City of London, "based on simultaneous bombs going off precisely at the railway stations where it happened this morning", when he heard that an attack was going on in real life. He described this as a coincidence. He also gave an interview to the "Manchester Evening News" where he spoke of "an exercise involving mock broadcasts when it happened for real". After a few days he dismissed it as a "spooky coincidence" on Canadian TV.


title: 7 July 2005 London bombings

text: Alexander Litvinenko, a former officer of Russia's Federal Security Service, was asked who he thought the culprits of the attacks were, in an interview. Litvinenko stated, "You know, I have spoken about it earlier and I shall say now, that I know only one organization, which has made terrorism the main tool of solving of political problems. It is the Russian special services."


title: 7 July 2005 London bombings

text: Initially, there was much confused information from police sources as to the origin, method, and even timings of the explosions. Forensic examiners had thought initially that military-grade plastic explosives were used, and, as the blasts were thought to have been simultaneous, that synchronised timed detonators were employed. This hypothesis changed as more information became available. Home-made organic peroxide-based devices were used, according to a May 2006 report from the British government's Intelligence and Security Committee. The explosive was triacetone triperoxide.


title: 7 July 2005 London bombings

text: Fifty-six people, including the four suicide bombers, were killed by the attacks and about 700 were injured, of whom about 100 were hospitalised for at least one night. The incident was the deadliest single act of terrorism in the United Kingdom since the 1988 bombing of Pan Am Flight 103, which crashed on Lockerbie and killed 270 people, and the deadliest bombing in London since the Second World War.


title: 7 July 2005 London bombings

text: Police examined about 2,500 items of CCTV footage and forensic evidence from the scenes of the attacks. The bombs were probably placed on the floors of the trains and bus. Investigators identified four men whom they alleged had been the suicide bombers. This made the bombings the first ever suicide attack in the British Isles.


title: 7 July 2005 London bombings

text: Vincent Cannistraro, former head of the Central Intelligence Agency's anti-terrorism centre, told "The Guardian" that "two unexploded bombs" were recovered as well as "mechanical timing devices"; this claim was explicitly rejected by London's Metropolitan Police Service.


title: 7 July 2005 London bombings

text: West Yorkshire Police raided six properties in the Leeds area on 12 July: two houses in Beeston, two in Thornhill, one in Holbeck and one in Alexandra Grove in Hyde Park. One man was arrested. Officers also raided a residential property on Northern Road in the Buckinghamshire town of Aylesbury on 13 July.


title: 7 July 2005 London bombings

text: The police service say a significant amount of explosive material was found in the Leeds raids and a controlled explosion was carried out at one of the properties. Explosives were also found in the vehicle associated with one of the bombers, Shehzad Tanweer, at Luton railway station and subjected to controlled explosion.


title: 7 July 2005 London bombings

text: There was speculation about a possible association between the bombers and another alleged Islamist cell in Luton which was ended during August 2004. The Luton group was uncovered after Muhammad Naeem Noor Khan was arrested in Lahore, Pakistan. His laptop computer was said to contain plans for tube attacks in London, as well as attacks on financial buildings in New York City and Washington, D.C. The group was subject to surveillance but on 2 August 2004 "The New York Times" published Khan's name, citing Pakistani sources. The news leak forced police in Britain and Canada to make arrests before their investigations were complete.


title: 7 July 2005 London bombings

text: When the Luton cell was ended, one of the London bombers, Mohammad Sidique Khan (no known relation), was scrutinised briefly by MI5 who determined that he was not a likely threat and he was not surveilled.


title: 7 July 2005 London bombings

text: On March 22, 2007, three people were arrested in connection with these bombings. Two were arrested at 1p.m. at Manchester Airport, attempting to board a flight bound for Pakistan that afternoon. They were apprehended by undercover officers who had been following the men as part of a surveillance operation. They had not intended to arrest the men that day, but believed they could not risk letting the suspects leave the country. A third man was arrested in the Beeston area of Leeds at an address on the street where one of the suicide bombers had lived before the attacks.


