mathematical physics, Branch of mathematical analysis that emphasizes tools and techniques of particular use to physicists and engineers. It focuses on vector spaces, matrix algebra, differential equations (especially for boundary value problems), integral equations, integral transforms, infinite

mathematical Platonism, in metaphysics and the philosophy of mathematics, the doctrine that there exist abstract objects—objects that are wholly nonspatiotemporal, nonphysical, and nonmental—and that there are true mathematical sentences that express true descriptions of such objects. The

Principia, book about physics by Isaac Newton, the fundamental work for the whole of modern science. Published in 1687, the Principia lays out Newton’s three laws of motion (the basic principles of modern physics), which resulted in the formulation of the law of universal gravitation. The Principia

mathematical programming, theoretical tool of management science and economics in which management operations are described by mathematical equations that can be manipulated for a variety of purposes. If the basic descriptions involved take the form of linear algebraic equations, the technique is

completeness: In proof theory, a formal system is said to be syntactically complete if and only if every closed sentence in the system is such that either it or its negation is provable in the system. In model theory, a formal system is said to be semantically…

Francis Ysidro Edgeworth: His most famous work, Mathematical Psychics (1881), presented his new ideas on the generalized utility function, the indifference curve, and the contract curve, all of which have become standard devices of economic theory.

number game, any of various puzzles and games that involve aspects of mathematics. Mathematical recreations comprise puzzles and games that vary from naive amusements to sophisticated problems, some of which have never been solved. They may involve arithmetic, algebra, geometry, theory of numbers,

number game, any of various puzzles and games that involve aspects of mathematics. Mathematical recreations comprise puzzles and games that vary from naive amusements to sophisticated problems, some of which have never been solved. They may involve arithmetic, algebra, geometry, theory of numbers,

number game: 20th century: Rouse Ball’s Mathematical Recreations and Essays appeared in 1892; it soon became a classic, largely because of its scholarly approach. After passing through 10 editions it was revised by the British professor H.S.M. Coxeter in 1938; it is still a standard reference.

information theory: Historical background: …1948 of Claude Shannon’s “A Mathematical Theory of Communication” in the Bell System Technical Journal. A key step in Shannon’s work was his realization that, in order to have a theory, communication signals must be treated in isolation from the meaning of the messages that they transmit. This view…

Edward Thomas Copson: Baker, The Mathematical Theory of Huygens’ Principle (1939), concerning the generation and structure of waves. His other publications include Asymptotic Expansions (1965) and Metric Spaces (1968).

Arthur Eddington: Early life: … (1920) and his great treatise The Mathematical Theory of Relativity (1923)—the latter considered by Einstein the finest presentation of the subject in any language—made Eddington a leader in the field of relativity physics. His own contribution was chiefly a brilliant modification of affine (non-Euclidean) geometry, leading to a geometry of…

Sir Horace Lamb: …was enlarged and transformed into Hydrodynamics (1895); the latter was for many years the standard work on hydrodynamics. His other publications include Infinitesimal Calculus (1897), Dynamical Theory of Sound (1910), Statics (1912), Dynamics (1914), and Higher Mechanics (1920). His many papers, principally on applied mathematics, detailed his researches on wave…

Pythagoreanism: Two Pythagorean sects: , the esoteric teachings) and mathēmatikoi (from mathēmatikos, “scientific”), may have occurred at that time. The acousmatics devoted themselves to the observance of rituals and rules and to the interpretation of the sayings of the master; the “mathematics” were concerned with the scientific aspects of Pythagoreanism. Philolaus, who was rather…

G.H. Hardy: A Mathematician’s Apology (1940), which gives a completely personal account of how mathematicians think, continues to be widely read. He was widely honoured for his work, being elected a fellow of the Royal Society (1910) and president of the London Mathematical Society (1926–28, 1939–41).

mathematicism, the effort to employ the formal structure and rigorous method of mathematics as a model for the conduct of philosophy. Mathematicism is manifested in Western philosophy in at least three ways: (1) General mathematical methods of investigation can be used to establish consistency of

Clark L. Hull: …theories were first presented in Mathematico-Deductive Theory of Rote Learning (1940), a collaboration with several coworkers, in which he expressed his findings through postulates stated in both mathematical and verbal forms. Hull believed that psychology had its own quantitative laws that could be stated in mathematical equations. He further developed…

mathematics, the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation, and its development has involved an increasing degree of idealization and

logic puzzle: The brakeman, the fireman, and the engineer: …Oswald Jacoby and William Benson’s Mathematics for Pleasure (1962).

