title: Sasha Vujačić

text: On January 2, 2015, he signed with İstanbul BB of Turkey for the rest of the 2014–15 Turkish Basketball League season.


title: Sasha Vujačić

text: On August 7, 2015, Vujačić signed with the New York Knicks. He made his debut for the Knicks in the team's season opener against the Milwaukee Bucks on October 28, recording 11 points, 6 rebounds, 3 assists and 4 steals in a 122–97 win. On March 9, 2016, Vujačić scored a season-high 23 points to help the Knicks defeat the Phoenix Suns 128–97.


title: Sasha Vujačić

text: Vujačić re-signed with the Knicks on July 14, 2016. On February 1, 2017, he made Knicks history by converting two four-point plays during the Knicks 95–90 win over the Brooklyn Nets.


title: Sasha Vujačić

text: Vujačić signed with Italian club Auxilium Torino for the 2017–18 season on August 29, 2017. On February 18, 2018, Vujačić scored the game-winning layup to win the 2018 edition of the Italian Basketball Cup with Fiat Torino, beating Germani Basket Brescia 69–67 in the Finals.


title: Sasha Vujačić

text: Vujačić was born in Maribor, Slovenia, to a Serbian father and Slovenian mother. His father was a Serbian basketball coach, while his mother Ksenija was a Slovenian volleyball player.


title: Sasha Vujačić

text: His mother was playing volleyball for a top Yugoslav women's club, Branik Maribor, but quit her career at the age of 19 when she got pregnant with Sasha. His parents divorced when he was 2, and he lived with his mother and stepfather Goran Bjeković . He has two siblings, a sister named Nina, and a brother named Aljosa. In addition to playing basketball, he enjoys volleyball, tennis, and soccer.


title: Michael Powell

text: Michael Latham Powell (30 September 1905 – 19 February 1990) was an English filmmaker, celebrated for his partnership with Emeric Pressburger. Through their production company The Archers, they together wrote, produced and directed a series of classic British films, notably "The Life and Death of Colonel Blimp" (1943), "A Canterbury Tale" (1944), "I Know Where I'm Going!" (1945), "A Matter of Life and Death" (1946, also called "Stairway to Heaven"), "Black Narcissus" (1947), "The Red Shoes" (1948), and "The Tales of Hoffmann" (1951). His later controversial 1960 film "Peeping Tom", while today considered a classic, and a contender as the first "slasher", was so vilified on first release that his career was seriously damaged.


title: Michael Powell

text: Many filmmakers such as Martin Scorsese, Francis Ford Coppola and George A. Romero have cited Powell as an influence. In 1981, he received the BAFTA Academy Fellowship Award along with his partner Pressburger, the highest honour the British Film Academy can give a filmmaker. He has been played on screen by Alastair Thomson Mills in the award-winning short film (2022) which explores Moira Shearer's life changing decision to appear in "The Red Shoes".


title: Michael Powell

text: Powell was the second son and youngest child of Thomas William Powell, a hop farmer, and Mabel, daughter of Frederick Corbett, of Worcester, England. Powell was born in Bekesbourne, Kent, and educated at The King's School, Canterbury and then at Dulwich College. He started work at the National Provincial Bank in 1922 but quickly realised he was not cut out to be a banker.


title: Michael Powell

text: Powell entered the film industry in 1925 through working with director Rex Ingram at the Victorine Studios in Nice, France (the contact with Ingram was made through Powell's father, who owned a hotel in Nice). He first started out as a general studio hand, the proverbial "gofer": sweeping the floor, making coffee, fetching and carrying. Soon he progressed to other work such as stills photography, writing titles (for the silent films) and many other jobs including a few acting roles, usually as comic characters. Powell made his film début as a "comic English tourist" in "The Magician" (1926).


title: Michael Powell

text: Returning to England in 1928, Powell worked at a diverse series of jobs for various filmmakers including as a stills photographer on Alfred Hitchcock's silent film "Champagne" (1928). He also signed on in a similar role on Hitchcock's first "talkie", "Blackmail" (1929). In his autobiography, Powell claims he suggested the ending in the British Museum which was the first of Hitchcock's "monumental" climaxes to his films. Powell and Hitchcock remained friends for the remainder of Hitchcock's life.


title: Michael Powell

text: After scriptwriting on two productions, Powell entered into a partnership with American producer Jerry Jackson in 1931 to make "quota quickies", hour-long films needed to satisfy a legal requirement that British cinemas screen a certain quota of British films. During this period, he developed his directing skills, sometimes making up to seven films a year.


title: Michael Powell

text: Although he had taken on some directing responsibilities in other films, Powell had his first screen credit as a director on "Two Crowded Hours" (1931). This thriller was considered a modest success at the box office despite its limited budget. From 1931 to 1936, Powell was the director of 23 films, including the critically received "Red Ensign" (1934) and "The Phantom Light" (1935).


title: Michael Powell

text: In 1937 Powell completed his first truly personal project, "The Edge of the World". Powell gathered together a cast and crew who were willing to take part in an expedition to what was then a very isolated part of the UK. They had to stay there for quite a few months and finished up with a film which not only told the story he wanted but also captured the raw natural beauty of the location.


title: Michael Powell

text: By 1939, Powell had been hired as a contract director by Alexander Korda on the strength of "The Edge of the World". Korda set him to work on some projects such as "Burmese Silver" that were subsequently cancelled. Nonetheless, Powell was brought in to save a film that was being made as a vehicle for two of Korda's star players, Conrad Veidt and Valerie Hobson. The film was "The Spy in Black", where Powell first met Emeric Pressburger in 1939.


title: Michael Powell

text: The original script of "The Spy in Black" followed the book quite closely, but was too verbose and did not have a good role for either Veidt or Hobson. Korda called a meeting where he introduced a diminutive man, saying, "Well now, I have asked Emeric to read the script, and he has things to say to us."


title: Michael Powell

text: "Emeric produced a very small piece of rolled-up paper, and addressed the meeting. I listened spellbound. Since talkies took over the movies, I had worked with some good writers, but I had never met anything like this. In the silent days, the top [American] screenwriters were technicians rather than dramatists ... the European cinema remained highly literate and each country, conscious of its separate culture and literature, strove to outdo the other. All this was changed by the talkies. America, with its enormous wealth and enthusiasm and it technical resources, waved the big stick. ... The European film no longer existed. ... Only the great German film business was prepared to fight the American monopoly, and Dr. Goebbels soon put a stop to that in 1933. But the day that Emeric walked out of his flat, leaving the key in the door to save the storm-troopers the trouble of breaking it down, was the worst day's work that the clever doctor ever did for his country's reputation, as he was soon to find out.


title: Michael Powell

text: As I said, I listened spellbound to this small Hungarian wizard, as Emeric unfolded his notes, until they were at least six inches long. He had stood Storer Clouston's plot on its head and completely restructured the film."


title: Michael Powell

text: They both soon recognised that although they were total opposites in background and personality, they had a common attitude to film-making and that they could work very well together. After making two more films together, "Contraband" (1940) and "49th Parallel", with separate credits, the pair decided to form a partnership and to sign their films jointly as "Written, Produced and Directed by Michael Powell and Emeric Pressburger."


title: Michael Powell

text: Working together as co-producers, writers and directors in a partnership they dubbed "The Archers", they made 19 feature films, many of which received critical and commercial success. Their best films are still regarded as classics of 20th century British cinema. The BFI 100 list of "the favourite British films of the 20th century" contains five of Powell's films, four with Pressburger.


title: Michael Powell

text: Although admirers would argue that Powell ought to rank alongside fellow British directors Alfred Hitchcock and David Lean, his career suffered a severe reversal after the release of the controversial psychological thriller film "Peeping Tom", made in 1960 as a solo effort. The film was excoriated by mainstream British critics, who were offended by its sexual and violent images; Powell was ostracized by the film industry and found it almost impossible to work thereafter.


title: Michael Powell

text: The film did, however, meet with the rapturous approval of the young critics of "Positif" and "Midi-Minuit Fantastique" in France, and those of "Motion" in England, and in 1965 he was subject of a major positive revaluation by Raymond Durgnat in the auteurist magazine "Movie", later included in Durgnat's influential book "A Mirror for England".


title: Michael Powell

text: Powell's films came to have a cult reputation, broadened during the 1970s and early 1980s by a series of retrospectives and rediscoveries, as well as further articles and books. By the time of his death, he and Pressburger were recognised as one of the foremost film partnerships of all time – and cited as a key influence by many noted filmmakers such as Martin Scorsese, Brian De Palma, and Francis Ford Coppola.


title: Michael Powell

text: In 1927 Powell married Gloria Mary Rouger, an American dancer; they were married in France and stayed together for only three weeks. During the 1940s, Powell had love affairs with actresses Deborah Kerr and Kathleen Byron. From 1 July 1943 until her death on 5 July 1983, Powell was married to Frances "Frankie" May Reidy, the daughter of medical practitioner Jerome Reidy; they had two sons: Kevin Michael Powell (b. 1945) and Columba Jerome Reidy Powell (b. 1951). He also lived with actress Pamela Brown for many years until her death from cancer in 1975.


title: Michael Powell

text: Subsequently, Powell was married to film editor Thelma Schoonmaker from 19 May 1984 until his own death from cancer at his home in Avening, Gloucestershire. His niece was the Australian actress Cornelia Frances, who appeared in bit parts in her uncle's early films.


title: Michael Powell

text: The Academy Film Archive has preserved "A Matter of Life and Death" and "The Life and Death of Colonel Blimp" by Michael Powell and Emeric Pressburger.


title: Michael Powell

text: Many of these titles were also published in other countries or republished. The list above deals with initial publications except where the name was changed in a subsequent edition or printing.


title: History of algebra

text: Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra (in fact, every proof must use the completeness of the real numbers, which is not an algebraic property).


title: History of algebra

text: This article describes the history of the theory of equations, called here "algebra", from the origins to the emergence of algebra as a separate area of mathematics.