title: 7 July 2005 London bombings

text: On 9 May 2007, police made four further arrests, three in Yorkshire and one in Selly Oak, Birmingham. The widow of the presumed ringleader Mohammed Sidique Khan, was among those arrested for "commissioning, preparing or instigating acts of terrorism".


title: 7 July 2005 London bombings

text: Three of those arrested, including Khan's widow, were released on 15 May. The fourth, Khalid Khaliq, an unemployed single father of three, was charged on 17 July 2007 with possessing an al-Qaeda training manual, but the charge was not related to the 2005 London attacks. Conviction for possession of a document containing information likely to be useful to a person committing or preparing an act of terrorism carried a maximum ten-year jail sentence.


title: 7 July 2005 London bombings

text: Abdullah el-Faisal was deported to Jamaica, his country of origin, from Britain on 25 May 2006 after reaching the parole date in his prison sentence. He was found guilty of three charges of soliciting the murder of Jews, Americans and Hindus and two charges of using threatening words to incite racial hatred in 2003 and, despite an appeal, was sentenced to seven years imprisonment. In 2006 John Reid alleged to MPs that el-Faisal had influenced Jamaican-born Briton Germaine Lindsay into participating in the 7/7 bombings.


title: 7 July 2005 London bombings

text: "The Guardian" reported on 3 May 2007 that police had investigated Mohammad Sidique Khan twice during 2005. The newspaper said it "learned that on 27 January 2005, police took a statement from the manager of a garage in Leeds which had loaned Khan a courtesy car while his vehicle was being repaired." It also said that "on the afternoon of 3 February an officer from Scotland Yard's anti-terrorism branch carried out inquiries with the company which had insured a car in which Khan was seen driving almost a year earlier". Nothing about these inquiries appeared in the report by Parliament's intelligence and security committee after it investigated the 7 July attacks. Scotland Yard described the 2005 inquiries as "routine", while security sources said they were related to the fertiliser bomb plot.


title: 7 July 2005 London bombings

text: While no warnings before 7 July bombings have been documented officially or acknowledged, the following are sometimes quoted as indications either of the events to come or of some foreknowledge.


title: 7 July 2005 London bombings

text: "The Daily Telegraph" reported that radical imam Anwar al-Awlaki had inspired the bombers. The bombers transcribed lectures of al-Awlaki while plotting the bombings. His materials were found in the possession of accused accomplices of the suicide bombers. Al-Awlaki was killed by a US drone attack in 2011.


title: 7 July 2005 London bombings

text: In 2006, the government refused to hold a public inquiry, stating that "it would be a ludicrous diversion". Prime Minister Tony Blair said an independent inquiry would "undermine support" for MI5, while the leader of the opposition, David Cameron, said only a full inquiry would "get to the truth". In reaction to revelations about the extent of security service investigations into the bombers prior to the attack, the Shadow Home Secretary, David Davis, said: "It is becoming more and more clear that the story presented to the public and Parliament is at odds with the facts."


title: 7 July 2005 London bombings

text: After Cameron became Prime Minister in 2010, an independent coroner's inquest of the bombings began. Lady Justice Hallett was appointed to hear the inquest, which would consider how each victim died and whether MI5, if it had worked better, could have prevented the attack, and also the emergency service response.


title: 7 July 2005 London bombings

text: After seven months of evidence and deliberation, the verdict of the inquiry was released and read in the Houses of Parliament on 9 May 2011. It determined that the 52 victims had been unlawfully killed; their deaths could not have been prevented, and they would probably have died "whatever time the emergency services reached and rescued them". Hallett concluded that MI5 had not made every possible improvement since the attacks but that it was not "right or fair" to say more attention should have been paid to ringleader Mohammad Sidique Khan prior to 7 July. She also decided that there should be no public inquiry.


title: 7 July 2005 London bombings

text: It was reported in July 2011 that relatives of some of the victims of the bombings may have had their telephones accessed by the "News of the World" in the aftermath of the attacks. The revelations added to an existing controversy over phone hacking by the tabloid newspaper.