East Asian mathematics, the discipline of mathematics as it developed in China and Japan. When speaking of mathematics in East Asia, it is necessary to take into account China, Japan, Korea, and Vietnam as a whole. At a very early time in their histories, Japan, Korea, and Vietnam all adopted the

foundations of mathematics, the study of the logical and philosophical basis of mathematics, including whether the axioms of a given system ensure its completeness and its consistency. Because mathematics has served as a model for rational inquiry in the West and is used extensively in the

Indian mathematics, the discipline of mathematics as it developed in the Indian subcontinent. The mathematics of classical Indian civilization is an intriguing blend of the familiar and the strange. For the modern individual, Indian decimal place-value numerals may seem familiar—and, in fact, they

philosophy of mathematics, branch of philosophy that is concerned with two major questions: one concerning the meanings of ordinary mathematical sentences and the other concerning the issue of whether abstract objects exist. The first is a straightforward question of interpretation: What is the

Eric Temple Bell: …Men of Mathematics (1937) and Mathematics, Queen and Servant of Science (1951). He also wrote a history of Fermat’s last theorem, The Last Problem (1961). Although rather fanciful and not always historically accurate, these works, particularly Men of Mathematics, continue to attract a wide readership. Under the pen name of…

Pythagoreanism: Two Pythagorean sects: , the esoteric teachings) and mathēmatikoi (from mathēmatikos, “scientific”), may have occurred at that time. The acousmatics devoted themselves to the observance of rituals and rules and to the interpretation of the sayings of the master; the “mathematics” were concerned with the scientific aspects of Pythagoreanism. Philolaus, who was rather…

Cotton Mather was an American Congregational minister and author, supporter of the old order of the ruling clergy, who became the most celebrated of all New England Puritans. He combined a mystical strain (he believed in the existence of witchcraft) with a modern scientific interest (he supported

Increase Mather was a Boston Congregational minister, author, and educator, who was a determining influence in the councils of New England during the crucial period when leadership passed into the hands of the first native-born generation. He was the son of Richard Mather, son-in-law of John

John C. Mather is an American physicist, who was corecipient, with George F. Smoot, of the 2006 Nobel Prize for Physics for discoveries supporting the big-bang model. Mather studied physics at Swarthmore University (B.S., 1968) and the University of California at Berkeley (Ph.D., 1974). He later

Richard Mather was an English-born American Congregational minister, father of Increase Mather and three other Puritan ministers. After joining the Great Migration of Puritans from England to New England (1635), he was elected “teacher” minister at Dorchester, Mass., and became locally celebrated

National Park Service: Establishment of the NPS: In 1914 Stephen Mather, a wealthy businessman, wrote the secretary of the interior about the poor condition of parks he had visited that summer in the Sierra Nevada. The secretary suggested that Mather work to improve the system by joining the department in Washington, D.C. Two years…

Matheran, hill station (resort town) in western Maharashtra state, west-central India. It is located at an elevation of about 2,625 feet (800 metres) on the western side of the Western Ghats range, about 28 miles (45 km) east of Mumbai (formerly Bombay). Matheran was first frequented in the

Eminem is an American rapper, record producer, and actor who is known as one of the most-controversial and best-selling artists of the early 21st century. He was the first recording artist to have 10 consecutive albums debut at number one on the Billboard album chart. Born Marshall Mathers, he had

astrology: In western Europe: 15–20 ce), the Matheseos libri (“Books on Astrology”) of Firmicus Maternus (c. 335), and the anonymous Liber Hermetis (“Book of Hermes”) from the 6th century. In the absence of astronomical tables in Latin, however, none of these was works of any use, and astrology for all practical purposes…

John Wallis: In 1657 Wallis published the Mathesis Universalis (“Universal Mathematics”), on algebra, arithmetic, and geometry, in which he further developed notation. He invented and introduced the symbol ∞ for infinity. This symbol found use in treating a series of squares of indivisibles. His introduction of negative and fractional exponential notation was…

Vilém Mathesius was a Czech linguist and scholar of English language and literature. He was the founder (1926) and president of the Prague Linguistic Circle, famous for its influence on structural linguistics and for its phonological studies. Mathesius taught at Charles University in Prague,

I Am Legend: …novel written by American author Richard Matheson, published in 1954.

