Modernism was an early 20th-century movement in literature, visual arts, and music that emphasized experimentation, abstraction, and subjective experience. Philosophy, politics, architecture, and social issues were all aspects of this movement. Modernism centered around beliefs in a "growing alienation" from prevailing "morality, optimism, and convention" and a desire to change how "human beings in a society interact and live together".
Martin Gardner was an American popular mathematics and popular science writer with interests also encompassing magic, scientific skepticism, micromagic, philosophy, religion, and literature – especially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton. He was a leading authority on Lewis Carroll; The Annotated Alice, which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies. He had a lifelong interest in magic and illusion and in 1999, MAGIC magazine named him as one of the "100 Most Influential Magicians of the Twentieth Century". He was considered the doyen of American puzzlers. He was a prolific and versatile author, publishing more than 100 books.
Arnold Schoenberg or Schönberg was an Austrian and American composer, music theorist, teacher and writer. He was among the first modernists who transformed the practice of harmony in 20th-century classical music, and a central element of his music was its use of motives as a means of coherence. He propounded concepts like developing variation, the emancipation of the dissonance, and the "unity of musical space".
The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and twelve-note composition—is a method of musical composition. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any one note through the use of tone rows, orderings of the 12 pitch classes. All 12 notes are thus given more or less equal importance, and the music avoids being in a key.
Modern art includes artistic work produced during the period extending roughly from the 1860s to the 1970s, and denotes the styles and philosophies of the art produced during that era. The term is usually associated with art in which the traditions of the past have been thrown aside in a spirit of experimentation. Modern artists experimented with new ways of seeing and with fresh ideas about the nature of materials and functions of art. A tendency away from the narrative, which was characteristic of the traditional arts, toward abstraction is characteristic of much modern art. More recent artistic production is often called contemporary art or Postmodern art.
Foundations of mathematics is the logical and mathematical framework that allows the development of mathematics without generating self-contradictory theories, and, in particular, to have reliable concepts of theorems, proofs, algorithms, etc. This may also include the philosophical study of the relation of this framework with reality.
Modernity, a topic in the humanities and social sciences, is both a historical period and the ensemble of particular socio-cultural norms, attitudes and practices that arose in the wake of the Renaissance—in the Age of Reason of 17th-century thought and the 18th-century Enlightenment. Commentators variously consider the era of modernity to have ended by 1930, with World War II in 1945, or as late as the period falling between the 1980s and 1990s; the following era is often referred to as "postmodernity". The term "contemporary history" is also used to refer to the post-1945 timeframe, without assigning it to either the modern or postmodern era.
Postmodern art is a body of art movements that sought to contradict some aspects of modernism or some aspects that emerged or developed in its aftermath. In general, movements such as intermedia, installation art, conceptual art and multimedia, particularly involving video are described as postmodern.
An art movement is a tendency or style in art with a specific art philosophy or goal, followed by a group of artists during a specific period of time, or, at least, with the heyday of the movement defined within a number of years. Art movements were especially important in modern art, when each consecutive movement was considered a new avant-garde movement. Western art had been, from the Renaissance up to the middle of the 19th century, underpinned by the logic of perspective and an attempt to reproduce an illusion of visible reality. By the end of the 19th century many artists felt a need to create a new style which would encompass the fundamental changes taking place in technology, science and philosophy.
The Elements is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid c. 300 BC. It is a collection of definitions, postulates, propositions, and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century.
In music, modernism is an aesthetic stance underlying the period of change and development in musical language that occurred around the turn of the 20th century, a period of diverse reactions in challenging and reinterpreting older categories of music, innovations that led to new ways of organizing and approaching harmonic, melodic, sonic, and rhythmic aspects of music, and changes in aesthetic worldviews in close relation to the larger identifiable period of modernism in the arts of the time. The operative word most associated with it is "innovation". Its leading feature is a "linguistic plurality", which is to say that no one music genre ever assumed a dominant position.