title: 7 July 2005 London bombings

text: The fathers of two victims, one in the Edgware Road blast and another at Russell Square, told the BBC that police officers investigating the alleged hacking had warned them that their contact details were found on a target list, while a former firefighter who helped injured passengers escape from Edgware Road also said he had been contacted by police who were looking into the hacking allegations. A number of survivors from the bombed trains also revealed that police had warned them their phones may have been accessed and their messages intercepted, and in some cases officers advised them to change security codes and PINs.


title: 7 July 2005 London bombings

text: Since the bombings, the United Kingdom and other nations have honoured the victims in several ways. Most of these memorials have included moments of silence, candlelit vigils, and the laying of flowers at the attack sites. Foreign leaders have also remembered the dead by ordering their flags to be flown at half-mast, signing books of condolences at embassies of the UK, and issuing messages of support and condolences to the British people.


title: 7 July 2005 London bombings

text: The government ordered the Union Flag to be flown at half-mast on 8 July. The following day, the Bishop of London led prayers for the victims during a service paying tribute to the role of women during the Second World War. A vigil, called by the Stop the War Coalition, Campaign for Nuclear Disarmament and Muslim Association of Britain, was held from 5p.m., at Friends Meeting House on Euston Road.


title: 7 July 2005 London bombings

text: A two-minute silence was held on 14 July 2005 throughout Europe. Thousands attended a vigil at 6p.m. on Trafalgar Square. After an initial silence there was a series of speakers for two hours. A memorial service was held at St Paul's Cathedral on 1 November 2005. To mark the first anniversary of the attack, a two-minute silence was observed at midday across the country.


title: 7 July 2005 London bombings

text: A permanent memorial was unveiled in 2009 by Charles, Prince of Wales in Hyde Park to mark the fourth anniversary of the bombings. On the eve of the ninth anniversary of the attacks in 2014 the memorial was defaced with messages including "Blair lied, thousands died". The graffiti was removed within hours.


title: 7 July 2005 London bombings

text: During the opening ceremony of the 2012 Olympic Games in London a minute's silence was held to commemorate those killed in the attacks.


title: 7 July 2005 London bombings

text: A memorial service was held in St. Paul's Cathedral on 7 July 2015, to mark the tenth anniversary of the bombings. This was broadcast on BBC One.


title: 7 July 2005 London bombings

text: US President George W. Bush visited the British embassy the day after the bombings, upon his return from the G8 summit in Scotland, and signed a book of condolence. In Washington, D.C., the US Army band played "God Save the Queen" (the British national anthem, the melody of which is also used in an American patriotic hymn, "My Country, 'Tis of Thee"), a suggestion that US Army veteran John Miska made to Vice Chief of Staff General Cody, outside the British embassy in the city. A similar tribute had been made by the Queen in the days following the September 11 attacks in 2001 where the Star Spangled Banner played at Buckingham Palace's Changing the Guard. On 12 July, a Detroit Symphony Orchestra brass ensemble played the British national anthem during the pre-game festivities of the Major League Baseball All-Star Game at Comerica Park in Detroit.


title: 7 July 2005 London bombings

text: Flags were ordered to fly at half-mast across Australia, New Zealand and Canada. The Union Flag was raised to half-mast alongside the Flag of Australia on Sydney Harbour Bridge as a show of "sympathy between nations".


title: 7 July 2005 London bombings

text: Moments of silence were observed in the European Parliament, the Polish parliament and by the Irish parliament on 14 July. The British national anthem was played at the changing of the royal guard at Plaza de Oriente in Madrid in memorial to the victims of the attacks. The ceremony was attended by the British ambassador to Spain and members of the Spanish Royal Family. After the 2004 Madrid train bombings, the UK had hosted a similar ceremony at Buckingham Palace.


title: 7 July 2005 London bombings

text: Mohammed Rehman and Sana Ahmed Khan were sentenced to life imprisonment on 29 December 2015 for preparing an act of terrorism, planning to coincide with the tenth anniversary of the 7/7 attacks. They had 10kg of urea nitrate. Rehman called himself the 'silent bomber' and asked his Twitter followers to choose between the Westfield London or the London Underground for the planned suicide bomb.