I Am Legend: …novel written by American author Richard Matheson, published in 1954.

wandering bishop: Arnold Harris Mathew, a former Roman Catholic priest, was consecrated in 1908 in Utrecht, Netherlands, by Old Catholic bishops. His consecration was later described as having been obtained by misrepresentation, and he was repudiated by the Old Catholics. He tried unsuccessfully to create an Old…

Theobald Mathew was an Irish priest and orator known as the “Apostle of Temperance.” Ordained in 1813, Mathew entered the Capuchin order, of which he was made provincial in 1822. Concurrently, the earliest European temperance organizations were forming in Ireland, and in 1838 Mathew became

Mother Bernardina Matthews was an American religious leader, the founder of the first monastery of a Roman Catholic order in the United States. Matthews grew up in a deeply religious home in a time when Roman Catholics laboured under legal disabilities and other discriminations in Maryland. In 1754

Charles Mathews was a prominent English stage personality and theatre manager who, renowned for his genius at mimicry and for his wit, was among the leading comedians of his day. The son of a bookseller, Mathews was educated at Merchant Taylors School, Crosby, Lancashire. After acting in the

Charles James Mathews was an English writer of comic sketches and one of the best high comedians ever to appear on the English stage. Mathews was the son of the celebrated entertainer Charles Mathews and his wife, the actress Anne Jackson. Although he possessed much of his parents’ theatrical

Eddie Mathews was an American professional baseball third baseman who is the only person to have played for the Braves franchise in all three of the cities it has called home: Boston (1952), Milwaukee (1953–65), and Atlanta (1966). Mathews and teammate Hank Aaron provided the Braves with an

Eddie Mathews was an American professional baseball third baseman who is the only person to have played for the Braves franchise in all three of the cities it has called home: Boston (1952), Milwaukee (1953–65), and Atlanta (1966). Mathews and teammate Hank Aaron provided the Braves with an

typography: Mechanical composition: …those of John Lane and Elkin Mathews, who published Oscar Wilde and the periodical The Yellow Book; J.M. Dent, who commissioned Aubrey Beardsley to illustrate Malory and who used Kelmscott-inspired endpapers for his Everyman’s Library; Stone and Kimball of Chicago

Great Railroad Strike of 1877: Henry M. Mathews dispatched the militia when police were unable to break up the supportive crowd that had gathered. When the militia then proved incapable of freeing the 600 or so trains stranded in Martinsburg (perhaps because many of the militiamen were themselves railroad workers…

Madame Vestris was a British actress, opera singer, and manager who inaugurated tasteful and beautiful stage decor and set a standard in stage costumes. After a brief unsuccessful marriage to Auguste-Armand Vestris, a ballet dancer, Mme Vestris first appeared in Italian opera in 1815 and enjoyed

Madame Vestris was a British actress, opera singer, and manager who inaugurated tasteful and beautiful stage decor and set a standard in stage costumes. After a brief unsuccessful marriage to Auguste-Armand Vestris, a ballet dancer, Mme Vestris first appeared in Italian opera in 1815 and enjoyed

computer music: …at the Bell Telephone Laboratories, Max Vernon Mathews and his coworkers devised a computer capable of synthesizing sound directly. The composer’s input, in the form of mathematical functions, is translated by the computer into synthesized musical sounds that are stored in digital form and can be played back at will.…

computer music: …at the Bell Telephone Laboratories, Max Vernon Mathews and his coworkers devised a computer capable of synthesizing sound directly. The composer’s input, in the form of mathematical functions, is translated by the computer into synthesized musical sounds that are stored in digital form and can be played back at will.…

Mother Bernardina Matthews was an American religious leader, the founder of the first monastery of a Roman Catholic order in the United States. Matthews grew up in a deeply religious home in a time when Roman Catholics laboured under legal disabilities and other discriminations in Maryland. In 1754