Inherent within musical modernism is the conviction that music is not a static phenomenon defined by timeless truths and classical principles, but rather something which is intrinsically historical and developmental. While belief in musical progress or in the principle of innovation is not new or unique to modernism, such values are particularly important within modernist aesthetic stances.
Daniel Albright was the Ernest Bernbaum Professor of Literature at Harvard and the editor of Modernism and Music: An Anthology of Sources. He was born and grew up in Chicago, Illinois and completed his undergraduate studies on a full scholarship at Rice in 1967. He received his MPhil in 1969 and PhD in 1970, both from Yale. Albright is also the author of the book Quantum Poetics which was published by Cambridge University Press in 1997. He held an NEH fellowship from 1973 to 1974, was a Guggenheim Fellow from 1976 to 1977, and more recently, he was a 2012 Berlin Prize Fellow at the American Academy in Berlin.
Cloisonnism is a style of post-Impressionist painting with bold and flat forms separated by dark contours. The term was coined by critic Édouard Dujardin on the occasion of the Salon des Indépendants, in March 1888. Artists Émile Bernard, Louis Anquetin, Paul Gauguin, Paul Sérusier, and others started painting in this style in the late 19th century. The name evokes the technique of cloisonné, where wires are soldered to the body of the piece, filled with powdered glass, and then fired. Many of the same painters also described their works as Synthetism, a closely related movement.
Les Demoiselles d'Avignon is a large oil painting created in 1907 by the Spanish artist Pablo Picasso. Part of the permanent collection of the Museum of Modern Art in New York, it portrays five nude female prostitutes in a brothel on Carrer d'Avinyó, a street in Barcelona, Spain. The figures are confrontational and not conventionally feminine, being rendered with angular and disjointed body shapes, some to a menacing degree. The far left figure exhibits facial features and dress of Egyptian or southern Asian style. The two adjacent figures are in an Iberian style of Picasso's Spain, while the two on the right have African mask-like features. Picasso said the ethnic primitivism evoked in these masks moved him to "liberate an utterly original artistic style of compelling, even savage force” leading him to add a shamanistic aspect to his project.
William Romeyn Everdell is an American teacher and author. He is Dean of Humanities, Emeritus, at Saint Ann's School.
Modernist literature originated in the late 19th and early 20th centuries, and is characterised by a self-conscious separation from traditional ways of writing in both poetry and prose fiction writing. Modernism experimented with literary form and expression, as exemplified by Ezra Pound's maxim to "Make it new." This literary movement was driven by a conscious desire to overturn traditional modes of representation and express the new sensibilities of the time. The immense human costs of the First World War saw the prevailing assumptions about society reassessed, and much modernist writing engages with the technological advances and societal changes of modernity moving into the 20th century. In Modernist Literature, Mary Ann Gillies notes that these literary themes share the "centrality of a conscious break with the past", one that "emerges as a complex response across continents and disciplines to a changing world".
Maurice Princet was a French mathematician and actuary who played a role in the birth of cubism. He was an associate of Pablo Picasso, Guillaume Apollinaire, Max Jacob, Jean Metzinger, and Marcel Duchamp. He is known as "le mathématicien du cubisme".
Mathematical beauty is the aesthetic pleasure derived from the abstractness, purity, simplicity, depth or orderliness of mathematics. Mathematicians may express this pleasure by describing mathematics as beautiful or describe mathematics as an art form, or, at a minimum, as a creative activity.
Julius Wilhelm Richard Dedekind was a German mathematician who made important contributions to number theory, abstract algebra, and the axiomatic foundations of arithmetic. His best known contribution is the definition of real numbers through the notion of Dedekind cut. He is also considered a pioneer in the development of modern set theory and of the philosophy of mathematics known as Logicism.
John Penn Mayberry was an American mathematical philosopher and creator of a distinctive Aristotelian philosophy of mathematics to which he gave expression in his book The Foundations of Mathematics in the Theory of Sets. Following completion of a Ph.D. at Illinois under the supervision of Gaisi Takeuti, he took up, in 1966, a position in the mathematics department of the University of Bristol. He remained there until his retirement in 2004 as a Reader in Mathematics.