title: Phosphorus

text: Phosphorus is a chemical element with the symbol P and atomic number 15. Elemental phosphorus exists in two major forms, white phosphorus and red phosphorus, but because it is highly reactive, phosphorus is never found as a free element on Earth. It has a concentration in the Earth's crust of about one gram per kilogram (compare copper at about 0.06 grams). In minerals, phosphorus generally occurs as phosphate.


title: Phosphorus

text: Elemental phosphorus was first isolated as white phosphorus in 1669. White phosphorus emits a faint glow when exposed to oxygen – hence the name, taken from Greek mythology, meaning 'light-bearer' (Latin ), referring to the "Morning Star", the planet Venus. The term "phosphorescence", meaning glow after illumination, derives from this property of phosphorus, although the word has since been used for a different physical process that produces a glow. The glow of phosphorus is caused by oxidation of the white (but not red) phosphorus — a process now called chemiluminescence. Together with nitrogen, arsenic, antimony, and bismuth, phosphorus is classified as a pnictogen.


title: Phosphorus

text: Phosphorus is an element essential to sustaining life largely through phosphates, compounds containing the phosphate ion, PO. Phosphates are a component of DNA, RNA, ATP, and phospholipids, complex compounds fundamental to cells. Elemental phosphorus was first isolated from human urine, and bone ash was an important early phosphate source. Phosphate mines contain fossils because phosphate is present in the fossilized deposits of animal remains and excreta. Low phosphate levels are an important limit to growth in some aquatic systems. The vast majority of phosphorus compounds mined are consumed as fertilisers. Phosphate is needed to replace the phosphorus that plants remove from the soil, and its annual demand is rising nearly twice as fast as the growth of the human population. Other applications include organophosphorus compounds in detergents, pesticides, and nerve agents.


title: Phosphorus

text: Phosphorus has several allotropes that exhibit strikingly diverse properties. The two most common allotropes are white phosphorus and red phosphorus.


title: Phosphorus

text: From the perspective of applications and chemical literature, the most important form of elemental phosphorus is white phosphorus, often abbreviated as WP. It is a soft, waxy solid which consists of tetrahedral molecules, in which each atom is bound to the other three atoms by a formal single bond. This tetrahedron is also present in liquid and gaseous phosphorus up to the temperature of when it starts decomposing to molecules. The molecule in the gas phase has a P-P bond length of "r" = 2.1994(3) Å as was determined by gas electron diffraction. The nature of bonding in this tetrahedron can be described by spherical aromaticity or cluster bonding, that is the electrons are highly delocalized. This has been illustrated by calculations of the magnetically induced currents, which sum up to 29 nA/T, much more than in the archetypical aromatic molecule benzene (11 nA/T).


title: Phosphorus

text: White phosphorus exists in two crystalline forms: α (alpha) and β (beta). At room temperature, the α-form is stable. It is more common, has cubic crystal structure and at , it transforms into β-form, which has hexagonal crystal structure. These forms differ in terms of the relative orientations of the constituent P tetrahedra. The β form of white phosphorus contains three slightly different molecules, i.e. 18 different P-P bond lengths between 2.1768(5) and 2.1920(5) Å. The average P-P bond length is 2.183(5) Å.


title: Phosphorus

text: White phosphorus is the least stable, the most reactive, the most volatile, the least dense and the most toxic of the allotropes. White phosphorus gradually changes to red phosphorus. This transformation is accelerated by light and heat, and samples of white phosphorus almost always contain some red phosphorus and accordingly appear yellow. For this reason, white phosphorus that is aged or otherwise impure (e.g., weapons-grade, not lab-grade WP) is also called yellow phosphorus. When exposed to oxygen, white phosphorus glows in the dark with a very faint tinge of green and blue. It is highly flammable and pyrophoric (self-igniting) upon contact with air. Owing to its pyrophoricity, white phosphorus is used as an additive in napalm. The odour of combustion of this form has a characteristic garlic smell, and samples are commonly coated with white phosphorus pentoxide, which consists of tetrahedra with oxygen inserted between the phosphorus atoms and at their vertices. White phosphorus is insoluble in water but soluble in carbon disulfide.