title: History of algebra

text: The word "algebra" is derived from the Arabic word الجبر "al-jabr", and this comes from the treatise written in the year 830 by the medieval Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī, whose Arabic title, "Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala", can be translated as "The Compendious Book on Calculation by Completion and Balancing". The treatise provided for the systematic solution of linear and quadratic equations. According to one history, "[i]t is not certain just what the terms "al-jabr" and "muqabalah" mean, but the usual interpretation is similar to that implied in the previous translation. The word 'al-jabr' presumably meant something like 'restoration' or 'completion' and seems to refer to the transposition of subtracted terms to the other side of an equation; the word 'muqabalah' is said to refer to 'reduction' or 'balancing'—that is, the cancellation of like terms on opposite sides of the equation. Arabic influence in Spain long after the time of al-Khwarizmi is found in "Don Quixote", where the word 'algebrista' is used for a bone-setter, that is, a 'restorer'." The term is used by al-Khwarizmi to describe the operations that he introduced, "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation.


title: History of algebra

text: Algebra did not always make use of the symbolism that is now ubiquitous in mathematics; instead, it went through three distinct stages. The stages in the development of symbolic algebra are approximately as follows:


title: History of algebra

text: Equally important as the use or lack of symbolism in algebra was the degree of the equations that were addressed. Quadratic equations played an important role in early algebra; and throughout most of history, until the early modern period, all quadratic equations were classified as belonging to one of three categories.


title: History of algebra

text: This trichotomy comes about because quadratic equations of the form formula_7with formula_5 and formula_6 positive, have no positive roots.


title: History of algebra

text: In between the rhetorical and syncopated stages of symbolic algebra, a geometric constructive algebra was developed by classical Greek and Vedic Indian mathematicians in which algebraic equations were solved through geometry. For instance, an equation of the form formula_10 was solved by finding the side of a square of area formula_11


title: History of algebra

text: In addition to the three stages of expressing algebraic ideas, some authors recognized four conceptual stages in the development of algebra that occurred alongside the changes in expression. These four stages were as follows:


title: History of algebra

text: The origins of algebra can be traced to the ancient Babylonians, who developed a positional number system that greatly aided them in solving their rhetorical algebraic equations. The Babylonians were not interested in exact solutions, but rather approximations, and so they would commonly use linear interpolation to approximate intermediate values. One of the most famous tablets is the Plimpton 322 tablet, created around 1900–1600 BC, which gives a table of Pythagorean triples and represents some of the most advanced mathematics prior to Greek mathematics.


title: History of algebra

text: Babylonian algebra was much more advanced than the Egyptian algebra of the time; whereas the Egyptians were mainly concerned with linear equations the Babylonians were more concerned with quadratic and cubic equations. The Babylonians had developed flexible algebraic operations with which they were able to add equals to equals and multiply both sides of an equation by like quantities so as to eliminate fractions and factors. They were familiar with many simple forms of factoring, three-term quadratic equations with positive roots, and many cubic equations, although it is not known if they were able to reduce the general cubic equation.


title: History of algebra

text: Ancient Egyptian algebra dealt mainly with linear equations while the Babylonians found these equations too elementary, and developed mathematics to a higher level than the Egyptians.


title: History of algebra

text: The Rhind Papyrus, also known as the Ahmes Papyrus, is an ancient Egyptian papyrus written c. 1650 BC by Ahmes, who transcribed it from an earlier work that he dated to between 2000 and 1800 BC. It is the most extensive ancient Egyptian mathematical document known to historians. The Rhind Papyrus contains problems where linear equations of the form formula_12 and formula_13 are solved, where formula_14 and formula_15 are known and formula_16 which is referred to as "aha" or heap, is the unknown. The solutions were possibly, but not likely, arrived at by using the "method of false position", or "regula falsi", where first a specific value is substituted into the left hand side of the equation, then the required arithmetic calculations are done, thirdly the result is compared to the right hand side of the equation, and finally the correct answer is found through the use of proportions. In some of the problems the author "checks" his solution, thereby writing one of the earliest known simple proofs.


title: History of algebra

text: It is sometimes alleged that the Greeks had no algebra, but this is inaccurate. By the time of Plato, Greek mathematics had undergone a drastic change. The Greeks created a geometric algebra where terms were represented by sides of geometric objects, usually lines, that had letters associated with them, and with this new form of algebra they were able to find solutions to equations by using a process that they invented, known as "the application of areas". "The application of areas" is only a part of geometric algebra and it is thoroughly covered in Euclid's "Elements".


title: History of algebra

text: An example of geometric algebra would be solving the linear equation formula_17 The ancient Greeks would solve this equation by looking at it as an equality of areas rather than as an equality between the ratios formula_18 and formula_19 The Greeks would construct a rectangle with sides of length formula_20 and formula_21 then extend a side of the rectangle to length formula_22 and finally they would complete the extended rectangle so as to find the side of the rectangle that is the solution.


title: History of algebra

text: Iamblichus in "Introductio arithmatica" says that Thymaridas (c. 400 BCE – c. 350 BCE) worked with simultaneous linear equations. In particular, he created the then famous rule that was known as the "bloom of Thymaridas" or as the "flower of Thymaridas", which states that:


title: History of algebra

text: If the sum of formula_23 quantities be given, and also the sum of every pair containing a particular quantity, then this particular quantity is equal to formula_24 of the difference between the sums of these pairs and the first given sum.


title: History of algebra

text: or using modern notation, the solution of the following system of formula_23 linear equations in formula_23 unknowns,


title: History of algebra

text: Iamblichus goes on to describe how some systems of linear equations that are not in this form can be placed into this form.


title: History of algebra

text: Euclid (Greek: ) was a Greek mathematician who flourished in Alexandria, Egypt, almost certainly during the reign of Ptolemy I (323–283 BCE). Neither the year nor place of his birth have been established, nor the circumstances of his death.


title: History of algebra

text: Euclid is regarded as the "father of geometry". His "Elements" is the most successful textbook in the history of mathematics. Although he is one of the most famous mathematicians in history there are no new discoveries attributed to him; rather he is remembered for his great explanatory skills. The "Elements" is not, as is sometimes thought, a collection of all Greek mathematical knowledge to its date; rather, it is an elementary introduction to it.


title: History of algebra

text: The geometric work of the Greeks, typified in Euclid's "Elements", provided the framework for generalizing formulae beyond the solution of particular problems into more general systems of stating and solving equations.


title: History of algebra

text: Book II of the "Elements" contains fourteen propositions, which in Euclid's time were extremely significant for doing geometric algebra. These propositions and their results are the geometric equivalents of our modern symbolic algebra and trigonometry. Today, using modern symbolic algebra, we let symbols represent known and unknown magnitudes (i.e. numbers) and then apply algebraic operations on them, while in Euclid's time magnitudes were viewed as line segments and then results were deduced using the axioms or theorems of geometry.


title: History of algebra

text: Many basic laws of addition and multiplication are included or proved geometrically in the "Elements". For instance, proposition 1 of Book II states:


title: History of algebra

text: But this is nothing more than the geometric version of the (left) distributive law, formula_33; and in Books V and VII of the "Elements" the commutative and associative laws for multiplication are demonstrated.


title: History of algebra

text: Many basic equations were also proved geometrically. For instance, proposition 5 in Book II proves that formula_34 and proposition 4 in Book II proves that formula_35


title: History of algebra

text: Furthermore, there are also geometric solutions given to many equations. For instance, proposition 6 of Book II gives the solution to the quadratic equation formula_36 and proposition 11 of Book II gives a solution to formula_37


title: History of algebra

text: "Data" is a work written by Euclid for use at the schools of Alexandria and it was meant to be used as a companion volume to the first six books of the "Elements". The book contains some fifteen definitions and ninety-five statements, of which there are about two dozen statements that serve as algebraic rules or formulas. Some of these statements are geometric equivalents to solutions of quadratic equations. For instance, "Data" contains the solutions to the equations formula_38 and the familiar Babylonian equation formula_39


title: History of algebra

text: A conic section is a curve that results from the intersection of a cone with a plane. There are three primary types of conic sections: ellipses (including circles), parabolas, and hyperbolas. The conic sections are reputed to have been discovered by Menaechmus (c. 380 BC – c. 320 BC) and since dealing with conic sections is equivalent to dealing with their respective equations, they played geometric roles equivalent to cubic equations and other higher order equations.


title: History of algebra

text: Menaechmus knew that in a parabola, the equation formula_40 holds, where formula_41 is a constant called the latus rectum, although he was not aware of the fact that any equation in two unknowns determines a curve. He apparently derived these properties of conic sections and others as well. Using this information it was now possible to find a solution to the problem of the duplication of the cube by solving for the points at which two parabolas intersect, a solution equivalent to solving a cubic equation.


title: History of algebra

text: We are informed by Eutocius that the method he used to solve the cubic equation was due to Dionysodorus (250 BC – 190 BC). Dionysodorus solved the cubic by means of the intersection of a rectangular hyperbola and a parabola. This was related to a problem in Archimedes' "On the Sphere and Cylinder". Conic sections would be studied and used for thousands of years by Greek, and later Islamic and European, mathematicians. In particular Apollonius of Perga's famous "Conics" deals with conic sections, among other topics.


title: History of algebra

text: Chinese mathematics dates to at least 300 BC with the "Zhoubi Suanjing", generally considered to be one of the oldest Chinese mathematical documents.


title: History of algebra

text: "Chiu-chang suan-shu" or "The Nine Chapters on the Mathematical Art", written around 250 BC, is one of the most influential of all Chinese math books and it is composed of some 246 problems. Chapter eight deals with solving determinate and indeterminate simultaneous linear equations using positive and negative numbers, with one problem dealing with solving four equations in five unknowns.


title: History of algebra

text: "Ts'e-yuan hai-ching", or "Sea-Mirror of the Circle Measurements", is a collection of some 170 problems written by Li Zhi (or Li Ye) (1192 – 1279 CE). He used "fan fa", or Horner's method, to solve equations of degree as high as six, although he did not describe his method of solving equations.


title: History of algebra

text: "Shu-shu chiu-chang", or "Mathematical Treatise in Nine Sections", was written by the wealthy governor and minister Ch'in Chiu-shao (c. 1202 – c. 1261). With the introduction of a method for solving simultaneous congruences, now called the Chinese remainder theorem, it marks the high point in Chinese .