Shailer Mathews was a leader of the Social Gospel movement of the late 19th and early 20th centuries in the United States, which interpreted the Kingdom of God as requiring social as well as individual salvation. Educated at Colby College, Waterville, Maine; Newton Theological Institution, Newton,

Christy Mathewson was an American professional baseball player, regarded as one of the greatest pitchers in the history of the game. Mathewson was one of the first “college men” to enter the major leagues, having played football and baseball at Bucknell University in Lewisburg, Pennsylvania. After

Christy Mathewson was an American professional baseball player, regarded as one of the greatest pitchers in the history of the game. Mathewson was one of the first “college men” to enter the major leagues, having played football and baseball at Bucknell University in Lewisburg, Pennsylvania. After

Christy Mathewson was an American professional baseball player, regarded as one of the greatest pitchers in the history of the game. Mathewson was one of the first “college men” to enter the major leagues, having played football and baseball at Bucknell University in Lewisburg, Pennsylvania. After

Kansas: Statehood of Kansas: …heroes of that era was William Mathewson, known as the original “Buffalo Bill” (a nickname also used later to greater fame by William F. Cody), who hunted buffalo for starving settlers for an entire winter without pay, providing meat by the wagonload. The coming of the railroads in the late…

Bob Mathias was an American athlete, the youngest to win a gold medal in the decathlon in Olympic competition. After his victory in 1948 at age 17, he returned to win a second Olympic gold medal in 1952. Afflicted with anemia in boyhood, Mathias developed strength by engaging in sports, and he was

Bob Mathias was an American athlete, the youngest to win a gold medal in the decathlon in Olympic competition. After his victory in 1948 at age 17, he returned to win a second Olympic gold medal in 1952. Afflicted with anemia in boyhood, Mathias developed strength by engaging in sports, and he was

Vince Cable: …seat to the Conservative candidate, Tania Mathias. In the June 2017 snap election, however, he was returned to Parliament, and in July he replaced Tim Farron as leader of the Liberal Democrats. Two years later, however, Cable stepped down as party leader and gave up his seat in Parliament.

Therkel Mathiassen was a Danish archaeologist and ethnographer whose excavations during 1921–23 to the west and north of Hudson Bay revealed the existence of the Thule prehistoric Eskimo culture. His doctoral dissertation for the University of Copenhagen, Archaeology of the Central Eskimos (1927),

Anna de Noailles was a poet, a leading literary figure in France in the pre-World War I period. The daughter of a Romanian prince and granddaughter of a Turkish pasha, she adopted France and its language for her life and writings even before her marriage to a French count. Her friends included the

Claude-Louis Mathieu was a French astronomer and mathematician who worked particularly on the determination of the distances of the stars. After a brief period as an engineer, Mathieu became an astronomer at the Observatoire de Paris and at the Bureau des Longitudes in 1817. He later served as

Happening: …and time-based art, as did Georges Mathieu’s theatrical demonstrations of painting, which he took to Japan.

French literature: Postwar poetry: …poetry of René Char and Pierre Emmanuel (pseudonym of Noël Mathieu), the prose poems of Francis Ponge developed a materialist discourse that aimed to allow the object to “speak” for itself, foregrounding devices such as wordplay that emphasized the act of poetic perception and the role of writing in the…

Graeco Roman Museum, museum of Greek and Roman antiquities in Alexandria, Egypt, that was founded in 1892. It is housed in a Greek Revival-style building that opened in 1895 and that was expanded in subsequent decades. The museum contains material found in Alexandria itself; Ptolemaic and Roman

Anabaptist: …followers, such as the Dutchman Jan Mathijs (died 1534) and John of Leiden (Jan Beuckelson; died 1536), and many persecuted Anabaptists settled in Münster, Westphalia. Hofmann’s disciples were attracted to the city by dramatic changes that occurred there in the early 1530s. Under the influence of the reformer Bernhard Rothman,…

Near Earth Asteroid Rendezvous Shoemaker: …1,200 km (740 miles) of Mathilde, an asteroid in the main belt between Mars and Jupiter. Rendezvous with Eros was originally scheduled for January 1999, but a spacecraft problem delayed the rendezvous for more than a year until Feb. 14, 2000—Valentine’s Day, a date chosen because the asteroid was named…

Henry I: Reign: By his marriage with Matilda, a Scottish princess of the old Anglo-Saxon royal line, he established the foundations for peaceable relations with the Scots and support from the English. And he recalled St. Anselm, the scholarly archbishop of Canterbury whom his brother, William II, had banished.