title: Phosphorus

text: Thermal decomposition of P at 1100 K gives diphosphorus, P. This species is not stable as a solid or liquid. The dimeric unit contains a triple bond and is analogous to N. It can also be generated as a transient intermediate in solution by thermolysis of organophosphorus precursor reagents. At still higher temperatures, P dissociates into atomic P.


title: Phosphorus

text: Red phosphorus is polymeric in structure. It can be viewed as a derivative of P wherein one P-P bond is broken, and one additional bond is formed with the neighbouring tetrahedron resulting in chains of P molecules linked by van der Waals forces. Red phosphorus may be formed by heating white phosphorus to or by exposing white phosphorus to sunlight. Phosphorus after this treatment is amorphous. Upon further heating, this material crystallises. In this sense, red phosphorus is not an allotrope, but rather an intermediate phase between the white and violet phosphorus, and most of its properties have a range of values. For example, freshly prepared, bright red phosphorus is highly reactive and ignites at about , though it is more stable than white phosphorus, which ignites at about . After prolonged heating or storage, the color darkens (see infobox images); the resulting product is more stable and does not spontaneously ignite in air.


title: Phosphorus

text: Violet phosphorus is a form of phosphorus that can be produced by day-long annealing of red phosphorus above 550 °C. In 1865, Hittorf discovered that when phosphorus was recrystallised from molten lead, a red/purple form is obtained. Therefore, this form is sometimes known as "Hittorf's phosphorus" (or violet or α-metallic phosphorus).


title: Phosphorus

text: Black phosphorus is the least reactive allotrope and the thermodynamically stable form below . It is also known as β-metallic phosphorus and has a structure somewhat resembling that of graphite. It is obtained by heating white phosphorus under high pressures (about ). It can also be produced at ambient conditions using metal salts, e.g. mercury, as catalysts. In appearance, properties, and structure, it resembles graphite, being black and flaky, a conductor of electricity, and has puckered sheets of linked atoms.


title: Phosphorus

text: Another form, scarlet phosphorus, is obtained by allowing a solution of white phosphorus in carbon disulfide to evaporate in sunlight.


title: Phosphorus

text: When first isolated, it was observed that the green glow emanating from white phosphorus would persist for a time in a stoppered jar, but then cease. Robert Boyle in the 1680s ascribed it to "debilitation" of the air. Actually, it is oxygen being consumed. By the 18th century, it was known that in pure oxygen, phosphorus does not glow at all; there is only a range of partial pressures at which it does. Heat can be applied to drive the reaction at higher pressures.


title: Phosphorus

text: In 1974, the glow was explained by R. J. van Zee and A. U. Khan. A reaction with oxygen takes place at the surface of the solid (or liquid) phosphorus, forming the short-lived molecules HPO and that both emit visible light. The reaction is slow and only very little of the intermediates are required to produce the luminescence, hence the extended time the glow continues in a stoppered jar.


title: Phosphorus

text: Since its discovery, "phosphors" and "phosphorescence" were used loosely to describe substances that shine in the dark without burning. Although the term phosphorescence is derived from phosphorus, the reaction that gives phosphorus its glow is properly called chemiluminescence (glowing due to a cold chemical reaction), not phosphorescence (re-emitting light that previously fell onto a substance and excited it).


title: Phosphorus

text: There are 23 known isotopes of phosphorus, ranging from to . Only is stable and is therefore present at 100% abundance. The half-integer nuclear spin and high abundance of P make phosphorus-31 NMR spectroscopy a very useful analytical tool in studies of phosphorus-containing samples.


title: Phosphorus

text: Two radioactive isotopes of phosphorus have half-lives suitable for biological scientific experiments. These are:


title: Phosphorus

text: The high energy beta particles from penetrate skin and corneas and any ingested, inhaled, or absorbed is readily incorporated into bone and nucleic acids. For these reasons, Occupational Safety and Health Administration in the United States, and similar institutions in other developed countries require personnel working with to wear lab coats, disposable gloves, and safety glasses or goggles to protect the eyes, and avoid working directly over open containers. Monitoring personal, clothing, and surface contamination is also required. Shielding requires special consideration. The high energy of the beta particles gives rise to secondary emission of X-rays via Bremsstrahlung (braking radiation) in dense shielding materials such as lead. Therefore, the radiation must be shielded with low density materials such as acrylic or other plastic, water, or (when transparency is not required), even wood.