title: History of algebra

text: The earliest known magic squares appeared in China. In "Nine Chapters" the author solves a system of simultaneous linear equations by placing the coefficients and constant terms of the linear equations into a magic square (i.e. a matrix) and performing column reducing operations on the magic square. The earliest known magic squares of order greater than three are attributed to Yang Hui (fl. c. 1261 – 1275), who worked with magic squares of order as high as ten.


title: History of algebra

text: "Ssy-yüan yü-chien"《四元玉鑒》, or "Precious Mirror of the Four Elements", was written by Chu Shih-chieh in 1303 and it marks the peak in the development of Chinese algebra. The four elements, called heaven, earth, man and matter, represented the four unknown quantities in his algebraic equations. The "Ssy-yüan yü-chien" deals with simultaneous equations and with equations of degrees as high as fourteen. The author uses the method of "fan fa", today called Horner's method, to solve these equations.


title: History of algebra

text: The "Precious Mirror" opens with a diagram of the arithmetic triangle (Pascal's triangle) using a round zero symbol, but Chu Shih-chieh denies credit for it. A similar triangle appears in Yang Hui's work, but without the zero symbol.


title: History of algebra

text: There are many summation equations given without proof in the "Precious mirror". A few of the summations are:


title: History of algebra

text: Diophantus was a Hellenistic mathematician who lived c. 250 CE, but the uncertainty of this date is so great that it may be off by more than a century. He is known for having written "Arithmetica", a treatise that was originally thirteen books but of which only the first six have survived. "Arithmetica" has very little in common with traditional Greek mathematics since it is divorced from geometric methods, and it is different from Babylonian mathematics in that Diophantus is concerned primarily with exact solutions, both determinate and indeterminate, instead of simple approximations.


title: History of algebra

text: It is usually rather difficult to tell whether a given Diophantine equation is solvable. There is no evidence that suggests Diophantus even realized that there could be two solutions to a quadratic equation. He also considered simultaneous quadratic equations. Also, no general method may be abstracted from all Diophantus' solutions.


title: History of algebra

text: In "Arithmetica", Diophantus is the first to use symbols for unknown numbers as well as abbreviations for powers of numbers, relationships, and operations; thus he used what is now known as "syncopated" algebra. The main difference between Diophantine syncopated algebra and modern algebraic notation is that the former lacked special symbols for operations, relations, and exponentials. So, for example, what we would write as


title: History of algebra

text: Unlike in modern notation, the coefficients come after the variables and that addition is represented by the juxtaposition of terms. A literal symbol-for-symbol translation of Diophantus's syncopated equation into a modern symbolic equation would be the following:


title: History of algebra

text: where to clarify, if the modern parentheses and plus are used then the above equation can be rewritten as:


title: History of algebra

text: "Arithmetica" is a collection of some 150 solved problems with specific numbers and there is no postulational development nor is a general method explicitly explained, although generality of method may have been intended and there is no attempt to find all of the solutions to the equations. "Arithmetica" does contain solved problems involving several unknown quantities, which are solved, if possible, by expressing the unknown quantities in terms of only one of them. "Arithmetica" also makes use of the identities:


title: History of algebra

text: The Indian mathematicians were active in studying about number systems. The earliest known Indian mathematical documents are dated to around the middle of the first millennium BC (around the 6th century BC).


title: History of algebra

text: The recurring themes in Indian mathematics are, among others, determinate and indeterminate linear and quadratic equations, simple mensuration, and Pythagorean triples.


title: History of algebra

text: Brahmagupta (fl. 628) was an Indian mathematician who authored "Brahma Sphuta Siddhanta". In his work Brahmagupta solves the general quadratic equation for both positive and negative roots. In indeterminate analysis Brahmagupta gives the Pythagorean triads formula_52 formula_53 but this is a modified form of an old Babylonian rule that Brahmagupta may have been familiar with. He was the first to give a general solution to the linear Diophantine equation formula_54 where formula_14 and formula_15 are integers. Unlike Diophantus who only gave one solution to an indeterminate equation, Brahmagupta gave "all" integer solutions; but that Brahmagupta used some of the same examples as Diophantus has led some historians to consider the possibility of a Greek influence on Brahmagupta's work, or at least a common Babylonian source.


title: History of algebra

text: Like the algebra of Diophantus, the algebra of Brahmagupta was syncopated. Addition was indicated by placing the numbers side by side, subtraction by placing a dot over the subtrahend, and division by placing the divisor below the dividend, similar to our modern notation but without the bar. Multiplication, evolution, and unknown quantities were represented by abbreviations of appropriate terms. The extent of Greek influence on this syncopation, if any, is not known and it is possible that both Greek and Indian syncopation may be derived from a common Babylonian source.


title: History of algebra

text: Bhāskara II (1114 – c. 1185) was the leading mathematician of the 12th century. In Algebra, he gave the general solution of Pell's equation. He is the author of "Lilavati" and "Vija-Ganita", which contain problems dealing with determinate and indeterminate linear and quadratic equations, and Pythagorean triples and he fails to distinguish between exact and approximate statements. Many of the problems in "Lilavati" and "Vija-Ganita" are derived from other Hindu sources, and so Bhaskara is at his best in dealing with indeterminate analysis.


title: History of algebra

text: Bhaskara uses the initial symbols of the names for colors as the symbols of unknown variables. So, for example, what we would write today as


title: History of algebra

text: where "ya" indicates the first syllable of the word for "black", and "ru" is taken from the word "species". The dots over the numbers indicate subtraction.


title: History of algebra

text: The first century of the Islamic Arab Empire saw almost no scientific or mathematical achievements since the Arabs, with their newly conquered empire, had not yet gained any intellectual drive and research in other parts of the world had faded. In the second half of the 8th century, Islam had a cultural awakening, and research in mathematics and the sciences increased. The Muslim Abbasid caliph al-Mamun (809–833) is said to have had a dream where Aristotle appeared to him, and as a consequence al-Mamun ordered that Arabic translation be made of as many Greek works as possible, including Ptolemy's "Almagest" and Euclid's "Elements". Greek works would be given to the Muslims by the Byzantine Empire in exchange for treaties, as the two empires held an uneasy peace. Many of these Greek works were translated by Thabit ibn Qurra (826–901), who translated books written by Euclid, Archimedes, Apollonius, Ptolemy, and Eutocius.


title: History of algebra

text: Arabic mathematicians established algebra as an independent discipline, and gave it the name "algebra" ("al-jabr"). They were the first to teach algebra in an elementary form and for its own sake. There are three theories about the origins of Arabic Algebra. The first emphasizes Hindu influence, the second emphasizes Mesopotamian or Persian-Syriac influence and the third emphasizes Greek influence. Many scholars believe that it is the result of a combination of all three sources.


title: History of algebra

text: Throughout their time in power, the Arabs used a fully rhetorical algebra, where often even the numbers were spelled out in words. The Arabs would eventually replace spelled out numbers (e.g. twenty-two) with Arabic numerals (e.g. 22), but the Arabs did not adopt or develop a syncopated or symbolic algebra until the work of Ibn al-Banna, who developed a symbolic algebra in the 13th century, followed by Abū al-Hasan ibn Alī al-Qalasādī in the 15th century.


title: History of algebra

text: The Muslim Persian mathematician Muhammad ibn Mūsā al-Khwārizmī was a faculty member of the "House of Wisdom" ("Bait al-Hikma") in Baghdad, which was established by Al-Mamun. Al-Khwarizmi, who died around 850 CE, wrote more than half a dozen mathematical and astronomical works, some of which were based on the Indian "Sindhind". One of al-Khwarizmi's most famous books is entitled "Al-jabr wa'l muqabalah" or "The Compendious Book on Calculation by Completion and Balancing", and it gives an exhaustive account of solving polynomials up to the second degree. The book also introduced the fundamental concept of "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation. This is the operation which Al-Khwarizmi originally described as "al-jabr". The name "algebra" comes from the ""al-jabr"" in the title of his book.


title: History of algebra

text: "Al-Jabr" is divided into six chapters, each of which deals with a different type of formula. The first chapter of "Al-Jabr" deals with equations whose squares equal its roots formula_58 the second chapter deals with squares equal to number formula_59 the third chapter deals with roots equal to a number formula_60 the fourth chapter deals with squares and roots equal a number formula_61 the fifth chapter deals with squares and number equal roots formula_62 and the sixth and final chapter deals with roots and number equal to squares formula_63


title: History of algebra

text: In "Al-Jabr", al-Khwarizmi uses geometric proofs, he does not recognize the root formula_64 and he only deals with positive roots. He also recognizes that the discriminant must be positive and described the method of completing the square, though he does not justify the procedure. The Greek influence is shown by "Al-Jabr"'s geometric foundations and by one problem taken from Heron. He makes use of lettered diagrams but all of the coefficients in all of his equations are specific numbers since he had no way of expressing with parameters what he could express geometrically; although generality of method is intended.


title: History of algebra

text: Al-Khwarizmi most likely did not know of Diophantus's "Arithmetica", which became known to the Arabs sometime before the 10th century. And even though al-Khwarizmi most likely knew of Brahmagupta's work, "Al-Jabr" is fully rhetorical with the numbers even being spelled out in words. So, for example, what we would write as


title: History of algebra

text: 'Abd al-Hamīd ibn Turk authored a manuscript entitled "Logical Necessities in Mixed Equations", which is very similar to al-Khwarzimi's "Al-Jabr" and was published at around the same time as, or even possibly earlier than, "Al-Jabr". The manuscript gives exactly the same geometric demonstration as is found in "Al-Jabr", and in one case the same example as found in "Al-Jabr", and even goes beyond "Al-Jabr" by giving a geometric proof that if the discriminant is negative then the quadratic equation has no solution. The similarity between these two works has led some historians to conclude that Arabic algebra may have been well developed by the time of al-Khwarizmi and 'Abd al-Hamid.


