Art

Art is a diverse range of human activities and the products of those activities; this article focuses primarily on the visual arts, which includes the creation of images or objects in fields including painting, sculpture,printmaking, photography, and other visual media. Architecture is often included as one of the visual arts; however, like the decorative arts, it involves the creation of objects where the practical considerations of use are essential—in a way that they are usually not for a painting, for example. Music, theatre, film, dance, and otherperforming arts, as well as literature, and other media such as interactive media are included in a broader definition of art or the arts. Until the 17th century, art referred to any skill or mastery and was not differentiated from crafts or sciences, but in modern usage the fine arts, where aesthetic considerations are paramount, are distinguished from acquired skills in general, and the decorative or applied arts.

Many definitions of art have been proposed by philosophers and others who have characterized art in terms ofmimesis, expression, communication of emotion, or other values. During the Romantic period, art came to be seen as "a special faculty of the human mind to be classified with religion and science". Though art's definition is disputed and has changed over time, general descriptions mention an idea of human agency and creation through imaginative or technical skill.

The nature of art, and related concepts such as creativity and interpretation, are explored in a branch ofphilosophy known as aesthetics.

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English

English is a West Germanic language that was first spoken in England and is now the most widely used language in the world. It is spoken as a first language by a majority of the inhabitants of several nations, including the United Kingdom, the United States, Canada, Australia, Ireland, New Zealand and a number of Caribbean nations. It is the third most common native language in the world, after Mandarin Chinese and Spanish. It is widely learned as a second language and is an official language of the European Union, many Commonwealth countries and the United Nations, as well as in many world organisations.

English arose in the Anglo-Saxon kingdoms of England and what is now southeast Scotland, but was then under the control of the kingdom of Northumbria. Following the extensive influence of Great Britain and the United Kingdom from the 17th century to the mid-20th century, through the British Empire, and also of the United States since the mid-20th century, it has been widely propagated around the world, becoming the leading language of international discourse and the lingua franca in many regions.

Historically, English originated from the fusion of closely related dialects, now collectively termed Old English, which were brought to the eastern coast of Great Britain by Germanic settlers (Anglo-Saxons) by the 5th century – with the word English being derived from the name of the Angles, and ultimately from their ancestral region of Angeln (in what is now Schleswig-Holstein). A significant number of English words are constructed based on roots from Latin, because Latin in some form was the lingua franca of the Christian Church and of European intellectual life. The language was further influenced by the Old Norse language because of Viking invasions in the 8th and 9th centuries.

The Norman conquest of England in the 11th century gave rise to heavy borrowings from Norman-French, and vocabulary and spelling conventions began to give the appearance of a close relationship withRomance languages  to what had then become Middle English. The Great Vowel Shift that began in the south of England in the 15th century is one of the historical events that mark the emergence of Modern English from Middle English.

Owing to the assimilation of words from many other languages throughout history, modern English contains a very large vocabulary, with complex and irregular spelling, particularly of vowels. Modern English has not only assimilated words from other European languages but also from all over the world, including words of Hindi and African origin. The Oxford English Dictionary lists over 250,000 distinct words, not including many technical, scientific, and slang terms.

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Thai

Thai (ภาษาไทย Phasa Thai [pʰāːsǎː tʰāj] ( listen)), more precisely Central Thai or Siamese,is the national and official language of Thailand and the native language of the Thai people, Thailand's dominant ethnic group. Thai is a member of the Tai group of the Tai–Kadai language family. Some words in Thai are borrowed from Pali, Sanskrit and Old Khmer. It is a tonal and analytic language. Thai also has a complex orthography and relational markers[citation needed]. Thai is mutually intelligible with Lao.Native speakers of these two languages can understand one another without great difficulty.

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Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the abstract study of topics encompassingquantity, structure, space, change, and other properties; it has no generally accepted definition.

Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and otherson axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truthby rigorous deduction from appropriately chosen axioms and definitions. When those mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature.

Through the use of abstraction and logical reasoning, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid'sElements. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.

Galileo Galilei (1564–1642) said, 'The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth.'  Carl Friedrich Gauss (1777–1855) referred to mathematics as 'the Queen of the Sciences.'  Benjamin Peirce (1809–1880) called mathematics 'the science that draws necessary conclusions' . David Hilbert said of mathematics: 'We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise.'  Albert Einstein (1879–1955) stated that 'as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.'

Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries, which has led to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered.


Etymology

The word "mathematics" comes from the Greek μάθημα (máthēma), which, in the ancient Greek language, means what one learns, what one gets to know, hence also study and science, and in modern Greek just lesson. The word máthēma is derived from μανθάνω (manthano), while the modern Greek equivalent is μαθαίνω (mathaino), both of which mean to learn. In Greece, the word for "mathematics" came to have the narrower and more technical meaning "mathematical study", even in Classical times.Its adjective is μαθηματικός (mathēmatikós), meaning related to learning or studious, which likewise further came to mean mathematical. In particular, μαθηματικὴ τέχνη (mathēmatikḗ tékhnē), Latin: ars mathematica, meant the mathematical art.