Matilda was the consort of the Holy Roman emperor Henry V and afterward claimant to the English throne in the reign of King Stephen. She was the only daughter of Henry I of England by Queen Matilda and was sister of William the Aetheling, heir to the English and Norman thrones. Both her marriages

Matilda Of Flanders was the queen consort of William I the Conqueror, whom she married c. 1053. During William’s absences in England, the duchy of Normandy was under her regency, with the aid of their son, Robert Curthose (see Robert II [Normandy]), except when he was in rebellion against his

Mathilde, Queen of the Belgians is the queen of Belgium, consort of Philippe, King of the Belgians, and mother of Princess Elisabeth, the heir to the Belgian throne. Mathilde was the daughter of a judge and a countess, and she completed her education in Bastogne before attending the Institut de la

Italy: Northern Italy: …able to hold onto the Mathildine lands in Tuscany for 15 years. He restored his position in Germany and recovered from the losses endured in Rome. In 1183 Frederick converted the truce of Venice into the Peace of Constance, in which he renounced the regalia claimed at Roncaglia but preserved…

Adoor Gopalakrishnan: The Walls is set in a British colonial prison in the 1940s and is about a political activist who falls in love with an unseen woman in a neighbouring prison after hearing her voice. Gopalakrishnan’s Kathapurushan (1995; “The Man of the Story”) examines the life…

Paul Hindemith: His greatest work, Mathis der Maler, an opera about the painter Matthias Grünewald and his struggles with society, caused a public imbroglio in Nazi Germany when Wilhelm Furtwängler conducted an orchestral version with the Berlin Philharmonic in 1934 and vigorously supported the opera in the press. The Nazi…

Joe Frazier: …in the Olympic trials to Buster Mathis in 1964 and made it to the Tokyo Olympic Games as a replacement boxer only when Mathis injured his hand. He won the gold medal in his weight division and then began his professional career in August 1965. A chunky man (5 feet…

Johnny Mathis is an American pop singer who achieved wide and enduring popularity as an angelic-voiced crooner of romantic ballads. He is perhaps best known for his affecting rendition of the Erroll Garner composition “Misty” (1959). Mathis grew up in a large working-class family in San Francisco,

Johnny Mathis is an American pop singer who achieved wide and enduring popularity as an angelic-voiced crooner of romantic ballads. He is perhaps best known for his affecting rendition of the Erroll Garner composition “Misty” (1959). Mathis grew up in a large working-class family in San Francisco,

June Mathis was an American scriptwriter, who helped establish the primacy of the script in American silent films. June Hughes adopted her stepfather’s surname, Mathis. After a brief career as a stage actress and scriptwriting work on several films in 1917, Mathis was hired in 1918 by Metro (later

Kirk Franklin is an American gospel singer, musician, and choir leader who became a huge commercial and critical success in contemporary Christian music in the 1990s and had tremendous crossover appeal in secular music. As a solo artist and as the leader of the choir groups the Family and the One

E.T. the Extra-Terrestrial: Background: Spielberg believed that Melissa Mathison, who had written the evocative 1979 movie The Black Stallion, would be perfect to tell the sensitive tale of E.T. and pitched her his idea. Initially hesitant, Mathison eventually connected with the script and worked closely with Spielberg to develop the film.

mas̄navī, a series of distichs (couplets) in rhymed pairs (aa, bb, cc, and so on) that makes up a characteristic type of Persian verse, used chiefly for heroic, historical, and romantic epic poetry and didactic poetry. The form originated in the Middle Persian period (roughly from the 3rd century

Reynold Alleyne Nicholson: …writings, culminating in his eight-volume Mathnawi of Jalalu’ddin Rumi (1925–40), eminently advanced the study of Muslim mystics. He combined exact scholarship with notable literary gifts; some of his versions of Arabic and Persian poetry entitle him to be considered a poet in his own right. His profound understanding of Islām…

psychomotor learning: Devices and tasks: Also employed is the selective mathometer, a device on which the subject’s problem is to discover, with cues provided by a signal lamp, which of some 20 pushbuttons should be pressed in response to each of a series of distinctive images projected on a screen. While using a star discrimeter,…

furniture: Modern: …to designs by Alvar Aalto, Bruno Mathsson, and Charles and Ray Eames. Rapid technical developments, in conjunction with an ever-increasing interest in human-factors engineering, or ergonomics, suggest that completely new chair forms will probably be evolved in the future.