title: History of algebra

text: Arabic mathematicians treated irrational numbers as algebraic objects. The Egyptian mathematician Abū Kāmil Shujā ibn Aslam (c. 850–930) was the first to accept irrational numbers (often in the form of a square root, cube root or fourth root) as solutions to quadratic equations or as coefficients in an equation. He was also the first to solve three non-linear simultaneous equations with three unknown variables.


title: History of algebra

text: Al-Karkhi (953–1029), also known as Al-Karaji, was the successor of Abū al-Wafā' al-Būzjānī (940–998) and he discovered the first numerical solution to equations of the form formula_68 Al-Karkhi only considered positive roots. Al-Karkhi is also regarded as the first person to free algebra from geometrical operations and replace them with the type of arithmetic operations which are at the core of algebra today. His work on algebra and polynomials gave the rules for arithmetic operations to manipulate polynomials. The historian of mathematics F. Woepcke, in "Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi" (Paris, 1853), praised Al-Karaji for being "the first who introduced the theory of algebraic calculus". Stemming from this, Al-Karaji investigated binomial coefficients and Pascal's triangle.


title: History of algebra

text: Omar Khayyám (c. 1050 – 1123) wrote a book on Algebra that went beyond "Al-Jabr" to include equations of the third degree. Omar Khayyám provided both arithmetic and geometric solutions for quadratic equations, but he only gave geometric solutions for general cubic equations since he mistakenly believed that arithmetic solutions were impossible. His method of solving cubic equations by using intersecting conics had been used by Menaechmus, Archimedes, and Ibn al-Haytham (Alhazen), but Omar Khayyám generalized the method to cover all cubic equations with positive roots. He only considered positive roots and he did not go past the third degree. He also saw a strong relationship between geometry and algebra.


title: History of algebra

text: In the 12th century, Sharaf al-Dīn al-Tūsī (1135–1213) wrote the "Al-Mu'adalat" ("Treatise on Equations"), which dealt with eight types of cubic equations with positive solutions and five types of cubic equations which may not have positive solutions. He used what would later be known as the "Ruffini-Horner method" to numerically approximate the root of a cubic equation. He also developed the concepts of the maxima and minima of curves in order to solve cubic equations which may not have positive solutions. He understood the importance of the discriminant of the cubic equation and used an early version of Cardano's formula to find algebraic solutions to certain types of cubic equations. Some scholars, such as Roshdi Rashed, argue that Sharaf al-Din discovered the derivative of cubic polynomials and realized its significance, while other scholars connect his solution to the ideas of Euclid and Archimedes.


title: History of algebra

text: the equation formula_69 for example, he begins by changing the equation's form to formula_70. He then states that the question of whether the equation has a solution depends on whether or not the “function” on the left side reaches the value formula_71. To determine this, he finds a maximum value for the function. He proves that the maximum value occurs when formula_72, which gives the functional value formula_73. Sharaf al-Din then states that if this value is less than formula_71, there are no positive solutions; if it is equal to formula_71, then there is one solution at formula_72; and if it is greater than formula_71, then there are two solutions, one between formula_78 and formula_79 and one between formula_79 and formula_20.


title: History of algebra

text: In the early 15th century, Jamshīd al-Kāshī developed an early form of Newton's method to numerically solve the equation formula_82 to find roots of formula_83. Al-Kāshī also developed decimal fractions and claimed to have discovered it himself. However, J. Lennart Berggrenn notes that he was mistaken, as decimal fractions were first used five centuries before him by the Baghdadi mathematician Abu'l-Hasan al-Uqlidisi as early as the 10th century.


title: History of algebra

text: Al-Hassār, a mathematician from Morocco specializing in Islamic inheritance jurisprudence during the 12th century, developed the modern symbolic mathematical notation for fractions, where the numerator and denominator are separated by a horizontal bar. This same fractional notation appeared soon after in the work of Fibonacci in the 13th century.


title: History of algebra

text: Abū al-Hasan ibn Alī al-Qalasādī (1412–1486) was the last major medieval Arab algebraist, who made the first attempt at creating an algebraic notation since Ibn al-Banna two centuries earlier, who was himself the first to make such an attempt since Diophantus and Brahmagupta in ancient times. The syncopated notations of his predecessors, however, lacked symbols for mathematical operations. Al-Qalasadi "took the first steps toward the introduction of algebraic symbolism by using letters in place of numbers" and by "using short Arabic words, or just their initial letters, as mathematical symbols."


title: History of algebra

text: Just as the death of Hypatia signals the close of the Library of Alexandria as a mathematical center, so does the death of Boethius signal the end of mathematics in the Western Roman Empire. Although there was some work being done at Athens, it came to a close when in 529 the Byzantine emperor Justinian closed the pagan philosophical schools. The year 529 is now taken to be the beginning of the medieval period. Scholars fled the West towards the more hospitable East, particularly towards Persia, where they found haven under King Chosroes and established what might be termed an "Athenian Academy in Exile". Under a treaty with Justinian, Chosroes would eventually return the scholars to the Eastern Empire. During the Dark Ages, European mathematics was at its nadir with mathematical research consisting mainly of commentaries on ancient treatises; and most of this research was centered in the Byzantine Empire. The end of the medieval period is set as the fall of Constantinople to the Turks in 1453.


title: History of algebra

text: The 12th century saw a flood of translations from Arabic into Latin and by the 13th century, European mathematics was beginning to rival the mathematics of other lands. In the 13th century, the solution of a cubic equation by Fibonacci is representative of the beginning of a revival in European algebra.


title: History of algebra

text: As the Islamic world was declining after the 15th century, the European world was ascending. And it is here that algebra was further developed.


title: History of algebra

text: Modern notation for arithmetic operations was introduced between the end of the 15th century and the beginning of the 16th century by Johannes Widmann and Michael Stifel. At the end of 16th century, François Viète introduced symbols, now called variables, for representing indeterminate or unknown numbers. This created a new algebra consisting of computing with symbolic expressions as if they were numbers.


title: History of algebra

text: Another key event in the further development of algebra was the general algebraic solution of the cubic and quartic equations, developed in the mid-16th century. The idea of a determinant was developed by Japanese mathematician Kowa Seki in the 17th century, followed by Gottfried Leibniz ten years later, for the purpose of solving systems of simultaneous linear equations using matrices. Gabriel Cramer also did some work on matrices and determinants in the 18th century.


title: History of algebra

text: By tradition, the first unknown variable in an algebraic problem is nowadays represented by the symbol formula_84 and if there is a second or a third unknown, then these are labeled formula_85 and formula_86 respectively. Algebraic formula_87 is conventionally printed in italic type to distinguish it from the sign of multiplication.


title: History of algebra

text: Mathematical historians generally agree that the use of formula_87 in algebra was introduced by René Descartes and was first published in his treatise "La Géométrie" (1637). In that work, he used letters from the beginning of the alphabet formula_89 for known quantities, and letters from the end of the alphabet formula_90 for unknowns. It has been suggested that he later settled on formula_87 (in place of formula_92) for the first unknown because of its relatively greater abundance in the French and Latin typographical fonts of the time.


title: History of algebra

text: Three alternative theories of the origin of algebraic formula_87 were suggested in the 19th century: (1) a symbol used by German algebraists and thought to be derived from a cursive letter formula_94 mistaken for formula_87; (2) the numeral "1" with oblique strikethrough; and (3) an Arabic/Spanish source (see below). But the Swiss-American historian of mathematics Florian Cajori examined these and found all three lacking in concrete evidence; Cajori credited Descartes as the originator, and described his formula_96 and formula_92 as "free from tradition[,] and their choice purely arbitrary."


title: History of algebra

text: Nevertheless, the Hispano-Arabic hypothesis continues to have a presence in popular culture today. It is the claim that algebraic formula_87 is the abbreviation of a supposed loanword from Arabic in Old Spanish. The theory originated in 1884 with the German orientalist Paul de Lagarde, shortly after he published his edition of a 1505 Spanish/Arabic bilingual glossary in which Spanish "cosa" ("thing") was paired with its Arabic equivalent, شىء ("shay"), transcribed as "xei". (The "sh" sound in Old Spanish was routinely spelled formula_99) Evidently Lagarde was aware that Arab mathematicians, in the "rhetorical" stage of algebra's development, often used that word to represent the unknown quantity. He surmised that "nothing could be more natural" ("Nichts war also natürlicher...") than for the initial of the Arabic word—romanized as the Old Spanish formula_87—to be adopted for use in algebra. A later reader reinterpreted Lagarde's conjecture as having "proven" the point. Lagarde was unaware that early Spanish mathematicians used, not a "transcription" of the Arabic word, but rather its "translation" in their own language, "cosa". There is no instance of "xei" or similar forms in several compiled historical vocabularies of Spanish.


title: History of algebra

text: Although the mathematical notion of function was implicit in trigonometric and logarithmic tables, which existed in his day, Gottfried Leibniz was the first, in 1692 and 1694, to employ it explicitly, to denote any of several geometric concepts derived from a curve, such as abscissa, ordinate, tangent, chord, and the perpendicular. In the 18th century, "function" lost these geometrical associations.


title: History of algebra

text: Leibniz realized that the coefficients of a system of linear equations could be arranged into an array, now called a matrix, which can be manipulated to find the solution of the system, if any. This method was later called Gaussian elimination. Leibniz also discovered Boolean algebra and symbolic logic, also relevant to algebra.


title: History of algebra

text: The ability to do algebra is a skill cultivated in mathematics education. As explained by Andrew Warwick, Cambridge University students in the early 19th century practiced "mixed mathematics", doing exercises based on physical variables such as space, time, and weight. Over time the association of variables with physical quantities faded away as mathematical technique grew. Eventually mathematics was concerned completely with abstract polynomials, complex numbers, hypercomplex numbers and other concepts. Application to physical situations was then called applied mathematics or mathematical physics, and the field of mathematics expanded to include abstract algebra. For instance, the issue of constructible numbers showed some mathematical limitations, and the field of Galois theory was developed.