In Latin, and in English until around 1700, the term "mathematics" more commonly meant "astrology" (or sometimes "astronomy") rather than "mathematics"; the meaning gradually changed to its present one from about 1500 to 1800. This has resulted in several mistranslations: a particularly notorious one is Saint Augustine's warning that Christians should beware of "mathematici" meaning astrologers, which is sometimes mistranslated as a condemnation of mathematicians.

The apparent plural form in English, like the French plural form les mathématiques (and the less commonly used singular derivative la mathématique), goes back to the Latin neuter plural mathematica (Cicero), based on the Greek plural τα μαθηματικά (ta mathēmatiká), used by Aristotle (384–322 BC), and meaning roughly "all things mathematical"; although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of physics and metaphysics, which were inherited from the Greek. In English, the noun mathematics takes singular verb forms. It is often shortened to maths or, in English-speaking North America, math.
Definitions of mathematics
Main article: Definitions of mathematics

Aristotle defined mathematics as "the science of quantity," and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and measurement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science. A great many professional mathematicians take no interest in a definition of mathematics, or consider it undefinable. Some just say, "Mathematics is what mathematicians do."

Three leading types of definition of mathematics are called logicist, intuitionist, and formalist, each reflecting a different philosophical school of thought.All have severe problems, none has widespread acceptance, and no reconciliation seems possible.

An early definition of mathematics in terms of logic was Benjamin Peirce's "the science that draws necessary conclusions" (1870). In the Principia Mathematica, Bertrand Russell and Alfred North Whitehead advanced the philosophical program known as logicism, and attempted to prove that all mathematical concepts, statements, and principles can be defined and proven entirely in terms of symbolic logic. A logicist definition of mathematics is Russell's "All Mathematics is Symbolic Logic" (1903).

Intuitionist definitions, developing from the philosophy of mathematician L. E. J. Brouwer, identify mathematics with certain mental phenomena. An example of an intuitionist definition is "Mathematics is the mental activity which consists in carrying out constructs one after the other."A peculiarity of intuitionism is that it rejects some mathematical ideas considered valid according to other definitions. In particular, while other philosophies of mathematics allow objects that can be proven to exist even though they cannot be constructed, intuitionism allows only mathematical objects that one can actually construct.

Formalist definitions identify mathematics with its symbols and the rules for operating on them. Haskell Curry defined mathematics simply as "the science of formal systems."A formal system is a set of symbols, or tokens, and some rules telling how the tokens may be combined into formulas. In formal systems, the word axiom has a special meaning, different from the ordinary meaning of "a self-evident truth". In formal systems, an axiom is a combination of tokens that is included in a given formal system without needing to be derived using the rules of the system.


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Science

Science (from Latin scientia, meaning "knowledge") is a systematic enterprise that builds and organizesknowledge in the form of testable explanations and predictions about the universe. In an older and closely related meaning (found, for example, in Aristotle), "science" refers to the body of reliable knowledge itself, of the type that can be logically and rationally explained (see History and philosophybelow). Since classical antiquity science as a type of knowledge was closely linked to philosophy. In the early modern era the words "science" and "philosophy" were sometimes used interchangeably in theEnglish language. By the 17th century, natural philosophy (which is today called "natural science") was considered a separate branch of philosophy. However, "science" continued to be used in a broad sense denoting reliable knowledge about a topic, in the same way it is still used in modern terms such aslibrary science or political science.

In modern use, "science" more often refers to a way of pursuing knowledge, not only the knowledge itself. It is "often treated as synonymous with 'natural and physical science', and thus restricted to those branches of study that relate to the phenomena of the material universe and their laws, sometimes with implied exclusion of pure mathematics. This is now the dominant sense in ordinary use." This narrower sense of "science" developed as scientists such as Johannes Kepler, Galileo Galilei and Isaac Newton began formulating laws of nature such as Newton's laws of motion. In this period it became more common to refer to natural philosophy as "natural science". Over the course of the 19th century, the word "science" became increasingly associated with the scientific method, a disciplined way to study the natural world, including physics, chemistry, geology and biology. It is in the 19th century also that the term scientist was created by the naturalist-theologian William Whewell to distinguish those who sought knowledge on nature from those who sought knowledge on other disciplines. The Oxford English Dictionary dates the origin of the word "scientist" to 1834. This sometimes left the study of human thought and society in a linguistic limbo, which was resolved by classifying these areas of academic study as social science. Similarly, several other major areas of disciplined study and knowledge exist today under the general rubric of "science", such as formal science and applied science.

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