title: Phosphorus

text: In 2013, astronomers detected phosphorus in Cassiopeia A, which confirmed that this element is produced in supernovae as a byproduct of supernova nucleosynthesis. The phosphorus-to-iron ratio in material from the supernova remnant could be up to 100 times higher than in the Milky Way in general.


title: Phosphorus

text: In 2020, astronomers analysed ALMA and ROSINA data from the massive star-forming region AFGL 5142, to detect phosphorus-bearing molecules and how they are carried in comets to the early Earth.


title: Phosphorus

text: Phosphorus has a concentration in the Earth's crust of about one gram per kilogram (compare copper at about 0.06 grams). It is not found free in nature, but is widely distributed in many minerals, usually as phosphates. Inorganic phosphate rock, which is partially made of apatite (a group of minerals being, generally, pentacalcium triorthophosphate fluoride (hydroxide)), is today the chief commercial source of this element. According to the US Geological Survey (USGS), about 50 percent of the global phosphorus reserves are in the Arab nations. 85% of Earth's known reserves are in Morocco with smaller deposits in China, Russia, Florida, Idaho, Tennessee, Utah, and elsewhere. Albright and Wilson in the UK and their Niagara Falls plant, for instance, were using phosphate rock in the 1890s and 1900s from Tennessee, Florida, and the Îles du Connétable (guano island sources of phosphate); by 1950, they were using phosphate rock mainly from Tennessee and North Africa.


title: Phosphorus

text: Organic sources, namely urine, bone ash and (in the latter 19th century) guano, were historically of importance but had only limited commercial success. As urine contains phosphorus, it has fertilising qualities which are still harnessed today in some countries, including Sweden, using methods for reuse of excreta. To this end, urine can be used as a fertiliser in its pure form or part of being mixed with water in the form of sewage or sewage sludge.


title: Phosphorus

text: The most prevalent compounds of phosphorus are derivatives of phosphate (PO), a tetrahedral anion. Phosphate is the conjugate base of phosphoric acid, which is produced on a massive scale for use in fertilisers. Being triprotic, phosphoric acid converts stepwise to three conjugate bases:


title: Phosphorus

text: Phosphate exhibits a tendency to form chains and rings containing P-O-P bonds. Many polyphosphates are known, including ATP. Polyphosphates arise by dehydration of hydrogen phosphates such as HPO and HPO. For example, the industrially important pentasodium triphosphate (also known as sodium tripolyphosphate, STPP) is produced industrially on by the megatonne by this condensation reaction:


title: Phosphorus

text: Phosphorus pentoxide (PO) is the acid anhydride of phosphoric acid, but several intermediates between the two are known. This waxy white solid reacts vigorously with water.


title: Phosphorus

text: With metal cations, phosphate forms a variety of salts. These solids are polymeric, featuring P-O-M linkages. When the metal cation has a charge of 2+ or 3+, the salts are generally insoluble, hence they exist as common minerals. Many phosphate salts are derived from hydrogen phosphate (HPO).


title: Phosphorus

text: PCl and PF are common compounds. PF is a colourless gas and the molecules have trigonal bipyramidal geometry. PCl is a colourless solid which has an ionic formulation of PCl PCl, but adopts the trigonal bipyramidal geometry when molten or in the vapour phase. PBr is an unstable solid formulated as PBrBrand PI is not known. The pentachloride and pentafluoride are Lewis acids. With fluoride, PF forms PF, an anion that is isoelectronic with SF. The most important oxyhalide is phosphorus oxychloride, (POCl), which is approximately tetrahedral.


title: Phosphorus

text: Before extensive computer calculations were feasible, it was thought that bonding in phosphorus(V) compounds involved "d" orbitals. Computer modeling of molecular orbital theory indicates that this bonding involves only s- and p-orbitals.


title: Phosphorus

text: All four symmetrical trihalides are well known: gaseous PF, the yellowish liquids PCl and PBr, and the solid PI. These materials are moisture sensitive, hydrolysing to give phosphorous acid. The trichloride, a common reagent, is produced by chlorination of white phosphorus:


title: Phosphorus

text: The trifluoride is produced from the trichloride by halide exchange. PF is toxic because it binds to haemoglobin.


title: Phosphorus

text: Phosphorus(III) oxide, PO (also called tetraphosphorus hexoxide) is the anhydride of P(OH), the minor tautomer of phosphorous acid. The structure of PO is like that of PO without the terminal oxide groups.


title: Phosphorus

text: These compounds generally feature P–P bonds. Examples include catenated derivatives of phosphine and organophosphines. Compounds containing P=P double bonds have also been observed, although they are rare.


title: Phosphorus

text: Phosphides arise by reaction of metals with red phosphorus. The alkali metals (group 1) and alkaline earth metals can form ionic compounds containing the phosphide ion, P. These compounds react with water to form phosphine. Other phosphides, for example NaP, are known for these reactive metals. With the transition metals as well as the monophosphides there are metal-rich phosphides, which are generally hard refractory compounds with a metallic lustre, and phosphorus-rich phosphides which are less stable and include semiconductors. Schreibersite is a naturally occurring metal-rich phosphide found in meteorites. The structures of the metal-rich and phosphorus-rich phosphides can be complex.


title: Phosphorus

text: Phosphine (PH) and its organic derivatives (PR) are structural analogues of ammonia (NH), but the bond angles at phosphorus are closer to 90° for phosphine and its organic derivatives. It is an ill-smelling, toxic compound. Phosphorus has an oxidation number of −3 in phosphine. Phosphine is produced by hydrolysis of calcium phosphide, CaP. Unlike ammonia, phosphine is oxidised by air. Phosphine is also far less basic than ammonia. Other phosphines are known which contain chains of up to nine phosphorus atoms and have the formula PH. The highly flammable gas diphosphine (PH) is an analogue of hydrazine.


title: Phosphorus

text: Phosphorous oxoacids are extensive, often commercially important, and sometimes structurally complicated. They all have acidic protons bound to oxygen atoms, some have nonacidic protons that are bonded directly to phosphorus and some contain phosphorus - phosphorus bonds. Although many oxoacids of phosphorus are formed, only nine are commercially important, and three of them, hypophosphorous acid, phosphorous acid, and phosphoric acid, are particularly important.


title: Phosphorus

text: The PN molecule is considered unstable, but is a product of crystalline phosphorus nitride decomposition at 1100 K. Similarly, HPN is considered unstable, and phosphorus nitride halogens like FPN, ClPN, BrPN, and IPN oligomerise into cyclic Polyphosphazenes. For example, compounds of the formula (PNCl) exist mainly as rings such as the trimer hexachlorophosphazene. The phosphazenes arise by treatment of phosphorus pentachloride with ammonium chloride:PCl + NHCl → 1/"n" (NPCl) + 4 HClWhen the chloride groups are replaced by alkoxide (RO), a family of polymers is produced with potentially useful properties.


title: Phosphorus

text: Phosphorus forms a wide range of sulfides, where the phosphorus can be in P(V), P(III) or other oxidation states. The three-fold symmetric PS is used in strike-anywhere matches. PS and PO have analogous structures. Mixed oxyhalides and oxyhydrides of phosphorus(III) are almost unknown.


title: Phosphorus

text: Compounds with P-C and P-O-C bonds are often classified as organophosphorus compounds. They are widely used commercially. The PCl serves as a source of P in routes to organophosphorus(III) compounds. For example, it is the precursor to triphenylphosphine:


title: Phosphorus

text: Treatment of phosphorus trihalides with alcohols and phenols gives phosphites, e.g. triphenylphosphite:


title: Phosphorus

text: The name "Phosphorus" in Ancient Greece was the name for the planet Venus and is derived from the Greek words (φῶς = light, φέρω = carry), which roughly translates as light-bringer or light carrier. (In Greek mythology and tradition, Augerinus (Αυγερινός = morning star, still in use today), Hesperus or Hesperinus (΄Εσπερος or Εσπερινός or Αποσπερίτης = evening star, still in use today) and Eosphorus (Εωσφόρος = dawnbearer, not in use for the planet after Christianity) are close homologues, and also associated with Phosphorus-the-morning-star).


title: Phosphorus

text: According to the Oxford English Dictionary, the correct spelling of the element is "phosphorus". The word "phosphorous" is the adjectival form of the P valence: so, just as sulfur forms "sulfurous" and "sulfuric" compounds, phosphorus forms phosphorous compounds (e.g., phosphorous acid) and P valence phosphoric compounds (e.g., phosphoric acids and phosphates).


title: Phosphorus

text: The discovery of phosphorus, the first element to be discovered that was not known since ancient times, is credited to the German alchemist Hennig Brand in 1669, although others might have discovered phosphorus around the same time. Brand experimented with urine, which contains considerable quantities of dissolved phosphates from normal metabolism. Working in Hamburg, Brand attempted to create the fabled philosopher's stone through the distillation of some salts by evaporating urine, and in the process produced a white material that glowed in the dark and burned brilliantly. It was named "phosphorus mirabilis" ("miraculous bearer of light").


title: Phosphorus

text: Brand's process originally involved letting urine stand for days until it gave off a terrible smell. Then he boiled it down to a paste, heated this paste to a high temperature, and led the vapours through water, where he hoped they would condense to gold. Instead, he obtained a white, waxy substance that glowed in the dark. Brand had discovered phosphorus. Specifically, Brand produced ammonium sodium hydrogen phosphate, . While the quantities were essentially correct (it took about of urine to make about 60 g of phosphorus), it was unnecessary to allow the urine to rot first. Later scientists discovered that fresh urine yielded the same amount of phosphorus.


title: Phosphorus

text: Brand at first tried to keep the method secret, but later sold the recipe for 200 thalers to D. Krafft from Dresden. Krafft toured much of Europe with it, including England, where he met with Robert Boyle. The secret—that the substance was made from urine—leaked out, and Johann Kunckel (1630–1703) was able to reproduce it in Sweden (1678). Later, Boyle in London (1680) also managed to make phosphorus, possibly with the aid of his assistant, Ambrose Godfrey-Hanckwitz. Godfrey later made a business of the manufacture of phosphorus.


title: Phosphorus

text: Boyle states that Krafft gave him no information as to the preparation of phosphorus other than that it was derived from "somewhat that belonged to the body of man". This gave Boyle a valuable clue, so that he, too, managed to make phosphorus, and published the method of its manufacture. Later he improved Brand's process by using sand in the reaction (still using urine as base material),


title: Phosphorus

text: Robert Boyle was the first to use phosphorus to ignite sulfur-tipped wooden splints, forerunners of our modern matches, in 1680.


title: Phosphorus

text: Phosphorus was the 13th element to be discovered. Because of its tendency to spontaneously combust when left alone in air, it is sometimes referred to as "the Devil's element".


title: Phosphorus

text: Antoine Lavoisier recognized phosphorus as an element in 1777 after Johan Gottlieb Gahn and Carl Wilhelm Scheele, in 1769, showed that calcium phosphate () is found in bones by obtaining elemental phosphorus from bone ash.


title: Phosphorus

text: Bone ash was the major source of phosphorus until the 1840s. The method started by roasting bones, then employed the use of fire clay retorts encased in a very hot brick furnace to distill out the highly toxic elemental phosphorus product. Alternately, precipitated phosphates could be made from ground-up bones that had been de-greased and treated with strong acids. White phosphorus could then be made by heating the precipitated phosphates, mixed with ground coal or charcoal in an iron pot, and distilling off phosphorus vapour in a retort. Carbon monoxide and other flammable gases produced during the reduction process were burnt off in a flare stack.


title: Phosphorus

text: In the 1840s, world phosphate production turned to the mining of tropical island deposits formed from bird and bat guano (see also Guano Islands Act). These became an important source of phosphates for fertiliser in the latter half of the 19th century.