title: History of algebra

text: The title of "the father of algebra" is frequently credited to the Persian mathematician Al-Khwarizmi, supported by historians of mathematics, such as Carl Benjamin Boyer, Solomon Gandz and Bartel Leendert van der Waerden. However, the point is debatable and the title is sometimes credited to the Hellenistic mathematician Diophantus. Those who support Diophantus point to the algebra found in "Al-Jabr" being more elementary than the algebra found in "Arithmetica", and "Arithmetica" being syncopated while "Al-Jabr" is fully rhetorical. However, the mathematics historian Kurt Vogel argues against Diophantus holding this title, as his mathematics was not much more algebraic than that of the ancient Babylonians.


title: History of algebra

text: Those who support Al-Khwarizmi point to the fact that he gave an exhaustive explanation for the algebraic solution of quadratic equations with positive roots, and was the first to teach algebra in an elementary form and for its own sake, whereas Diophantus was primarily concerned with the theory of numbers. Al-Khwarizmi also introduced the fundamental concept of "reduction" and "balancing" (which he originally used the term "al-jabr" to refer to), referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation. Other supporters of Al-Khwarizmi point to his algebra no longer being concerned "with a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study." They also point to his treatment of an equation for its own sake and "in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems." Victor J. Katz regards "Al-Jabr" as the first true algebra text that is still extant.


title: Scientific American

text: Scientific American, informally abbreviated SciAm or sometimes SA, is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it is the oldest continuously published magazine in the United States. "Scientific American" is owned by Springer Nature, which in turn is a subsidiary of Holtzbrinck Publishing Group.


title: Scientific American

text: "Scientific American" was founded by inventor and publisher Rufus Porter in 1845 as a four-page weekly newspaper. The first issue of the large format newspaper was released August 28, 1845.


title: Scientific American

text: Throughout its early years, much emphasis was placed on reports of what was going on at the U.S. Patent Office. It also reported on a broad range of inventions including perpetual motion machines, an 1860 device for buoying vessels by Abraham Lincoln, and the universal joint which now can be found in nearly every automobile manufactured. Current issues include a "this date in history" section, featuring excerpts from articles originally published 50, 100, and 150 years earlier. Topics include humorous incidents, wrong-headed theories, and noteworthy advances in the history of science and technology. It started as a weekly publication in August 1845 before turning into monthly in November 1921.


title: Scientific American

text: Porter sold the publication to Alfred Ely Beach and Orson Desaix Munn a mere ten months after founding it. Until 1948, it remained owned by Munn & Company. Under Munn's grandson, Orson Desaix Munn III, it had evolved into something of a "workbench" publication, similar to the twentieth-century incarnation of "Popular Science".


title: Scientific American

text: In the years after World War II, the magazine fell into decline. In 1948, three partners who were planning on starting a new popular science magazine, to be called "The Sciences", purchased the assets of the old "Scientific American" instead and put its name on the designs they had created for their new magazine. Thus the partnerspublisher Gerard Piel, editor Dennis Flanagan, and general manager Donald H. Miller, Jr.essentially created a new magazine. Miller retired in 1979, Flanagan and Piel in 1984, when Gerard Piel's son Jonathan became president and editor; circulation had grown fifteen-fold since 1948. In 1986, it was sold to the Holtzbrinck Publishing Group of Germany, which has owned it until the Springer-Nature merger. In the fall of 2008, "Scientific American" was put under the control of Holtzbrinck's Nature Publishing Group division.


title: Scientific American

text: Donald Miller died in December 1998, Gerard Piel in September 2004 and Dennis Flanagan in January 2005. Mariette DiChristina became editor-in-chief after John Rennie stepped down in June 2009, and stepped down herself in September 2019. In April 2020, Laura Helmuth assumed the role of editor-in-chief.


title: Scientific American

text: "Scientific American" published its first foreign edition in 1890, the Spanish-language "La America Cientifica". Publication was suspended in 1905, and another 63 years would pass before another foreign-language edition appeared: In 1968, an Italian edition, "Le Scienze", was launched, and a Japanese edition, ', followed three years later. A new Spanish edition, "Investigación y Ciencia" was launched in Spain in 1976, followed by a French edition, ', in France in 1977, and a German edition, ', in Germany in 1978. A Russian edition "V Mire Nauki" () was launched in the Soviet Union in 1983, and continues in the present-day Russian Federation. "Kexue" (科学, "Science" in Chinese), a simplified Chinese edition launched in 1979, was the first Western magazine published in the People's Republic of China. Founded in Chongqing, the simplified Chinese magazine was transferred to Beijing in 2001. Later in 2005, a newer edition, "Global Science" (环球科学), was published instead of "Kexue", which shut down due to financial problems. A traditional Chinese edition, known as ', was introduced to Taiwan in 2002. The Hungarian edition "Tudomány" existed between 1984 and 1992. In 1986, an Arabic edition, "", was published. In 2002, a Portuguese edition was launched in Brazil.


title: Scientific American

text: Today, "Scientific American" publishes 18 foreign-language editions around the globe: Arabic, Brazilian Portuguese, Simplified Chinese, Traditional Chinese, Czech, Dutch, French, German, Greek, Hebrew, Italian, Japanese, Korean, Lithuanian (discontinued after 15 issues), Polish, Romanian, Russian, and Spanish.


title: Scientific American

text: From 1902 to 1911, "Scientific American" supervised the publication of the "Encyclopedia Americana", which during some of that period was known as "The Americana".


title: Scientific American

text: Some famous individuals who penned articles in the magazine included Albert Einstein, Thomas Edison, Jonas Salk, Marie Curie, Stephen Hawking, Franklin D. Roosevelt, Stephen Jay Gould, Bill Gates, Nikola Tesla, and more.


title: Scientific American

text: In March 1996, "Scientific American" launched its own website that included articles from current and past issues, online-only features, daily news, special reports, and trivia, among other things. The website introduced a paywall in April 2019, with readers able to view a few articles for free each month.


title: Scientific American

text: From 1990 to 2005 "Scientific American" produced a television program on PBS called "Scientific American Frontiers" with hosts Woodie Flowers and Alan Alda.


title: Scientific American

text: From 1983 to 1997, "Scientific American" has produced an encyclopedia set of volumes from their publishing division, the Scientific American Library. These books were not sold in retail stores, but as a Book of the Month Club selection priced from $24.95 to $32.95. Topics covered dozens of areas of scientific knowledge and included in-depth essays on: The Animal Mind; Atmosphere, Climate, and Change; Beyond the Third Dimension; Cosmic Clouds; Cycles of Life • Civilization and the Biosphere; The Discovery Of Subatomic Particles; Diversity and the Tropical Rain Forest; Earthquakes and Geological Discovery; Exploring Planetary Worlds; Gravity's Fatal Attraction; Fire; Fossils And The History Of Life; From Quarks to the Cosmos; A Guided Tour Of The Living Cell; Human Diversity; Perception; The Solar System; Sun and Earth; The Science of Words (Linguistics); The Science Of Musical Sound; The Second Law (of Thermodynamics); Stars; Supercomputing and the Transformation of Science.


title: Scientific American

text: Scientific American launched a publishing imprint in 2010 in partnership with Farrar, Straus and Giroux.


title: Scientific American

text: In April 1950, the U.S. Atomic Energy Commission ordered "Scientific American" to cease publication of an issue containing an article by Hans Bethe that appeared to reveal classified information about the thermonuclear hydrogen bomb. Subsequent review of the material determined that the AEC had overreacted. The incident was important for the "new" "Scientific American"'s history, as the AEC's decision to burn 3,000 copies of an early press-run of the magazine containing the offending material appeared to be "book burning in a free society" when publisher Gerard Piel leaked the incident to the press.


title: Scientific American

text: In its January 2002 issue, "Scientific American" published a series of criticisms of the Bjørn Lomborg book "The Skeptical Environmentalist". Cato Institute fellow Patrick J. Michaels said the attacks came because the book "threatens billions of taxpayer dollars that go into the global change kitty every year". Journalist Ronald Bailey called the criticism "disturbing" and "dishonest", writing, "The subhead of the review section, 'Science defends itself against "The Skeptical Environmentalist",' gives the show away: Religious and political views need to defend themselves against criticism, but science is supposed to be a process for determining the facts."


title: Scientific American

text: The May 2007 issue featured a column by Michael Shermer calling for a United States pullout from the Iraq War. In response, "Wall Street Journal" online columnist James Taranto jokingly called "Scientific American" "a liberal political magazine".


title: Scientific American

text: An editorial in the September 2016 issue of "Scientific American" attacked U.S. presidential candidate Donald Trump for "anti-science" attitudes and rhetoric. This marked the first time that the publication forayed into commenting on U.S. presidential politics.


title: Scientific American

text: In the October 2020 issue of the magazine, it endorsed Joe Biden for the 2020 presidential election, citing Donald Trump's rejection of scientific evidence, especially during the COVID-19 pandemic in the United States. In the column reporting the endorsement, the magazine's editors said, ""Scientific American" has never endorsed a presidential candidate in its 175-year history. This year we are compelled to do so. We do not do this lightly."


title: Scientific American

text: The publisher was criticized in 2009 when it notified collegiate libraries that yearly subscription prices for the magazine would increase by nearly 500% for print and 50% for online access to $1,500 yearly.


title: Scientific American

text: In 2013, Danielle N. Lee, a female scientist who blogged at "Scientific American", was called a "whore" in an email by an editor at the science website "Biology Online" after refusing to write professional content without compensation. When Lee, outraged about the email, wrote a rebuttal on her "Scientific American" blog, the editor-in-chief of "Scientific American", Mariette DiChristina, removed the post, sparking an outrage by supporters of Lee. While DiChristina cited legal reasons for removing the blog, others criticized her for censoring Lee. The editor at "Biology Online" was fired after the incident.


title: Scientific American

text: The controversy widened in the ensuing days. The magazine's blog editor, Bora Zivkovic, was the subject of allegations of sexual harassment by another blogger, Monica Byrne. Although the alleged incident had occurred about a year earlier, editor Mariette DiChristina informed readers that the incident had been investigated and resolved to Byrne's satisfaction. However, the incident involving Lee had prompted Byrne to reveal the identity of Zivkovic, following the latter's support of Lee. Zivkovic responded on Twitter and his own blog, admitting the incident with Byrne had taken place. His blog post apologized to Byrne, and referred to the incident as "singular", stating that his behavior was not "engaged in before or since".