Mathura, city, western Uttar Pradesh state, northern India. It lies in the Ganges-Yamuna Doab, on the Yamuna River about 25 miles (40 km) northwest of Agra. The site of Mathura was inhabited before the 1st century ce, when the city flourished under the Kushan dynasty. In the 2nd century the city

Mathurā art, style of Buddhist visual art that flourished in the trading and pilgrimage centre of Mathura, Uttar Pradesh, India, from the 2nd century bc to the 12th century ad; its most distinctive contributions were made during the Kushān and Gupta periods (1st–6th century ad). Images in the

Indian philosophy: The new school: 1550), Mathuranatha Tarkavagisha (flourished c.1570), Jagadisha Tarkalankara (flourished c. 1625), and Gadadhara Bhattacharya (flourished c. 1650).

Trinitarian, member of the Order of the Most Holy Trinity for the Redemption of Captives (O.SS.T.), a Roman Catholic religious order that was founded in France in 1198 by St. John of Matha. The order’s original mission was to free enslaved Christians from captivity under the Moors in the Middle

Santo Tomás de Castilla, port, northeastern Guatemala. It lies on Amatique Bay off the Gulf of Honduras and is administratively a part of Puerto Barrios. Santo Tomás was settled originally by Belgians in the 19th century; although the name was changed officially to Matías de Gálvez in 1958, the

Native American music: Participation in art music: …Lienas of Mexico City and Juan Matías, who served as the chapelmaster at Oaxaca (now in Mexico) from about 1655 through 1667. The first published Native North American composer of European art music was Thomas Commuck, whose hymnal, as mentioned above, appeared in 1845. Native North American composers of the…

Alfredo Stroessner was a military leader, who became president of Paraguay after leading an army coup in 1954. One of Latin America’s longest-serving rulers, he was overthrown in 1989. Stroessner, the son of a German immigrant, attended the Military College in Asunción and was commissioned in the

Arthurian legend, the body of stories and medieval romances, known as the matter of Britain, centring on the legendary king Arthur. Medieval writers, especially the French, variously treated stories of Arthur’s birth, the adventures of his knights, and the adulterous love between his knight Sir

Henri Bergson: Philosophical triumphs: …du corps à l’esprit (Matter and Memory).

Ngugi wa Thiong’o: Matigari ma Njiruungi (1986; Matigari) is a novel in the same vein.

Ngugi wa Thiong’o: Matigari ma Njiruungi (1986; Matigari) is a novel in the same vein.

Danny DeVito: Career: …such as the fantasy comedy Matilda (1996; also directed by DeVito), the Andy Kaufman biopic Man on the Moon (1999), and the coming-of-age film Garden State (2004).

Roald Dahl: …the Chocolate Factory (1964) and Matilda (1988), both of which were adapted into popular films. He specialized in stories of plucky children who outwit cruel and hypocritical adults, told with a heavy dose of fantasy and wicked humor.

Henry I: Reign: By his marriage with Matilda, a Scottish princess of the old Anglo-Saxon royal line, he established the foundations for peaceable relations with the Scots and support from the English. And he recalled St. Anselm, the scholarly archbishop of Canterbury whom his brother, William II, had banished.

Matilda was the consort of the Holy Roman emperor Henry V and afterward claimant to the English throne in the reign of King Stephen. She was the only daughter of Henry I of England by Queen Matilda and was sister of William the Aetheling, heir to the English and Norman thrones. Both her marriages

Matilda of Canossa was the countess of Tuscany remembered for her role in the conflict between the papacy and the Holy Roman emperor. The climax of this struggle, the confrontation of the emperor Henry IV and Pope Gregory VII in 1077, took place at Matilda’s castle of Canossa. The assassination in