title: Scientific American

text: Zivkovic resigned from the board of Science Online, the popular science blogging conference that he co-founded with Anton Zuiker. Following Zivkovic's admission, several prominent female bloggers, including other bloggers for the magazine, wrote their own accounts, alleging additional incidents of sexual harassment, although none of these accounts have been independently investigated yet, nor do they meet either the legal or ethical definition of sexual harassment. A day after these new revelations, Zivkovic resigned his position at "Scientific American", according to a press release from the magazine.


title: ManBearPig

text: "ManBearPig" is the sixth episode in the tenth season of the American animated television series "South Park". The 145th episode of the series overall, it first aired on Comedy Central in the United States on April 26, 2006. In the episode, Al Gore visits South Park to warn everyone about a creature called ManBearPig, an allegory for global warming. Gore then gets Stan, Kyle, Cartman, and Kenny trapped inside the Cave of the Winds.


title: ManBearPig

text: Al Gore (voiced by Trey Parker) visits South Park Elementary and warns the school's students about an imaginary monster named ManBearPig which roams the Earth attacking humans. Gore describes the monster as “half human, half bear, half pig.” While Gore continues to spread awareness of the fictional cryptid, Randy advises Stan and the boys to not be involved with Gore as he is only seeking attention. One night, Gore calls Stan about ManBearPig and Stan tries to turn him down gently; Gore weeps from this rejection until Stan changes his mind. Gore then persuades Stan, Kyle, Cartman, and Kenny to attend a ManBearPig meeting, where Gore states that the creature is hiding in the Cave of the Winds. The boys agree to assist Gore in his hunt for ManBearPig in exchange for being officially dismissed from school that day.


title: ManBearPig

text: In the caves, the echo sound the cave is named for causes Gore to mistake the sound for the creature. He fires a shotgun wildly, which causes a cave-in that leaves the boys trapped in the caverns; all others escape before the cave-in and Gore believes ManBearPig is at fault. While the boys search for a way out of the cave, Cartman discovers a small cavern filled with what appears to be treasure. Greedily, he starts swallowing the treasure piece-by-piece to smuggle it out of the cave.


title: ManBearPig

text: As a rescue team assembles outside the cave to find the boys, Gore diverts the flow of a nearby stream in order to cause a flood which fills the cavern in an attempt to kill the still-unseen monster. The boys manage to escape just as a memorial service is being held for them. When Gore tries to take credit for saving them, Stan, having lost all sympathy for him, angrily yells at Gore and calls him a "loser" for using the situation 'as an excuse to draw attention to [himself]', but he is unfazed as he is certain that he killed ManBearPig. Cartman tries to walk away, but he does not get far before he begins painfully defecating pieces of treasure. It is revealed to Cartman that the treasure was a prop used for tourist photo ops and is only worth about $14; this upsets Cartman as he continually defecates the fake treasure and Kyle angrily admonishes him for all the trouble, of trying to save him. Gore announces his plans to make a film starring himself and dons a cape before pretending to fly away.


title: ManBearPig

text: Eric Goldman from "IGN" gave the episode a score of 6.0 out of 10. He thought it was a superior episode compared with "A Million Little Fibers", the previous episode of the season, but still called it an "okay, middle of the road" episode.


title: ManBearPig

text: "ManBearPig", along with the thirteen other episodes from "South Park"s tenth season, was released on a three-disc DVD set in the United States on August 21, 2007. The set includes brief audio commentaries by series co-creators Trey Parker and Matt Stone for each episode.


title: ManBearPig

text: ManBearPig is one of the antagonist characters shown in the "Imaginationland" trilogy in the eleventh season of "South Park".


title: ManBearPig

text: The episode is notorious as an allegory for climate change denial because the "South Park" creators Trey Parker and Matt Stone were initially unconvinced about Gore's film "An Inconvenient Truth". In apologies for their treatment of the issue at the time, Gore and ManBearPig returned in the sixth and seventh episodes of the 22nd season of "South Park", "Time to Get Cereal" and "Nobody Got Cereal?", in which the boys realise that ManBearPig exists and apologise to Gore. ManBearPig returned in the 2022 films "" and "South Park :The Streaming Wars Part 2", which reveals that ManPearPig has a family.


title: ManBearPig

text: The 2018 action-adventure game "Red Dead Redemption 2", developed and published by Rockstar Games, features a creature that looks like a cross between a human, a bear, and a pig chained to a wall.


title: Big Nate

text: Big Nate (stylized as big NATE in the comic collections and BiG NATE in the books) is an American comic strip written and illustrated by Lincoln Peirce, syndicated since January 7, 1991. The strip follows sixth-grader Nate Wright, alongside his family, friends, and foes.


title: Big Nate

text: The strip's success led to a media franchise, consisting of two series of children's books by Lincoln Peirce - the eponymous novel series and the "Little Big Nate" board books - and an animated television series, which premiered on Paramount+ in 2022.


title: Big Nate

text: "Big Nate" follows the adventures and misadventures of Nate Wright, an incompetent, spirited, and rebellious sixth-grader. He has three best friends, Francis, Teddy, and Dee Dee who occasionally get in trouble with him. Other characters include a variety of teachers and students at Nate’s school, Public School 38. Nate hates social studies teacher Mrs. Godfrey, whom he considers his nemesis, and calls her names like “the school's Godzilla”. He has a love-hate relationship with Artur, a foreign exchange student who is the boyfriend of Jenny, Nate’s crush. Nate also loathes Gina, a “teacher’s pet” who gets good grades and is constantly acting like a suck-up to Mrs. Godfrey. Peirce occasionally focuses on Nate's home life with his single father, Martin, and girly sister Ellen.


title: Big Nate

text: Answering questions from fans in "The Washington Post"", Peirce revealed the following about the creation of the strip:


title: Big Nate

text: Enslave the Mollusk (ETM) is a garage band featured in "Big Nate". It features Nate as backing vocalist and drummer, with best friends Francis on electric guitar and Teddy on keyboard, as well as Artur as lead vocalist. Chad is the band's roadie. Enslave the Mollusk had a big role in "Big Nate" the Musical. They performed 3 times: twice during the "In The Zone" novel when P.S 38 was starting a fitness zone but the first time Artur wasn't there because he quit the band, but eventually rejoined by their last performance, and also at one of the school dances. They tried to perform at another school dance but failed because of a power outage. Nate was originally lead singer as he formed the band but wasn't good enough, which was realized after Artur passed by the band playing one day. Artur then sang a rendition of "I Fought The Law" and was hired as the band's lead singer. He quit in the middle of Big Nate: In The Zone after he found a slip of paper with rude nicknames for him that Nate wrote, but was enticed back by the end of the book.


title: Big Nate

text: "Femme Fatality" is Nate's favorite super-hero comic. The images are never shown, but there were a few appearances of the eponymous character, as a life-size cardboard cut-out in a 2002 comic and as a cosplay actor visiting Klassic Komix in 2004. The character is highly suggestive, judging from the reaction of Nate and most of the other male characters (including adults). One comic claimed that she was wearing a skin tight tube top and leather mini-shorts. Some of the girls show exasperation over Nate's obsession with the comic, but Nate insists he reads it only for the stories. One of Nate's previous comic book crushes was Red Sonja. Femme Fatality later inspired Nate to create his own super-hero comic called "Eve of Destruction", though he later changed the character to male, and called the comic "Steve of Destruction".


title: Big Nate

text: P.S. 38 is the middle school Nate and his friends attend and is where most of the comics take place. The school is noted to be over 100 years old and is considerably run down, but was remodeled in "Big Nate: Lives It Up" after a painting by local folk artist Granny Peppers was found to be worth a lot of money.


title: Big Nate

text: Jefferson Middle School is a middle school near P.S. 38 and is the school's sister institution. In stark contrast to P.S. 38, Jefferson is portrayed as a large modern building with numerous 21st century features. It has been described as "more of a museum than a school." The middle school's kids are the rivals of P.S. 38's kids and beat them in almost everything. Most Jefferson kids are always obnoxious about this. P.S. 38 beat Jefferson in the 'Ultimate Snowdown', the 1st and 38th 'Mud Bowl', and their big 2008 soccer game. Jefferson lost the Snowdown, because they took an uncreative approach by packing snow around the spare knight statue.


title: Big Nate

text: In May 2013, a stage musical adaptation of the comic strip debuted at the Adventure Theatre MTC in Maryland. The production's story centers on Nate, who tries to enter his school's Battle of the Bands competition but must try to avoid getting anymore detentions, as too many would disqualify his band from competing. Critical reception for the musical has been positive.


title: Big Nate

text: On February 19, 2020, it was announced that "Big Nate" would receive a 26-episode animated TV adaptation, which was slated to air on Nickelodeon in September 2021 but was delayed to 2022. In December 2021, the voice cast was announced, as was that the series would instead be for Paramount+. It would eventually air on Nickelodeon on September 5, 2022.


title: Mobile Suit Gundam Thunderbolt

text: An original net animation (ONA) series adaptation by Sunrise was released between December 2015 and April 2016. A second part was released between March and July 2017.


title: Mobile Suit Gundam Thunderbolt

text: The series takes place concurrently with "Mobile Suit Gundam", during the One Year War but is not canonical to the original anime. In U.C. 0079, the Earth Federation's Moore Brotherhood and the Principality of Zeon's Living Dead Division engage in a fierce battle in the , a shoal zone littered with debris from destroyed space colonies, named for its frequent electrical discharges. Since the outbreak of the war, Zeon forces have secured the Thunderbolt Sector as it is a vital supply route to the Zeon-aligned A Baoa Qu asteroid fortress. The story focuses on Federation soldier Io Fleming as he battles Zeon's best sniper, Daryl Lorenz.


title: Mobile Suit Gundam Thunderbolt

text: The is an Earth Federation squadron consisting of former residents of the space colonies of Side 4: Moore, with the intent of punishing the Principality of Zeon for destroying their homeland.


title: Mobile Suit Gundam Thunderbolt

text: The is a Principality of Zeon squadron made of amputee pilots fitted with metal prosthetic limbs. The division is assigned to defend the Thunderbolt Sector from the Federation.


title: Mobile Suit Gundam Thunderbolt

text: The is a Buddhist radical cult faction aligned with the Earth Federation until U.C. 0080, when it calls for independence. Its military consists primarily of mobile suits cobbled together from Federation and Zeon units from the One Year War. Intelligence reports reveal that the South Sea Alliance possesses the remains of Daryl's Psycho Zaku and plans to mass-produce its Reuse P. Device technology.


title: Mobile Suit Gundam Thunderbolt

text: "Mobile Suit Gundam Thunderbolt" is written and illustrated by Yasuo Ohtagaki. In November 2011, Ohtagaki announced that he would put his other manga series, "Moonlight Mile", on hiatus to start a new project, which was later revelead to be a (originally planned) "Gundam" mini-series. "Mobile Suit Gundam Thunderbolt" started in Shogakukan's "seinen" manga magazine "Big Comic Superior" magazine on 23 March 2012. In February 2022, it was announced that the manga had entered its final stage; however, in October of the same year, Ohtagaki stated that he had planned to continue the manga "for another five to six years". Shogakukan has collected its chapters into individual "tankōbon" volumes. The first volume was released on 30 October 2012. As of 28 September 2022 twenty volumes have been released.


title: Mobile Suit Gundam Thunderbolt

text: North American publisher Viz Media announced their license to the series during their panel at Anime Expo on 1 July 2016.


title: Mobile Suit Gundam Thunderbolt

text: A 4-episode original net animation adaptation, produced by Sunrise, was confirmed on 28 October 2015. It was directed and written by Kō Matsuo, with character designs from Hirotoshi Takaya and mechanical designs from Morifumi Naka, Seiichi Nakatani and Hajime Katoki. It premiered on 25 December 2015 with the last episode officially aired on 8 April 2016 via pay to watch service in Japan, with early access from the Gundam Fan Club app service on 11 December 2015. The first episode was streamed outside Japan for a limited time from 25 December 2015 to 7 January 2016. A 4-episode second season was announced by Bandai Visual on 18 November 2016 and premiered on 24 March 2017. Sunrise announced in the 2017 Anime Expo that the second season will receive an English dub.


title: Mobile Suit Gundam Thunderbolt

text: A theatrical compilation film of the first season titled was released in Japanese theaters on 25 June 2016 with the Blu-ray release on 29 July 2016. Sunrise and Anime Limited distributed the film outside Japan. A theatrical compilation film of the second season titled was released in Japanese theaters between 18 November – 1 December 2017.


title: Bihar Legislative Council

text: Bihar Vidhan Parishad, also known as Bihar Legislative Council, is the upper house of the bicameral Bihar Legislature of the state of Bihar in India.


title: Bihar Legislative Council

text: A new Province of Bihar and Odisha was created by the Government of India on 12 December 1911. The Legislative Council with a total of 43 members belonging to different categories was formed in 1912. The first sitting of the Council was convened on 20 January 1913 at Patna College Bankipore. In 1920 Bihar and Orissa declared governor province, as per Government of India Act 1919. As per Government of India Act 1935 Bihar and Orissa was split into separate provinces of Bihar and Orissa. In 1936, [Bihar] attained its separate Statehood. Under the Government of India Act, 1919, the unicameral legislature got converted into bicameral one, i.e., the Bihar Legislative Council and the Bihar Legislative Assembly. Under the Government of India Act, 1935, the Bihar Legislative Council consisted of 29 members. On March 21, 1938, the session of the Bihar Legislative Council took place in a newly built building. On 1 April 1950, the secretariat of BLC started functioning. After the first General Elections 1952, the number of members was increased up to 72 and by 1958 the number was raised to 96. With the creation of Jharkhand, as a result of the Bihar Reorganisation Act, 2000 passed by the Parliament, the strength of the Bihar Legislative Council has been reduced from 96 to 75 members. Some veteran council members B. P. Mandal, Jagannath Mishra, Satyendra Narain Singh and Lalu Prasad Yadav have also served as Chief Minister of Bihar.


title: Bihar Legislative Council

text: Bihar Legislative Council is a permanent body and not subject to dissolution. But as nearly as possible, one-third of the members thereof retire as soon as may be on the expiration of every second year. Members are now elected or nominated for six years and one-third of them retire every second year. The presiding officers of Vidhan Parishad are now known as Chairman and Deputy Chairman. Members of the upper house, the Legislative Council are indirectly elected through an electoral college. There are 27 Committees which are, at present, functional in the Council. Besides, there are three Financial Committees consisting of the members of the two Houses of the State Legislature.


title: Religious pluralism

text: Religious pluralism is an attitude or policy regarding the diversity of religious belief systems co-existing in society. It can indicate one or more of the following:


title: Religious pluralism

text: Religious pluralism, to paraphrase the title of a recent academic work, goes beyond mere toleration. Chris Beneke, in "Beyond Toleration: The Religious Origins of American Pluralism", explains the difference between religious tolerance and religious pluralism by pointing to the situation in the late 18th century United States. By the 1730s, in most colonies religious minorities had obtained what contemporaries called religious toleration: "The policy of toleration relieved religious minorities of some physical punishments and some financial burdens, but it did not make them free from the indignities of prejudice and exclusion. Nor did it make them equal. Those 'tolerated' could still be barred from civil offices, military positions, and university posts." In short, religious toleration is only the absence of religious persecution, and does not necessarily preclude religious discrimination. However, in the following decades something extraordinary happened in the Thirteen Colonies, at least if one views the events from "a late eighteenth-century perspective". Gradually the colonial governments expanded the policy of religious toleration, but then, between the 1760s and the 1780s, they replaced it with "something that is usually called religious liberty". Mark Silka, in "Defining Religious Pluralism in America: A Regional Analysis", states that religious pluralism "enables a country made up of people of different faiths to exist without sectarian warfare or the persecution of religious minorities. Understood differently in different times and places, it is a cultural construct that embodies some shared conception of how a country's various religious communities relate to each other and to the larger nation whole."


title: Religious pluralism

text: Religious pluralism can be defined as "respecting the otherness of others". Freedom of religion encompasses all religions acting within the law in a particular region. Exclusivist religions teach that theirs is the only way to salvation and to religious truth, and some of them would even argue that it is necessary to suppress the falsehoods taught by other religions. Some Protestant sects argue fiercely against Roman Catholicism, and fundamentalist Christians of all kinds teach that religious practices like those of Paganism and witchcraft are pernicious. This was a common historical attitude prior to the Enlightenment, and has appeared as governmental policy into the present day under systems like Afghanistan's Taliban regime, which destroyed the ancient Buddhas of Bamyan. Of course, many religious communities have long been engaged in building peace, justice, and development themselves, and the emergence of the secular peacemaking field has led religious communities to systematize and institutionalize their own peacebuilding and interfaith work. The Catholic Church has worked in development and poverty reduction, human rights, solidarity, and peace, and after World War II, it began to develop specific tools and apply conflict transformation practices.


title: Religious pluralism

text: Giving one religion or denomination special rights that are denied to others can weaken religious pluralism. This situation was observed in Europe through the Lateran Treaty and Church of England. In modern era, many Islamic countries have laws that criminalize the act of leaving Islam to someone born in Muslim family, forbid entry to non-Muslims into Mosques, and forbid construction of Church, Synagogue or Temples inside their countries.


title: Religious pluralism

text: Relativism, the belief that all religions are equal in their value and that none of the religions give access to absolute truth, is an extreme form of inclusivism. Likewise, syncretism, the attempt to take over creeds of practices from other religions or even to blend practices or creeds from different religions into one new faith is an extreme form of inter-religious dialogue. Syncretism must not be confused with ecumenism, the attempt to bring closer and eventually reunite different denominations of one religion that have a common origin but were separated by a schism.


title: Religious pluralism

text: Cultural and religious pluralism has a long history and development that reaches from antiquity to contemporary trends in post-modernity.


title: Religious pluralism

text: German philosophers of religion Ludwig Feuerbach and Ernst Troeltsch concluded that Asian religious traditions, in particular Hinduism and Buddhism, were the earliest proponents of religious pluralism and granting of freedom to the individuals to choose their own faith and develop a personal religious construct within it (see also Relationship between Buddhism and Hinduism); Jainism, another ancient Indian religion, as well as Daoism have also always been inclusively flexible and have long favored religious pluralism for those who disagree with their religious viewpoints. The Age of Enlightenment in Europe triggered a sweeping transformation about religion after the French Revolution (liberalism, democracy, civil and political rights, freedom of thought, separation of Church and State, secularization), with rising acceptance of religious pluralism and decline of Christianity. According to Chad Meister, these pluralist trends in the Western thought, particularly since the 18th century, brought mainstream Christianity and Judaism closer to the Asian traditions of philosophical pluralism and religious tolerance.


title: Religious pluralism

text: Bahá'u'lláh, founder of Baháʼí Faith, a religion that developed in Persia, having roots in Islam, urged the elimination of religious intolerance. He taught that God is one, and religion has been progressively revealed over time through Manifestations of God, the founders of religion. Bahá'u'lláh taught that Baháʼís must associate with peoples of all religions, whether this is reciprocated or not.


title: Religious pluralism

text: Baháʼís refer to this concept as Progressive revelation, meaning that each religion brings a more advanced understanding of divinity and updated social laws as mankind matures. In this view, God's word is revealed through a series of messengers: Abraham, Krishna, Moses, Buddha, Jesus, Muhammad, Báb and Bahá'u'lláh (the founder of the Baháʼí Faith) among them. According to Baháʼí writings, there will not be another messenger for many hundreds of years. .


title: Religious pluralism

text: There is also a respect for the religious traditions of the native peoples of the planet who may have little other than oral traditions as a record of their religious figures.


title: Religious pluralism

text: Buddhist doctrine, fundamentally based upon minimizing or negating the suffering which arises from attachment, like its sister Indic religions, opposes exclusivism and emphasizes pluralism. This is not only encapsulated in the life story of the Buddha, who sought many gurus himself before resolving to seek Enlightenment on his own, but also in Buddhist scripture.


title: Religious pluralism

text: The Buddha also himself stated that truth is compromised when an individual is not open to entertaining a wide array of teachings. Moreover, without a pluralist understanding, the Buddha stated that truth cannot be discovered or ascertained such that it is truly known:


title: Religious pluralism

text: In the Lankavatara Sutra, the Buddha gave a long treatise on the idea that various expressions of Truth may seem contradictory or boundless, yet they all speak of Truth itself - emphasizing that an Enlightened One both accepts pluralism in that there are many ways to referring to Truth, but rises above it through the understanding that Truth transcends all labels.


title: Religious pluralism

text: When asked, "Don't all religions teach the same thing? Is it possible to unify them?" the Dalai Lama said:


title: Religious pluralism

text: For the Romans, religion was part of the daily life. Each home had a household shrine at which prayers and libations to the family's domestic deities were offered. Neighborhood shrines and sacred places such as springs and groves dotted the city. The Roman calendar was structured around religious observances; in the Imperial Era, as many as 135 days of the year were devoted to religious festivals and games ("ludi)". Women, slaves and children all participated in a range of religious activities. Some public rituals could be conducted only by women, and women formed what is perhaps Rome's most famous priesthood, the state-supported Vestal Virgins, who tended Rome's sacred hearth for centuries, until disbanded under Christian persecution and domination.


title: Religious pluralism

text: The Romans are known for the great number of deities they honored. The presence of Greeks on the Italian peninsula from the beginning of the historical period influenced Roman culture, introducing some religious practices that became as fundamental as the cult of Apollo. The Romans looked for common ground between their major gods and those of the Greeks, adapting Greek myths and iconography for Latin literature and Roman art. Etruscan religion was also a major influence, particularly on the practice of augury, since Rome had once been ruled by Etruscan kings.


title: Religious pluralism

text: Mystery religions imported from the Near East (Ptolemaic Egypt, Persia and Mesopotamia), which offered initiates salvation through a personal God and eternal life after the death, were a matter of personal choice for an individual, practiced in addition to carrying on one's family rites and participating in public religion. The mysteries, however, involved exclusive oaths and secrecy, conditions that conservative Romans viewed with suspicion as characteristic of "magic", conspiracy ("coniuratio"), and subversive activity. Sporadic and sometimes brutal attempts were made to suppress religionists who seemed to threaten traditional Roman morality and unity, as with the Senate's efforts to restrict the Bacchanals in 186 BC.


title: Religious pluralism

text: As the Romans extended their dominance throughout the Mediterranean world, their policy in general was to absorb the deities and cults of other peoples rather than try to eradicate them, since they believed that preserving tradition promoted social stability.


title: Religious pluralism

text: One way that Rome incorporated diverse peoples was by supporting their religious heritage, building temples to local deities that framed their theology within the hierarchy of Roman religion. Inscriptions throughout the Empire record the side-by-side worship of local and Roman deities, including dedications made by Romans to local Gods. By the height of the Empire, numerous international deities were cultivated at Rome and had been carried to even the most remote provinces (among them Cybele, Isis, Osiris, Serapis, Epona), and Gods of solar monism such as Mithras and Sol Invictus, found as far north as Roman Britain. Because Romans had never been obligated to cultivate one deity or one cult only, religious tolerance was not an issue in the sense that it is for competing monotheistic religions. The monotheistic rigor of Judaism posed difficulties for Roman policy that led at times to compromise and the granting of special exemptions, but sometimes to intractable conflict.


title: Religious pluralism

text: Maximal forms of religious pluralism claim that all religions are equally true, or that one religion can be true for some and another for others. Most Christians hold this idea to be logically impossible from the Principle of contradiction. The two largest Christian branches, the Catholic Church and the Eastern Orthodox Church, both claim to be the "one true church" and that "outside the true Church there is no salvation"; Protestantism however, which has many different denominations, has no consistent doctrine in this regard, and has a variety of different positions regarding religious pluralism.


title: Religious pluralism

text: Other Christians have held that there can be truth value and salvific value in other faith traditions. John Macquarrie, described in the "Handbook of Anglican Theologians" (1998) as "unquestionably Anglicanism's most distinguished systematic theologian in the second half of the twentieth century", wrote that "there should be an end to proselytizing but that equally there should be no syncretism of the kind typified by the Baháʼí movement" (p. 2). In discussing 9 founders of major faith traditions (Moses, Zoroaster, Lao-zu, Buddha, Confucius, Socrates, Krishna, Jesus, and Muhammad), which he called "mediators between the human and the divine", Macquarrie wrote that:


title: Religious pluralism

text: The Church of Jesus Christ of Latter-day Saints also teaches a form of religious pluralism, that there is at least some truth in almost all religions and philosophies.


title: Religious pluralism

text: Before the Great Schism, mainstream Christianity confessed "one holy catholic and apostolic church", in the words of the Nicene Creed. Roman Catholics, Orthodox Christians, Episcopalians and most Protestant Christian denominations still maintain this belief. Furthermore, the Catholic Church makes the claim that it alone is the one and only true Church founded by Jesus Christ, but the Eastern Orthodox and Oriental Orthodox Churches also make this claim in respect to themselves.


title: Religious pluralism

text: Church unity for these groups, as in the past, is something very visible and tangible, and schism was just as serious an offense as heresy. Following the Great Schism, Roman Catholicism sees and recognizes the Orthodox Sacraments as valid but illicit and without canonical jurisdiction. Eastern Orthodoxy does not have the concept of "validity" when applied to Sacraments, but it considers the "form" of Roman Catholic Sacraments to be acceptable, and there is some recognition of Catholic sacraments among some, but not all, Orthodox. Both generally mutually regard each other as "heterodox" and "schismatic", while continuing to recognize each other as Christian, at least secundum quid (see ecumenicism).


title: Religious pluralism

text: Some other Protestants hold that only believers who believe in certain fundamental doctrines know the true pathway to salvation. The core of this doctrine is that Jesus Christ was a perfect man, is the Son of God and that he died and rose again for the wrongdoing of those who will accept the gift of salvation. They continue to believe in "one" church, an "invisible church" which encompasses different types of Christians in different sects and denominations, believing in certain issues they deem fundamental, while disunited on a variety of doctrines they deem non-fundamental. Some evangelical Protestants are doubtful if Roman Catholics or Eastern Orthodox can possibly be members of this "invisible church", and usually they reject religious (typically restorationist) movements rooted in 19th century American Christianity, such as Mormonism, Christian Science, or Jehovah's Witnesses as not distinctly Christian.


title: Religious pluralism

text: The Catholic Church, unlike some Protestant denominations, affirms "developmental theology," understood to mean that the "Holy Spirit, in and through the evolving and often confused circumstances of concrete history, is gradually bringing the Church to an ever more mature understanding of the deposit of faith (the saving truths entrusted by Jesus Christ to the Apostles—these as such cannot be changed or added to). The Church comes to recognize baptism of desire quite early in its history. Later, the Church realizes that Romans 2:14–16, for example, allows for the salvation of non-Christians who do not have unobstructed exposure to Christian teachings: "When Gentiles who have not the law do by nature what the law requires… They show that what the law requires is written on their hearts… Various forms of "implicit faith" come to hold standing, until at Vatican Council II, the Church declares: "Nor shall divine providence deny the assistance necessary for salvation to those who, without any fault of theirs, have not yet arrived at an explicit knowledge of God, and who, not without grace, strive to lead a good life" (#16). Vatican Council II in its Declaration Nostra aetate addresses the non-Christian religions with respect and appreciation, affirming the goodness found in them. Since Vatican Council II, Catholic dialogists in particular are working out the implications of John Paul II's statement, in Redemptor hominis #6 that Christians should recognize "the Holy Spirit operating outside the visible confines of the Mystical Body of Christ." Among these dialogists, Robert Magliola, an affiliate of the Italian community "Vangelo e Zen" ("The Gospel and Zen"), Desio and Milano, Italy, who taught in predominantly Buddhist cultures for years, and practiced Buddhist-Catholic dialogue there and in the West, and who is widely published in this dialogue, argues the following:


title: Religious pluralism

text: Hinduism is naturally pluralistic as it "acknowledges different forms and representations of the divine, all understood in their relation to the supreme being, Brahman." Historians argue that the differentiations between the various Indic religions of the subcontinent were blurred before their specific codification and separation during British efforts to catalog different Indic philosophies. . Moreover, Hinduism itself is the oldest major religion, explaining a relative lack of antipathy towards specifiable religious traditions - and so the Hindu religion has no theological difficulties in accepting degrees of truth in other religions. . From a Vedantic perspective, Swami Bhaskarananda argues that Hinduism emphasizes that everyone actually worships the same God, whether one knows it or not. In the 8th sutra of the Pratyabhijñahrdyam, the Indian philosopher Ksemaraja says that all the siddhantas or theses of all the darsanas (schools of thought) are just the different aspects of the one Atman. It being all-pervading and all-inclusive, from matter to consciousness to nothingness, all are its aspects or its different roles. The Advaita Vedanta philosophy, a widely held view of many Hindus who follow Sanatana Dharma, encompasses pluralism.. Other, lesser-known philosophers have strived to encompass Indic philosophies under traditions other than Advaita, including the Indian philosopher Vijñabhikshu. Thus, the culture of open boundaries and continuous interaction and synthesis between all schools of thought is a very important aspect in understanding Hinduism and its fundamental nature of plurality.


title: Religious pluralism

text: In several mantras, sutras, smriti, and shruti, the idea that there are many ways to approach Truth or an underlying Reality is emphasized.


title: Religious pluralism

text: The Rig Veda also envisions an ideal world where a diverse collective speaks together to focus upon an idea that pervades all:


title: Religious pluralism

text: The Uddhava Gita is explicit that those interested in spirituality should learn the perspectives of a diverse group of proficient practitioners rather than a singular one who espouses a specific doctrine: