# Maurits Cornelis Escher

Maurits Cornelis Escher (Dutch pronunciation: [ˈmʌurɪt͡s kɔrˈneːlɪs ˈɛʃər]; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made mathematically inspired woodcuts, lithographs, and mezzotints. Despite wide popular interest, Escher was for long somewhat neglected in the art world, even in his native Netherlands. He was 70 before a retrospective exhibition was held. In the twenty-first century, he became more widely appreciated, with exhibitions across the world. His work features mathematical objects and operations including impossible objects, explorations of infinity, reflection, symmetry, perspective, truncated and stellated polyhedra, hyperbolic geometry, and tessellations. Although Escher believed he had no mathematical ability, he interacted with the mathematicians George Pólya, Roger Penrose, Harold Coxeter and crystallographer Friedrich Haag, and conducted his own research into tessellation. Early in his career, he drew inspiration from nature, making studies of insects, landscapes, and plants such as lichens, all of which he used as details in his artworks. He traveled in Italy and Spain, sketching buildings, townscapes, architecture and the tilings of the Alhambra and the Mezquita of Cordoba, and became steadily more interested in their mathematical structure. Escher’s art became well known among scientists and mathematicians, and in popular culture, especially after it was featured by Martin Gardner in his April 1966 Mathematical Games column in Scientific American. Apart from being used in a variety of technical papers, his work has appeared on the covers of many books and albums. He was one of the major inspirations of Douglas Hofstadter’s Pulitzer Prize-winning 1979 book Gödel, Escher, Bach. Contents Escher’s birth house, now part of the Princessehof Ceramics Museum, in Leeuwarden, Friesland, the Netherlands In 1918, he went to the Technical College of Delft.[1][2] From 1919 to 1922, Escher attended the Haarlem School of Architecture and Decorative Arts, learning drawing and the art of making woodcuts.[1] He briefly studied architecture, but he failed a number of subjects (due partly to a persistent skin infection) and switched to decorative arts,[3] studying under the graphic artist Samuel Jessurun de Mesquita.[4] Study journeys Moorish tessellations including this one at the Alhambra inspired Escher’s work with tilings of the plane. He made sketches of this and other Alhambra patterns in 1936.[5] Escher’s painstaking[b][8] study of the same Moorish tiling in the Alhambra, 1936, demonstrates his growing interest in tessellation. He travelled frequently, visiting (among other places) Viterbo in 1926, the Abruzzi in 1927 and 1929, Corsica in 1928 and 1933, Calabria in 1930, the Amalfi coast in 1931 and 1934, and Gargano and Sicily in 1932 and 1935. The townscapes and landscapes of these places feature prominently in his artworks. In May and June 1936, Escher travelled back to Spain, revisiting the Alhambra and spending days at a time making detailed drawings of its mosaic patterns. It was here that he became fascinated, to the point of obsession, with tessellation, explaining:[4] It remains an extremely absorbing activity, a real mania to which I have become addicted, and from which I sometimes find it hard to tear myself away.[8] The sketches he made in the Alhambra formed a major source for his work from that time on.[8] He also studied the architecture of the Mezquita, the Moorish mosque of Cordoba. This turned out to be the last of his long study journeys; after 1937, his artworks were created in his studio rather than in the field. His art correspondingly changed sharply from being mainly observational, with a strong emphasis on the realistic details of things seen in nature and architecture, to being the product of his geometric analysis and his visual imagination. All the same, even his early work already shows his interest in the nature of space, the unusual, perspective, and multiple points of view.[4][8] Later life The Netherlands post office had Escher design a semi-postal stamp for the “Air Fund” in 1935,[10] and again in 1949 he designed Netherlands stamps. These were for the 75th anniversary of the Universal Postal Union; a different design was used by Surinam and the Netherlands Antilles for the same commemoration.[11][12] Escher, who had been very fond of and inspired by the landscapes in Italy, was decidedly unhappy in Switzerland. In 1937, the family moved again, to Uccle (Ukkel), a suburb of Brussels, Belgium.[1][2] World War II forced them to move in January 1941, this time to Baarn, Netherlands, where Escher lived until 1970.[1] Most of Escher’s best-known works date from this period. The sometimes cloudy, cold, and wet weather of the Netherlands allowed him to focus intently on his work.[1] After 1953, Escher lectured widely. A planned series of lectures in North America in 1962 was cancelled after an illness, and he stopped creating artworks for a time,[1] but the illustrations and text for the lectures were later published as part of the book Escher on Escher.[13] He was awarded the Knighthood of the Order of Orange-Nassau in 1955;[1] he was later made an Officer in 1967.[14] In July 1969 he finished his last work, a large woodcut with threefold rotational symmetry called Snakes,{{efn|See [[Snakes (M. C. Escher) article for image.}} in which snakes wind through a pattern of linked rings. These shrink to infinity toward both the center and the edge of a circle. It was exceptionally elaborate, being printed using three blocks, each rotated three times about the center of the image and precisely aligned to avoid gaps and overlaps, for a total of nine print operations for each finished print. The image encapsulates Escher’s love of symmetry; of interlocking patterns; and, at the end of his life, of his approach to infinity.[15][16][17] The care that Escher took in creating and printing this woodcut can be seen in a video recording.[18] Escher moved to the Rosa Spier Huis in Laren in 1970, an artists’ retirement home in which he had his own studio. He died in a hospital in Hilversum on 27 March 1972, aged 73.[1][2] He is buried at the New Cemetery in Baarn.[19][20] Mathematically inspired work Escher is not the first artist to explore mathematical themes: Parmigianino (1503–1540) had explored spherical geometry and reflection in his 1524 Self-portrait in a Convex Mirror, depicting his own image in a curved mirror, while William Hogarth’s 1754 Satire on False Perspective foreshadows Escher’s playful exploration of errors in perspective.[22][23] Another early artistic forerunner is Giovanni Battista Piranesi (1720–1778), whose dark “fantastical”[24] prints such as The Drawbridge in his Carceri (“Prisons”) sequence depict perspectives of complex architecture with many stairs and ramps, peopled by walking figures.[24][25] Only with 20th century movements such as Cubism, De Stijl, Dadaism, and Surrealism did mainstream art start to explore Escher-like ways of looking at the world with multiple simultaneous viewpoints.[21] However, although Escher had much in common with, for example, Magritte’s surrealism, he did not make contact with any of these movements.[26] Forerunner of Escher’s curved perspectives, geometries, and reflections: Parmigianino’s Self-portrait in a Convex Mirror, 1524 Forerunner of Escher’s impossible perspectives: William Hogarth’s Satire on False Perspective, 1753 Forerunner of Escher’s fantastic endless stairs: Piranesi’s Carceri Plate VII – The Drawbridge, 1745, reworked 1761 Tessellation Hexagonal tessellation with animals: Study of Regular Division of the Plane with Reptiles (1939). Escher reused the design in his 1943 lithograph Reptiles. His first study of mathematics began with papers by George Pólya[32] and by the crystallographer Friedrich Haag[33] on plane symmetry groups, sent to him by his brother Berend, a geologist.[34] He carefully studied the 17 canonical wallpaper groups and created periodic tilings with 43 drawings of different types of symmetry.[c] From this point on, he developed a mathematical approach to expressions of symmetry in his artworks using his own notation. Starting in 1937, he created woodcuts based on the 17 groups. His Metamorphosis I (1937) began a series of designs that told a story through the use of pictures. In Metamorphosis I, he transformed convex polygons into regular patterns in a plane to form a human motif. He extended the approach in his piece Metamorphosis III, which is four metres long.[8][35] In 1941 and 1942, Escher summarized his findings for his own artistic use in a sketchbook, which he labeled (following Haag) Regelmatige vlakverdeling in asymmetrische congruente veelhoeken (“Regular division of the plane with asymmetric congruent polygons”).[36] The mathematician Doris Schattschneider unequivocally described this notebook as recording “a methodical investigation that can only be termed mathematical research.”[34] She defined the research questions he was following as (1) What are the possible shapes for a tile that can produce a regular division of the plane, that is, a tile that can fill the plane with its congruent images such that every tile is surrounded in the same manner? Geometries Escher was interested enough in Hieronymus Bosch’s 1500 triptych The Garden of Earthly Delights to re-create part of its right-hand panel, Hell, as a lithograph in 1935. He reused the figure of a Mediaeval woman in a two-pointed headdress and a long gown in his lithograph Belvedere in 1958; the image is, like many of his other “extraordinary invented places”,[41] peopled with “jesters, knaves, and contemplators”.[41] Thus, Escher not only was interested in possible or impossible geometry but was, in his own words, a “reality enthusiast”;[41] he combined “formal astonishment with a vivid and idiosyncratic vision”.[41] Escher worked primarily in the media of lithographs and woodcuts, although the few mezzotints he made are considered to be masterpieces of the technique. In his graphic art, he portrayed mathematical relationships among shapes, figures, and space. Integrated into his prints were mirror images of cones, spheres, cubes, rings, and spirals.[42] Escher was also fascinated by mathematical objects such as the Möbius strip, which has only one surface. His wood engraving Möbius Strip II (1963) depicts a chain of ants marching forever over what, at any one place, are the two opposite faces of the object—which are seen on inspection to be parts of the strip’s single surface. In Escher’s own words:[43] An endless ring-shaped band usually has two distinct surfaces, one inside and one outside. Yet on this strip nine red ants crawl after each other and travel the front side as well as the reverse side. Therefore the strip has only one surface.[43] The mathematical influence in his work became prominent after 1936, when, having boldly asked the Adria Shipping Company if he could sail with them as travelling artist in return for making drawings of their ships, they surprisingly agreed, and he sailed the Mediterranean, becoming interested in order and symmetry. Escher described this journey, including his repeat visit to the Alhambra, as “the richest source of inspiration I have ever tapped”.[8] Escher’s interest in curvilinear perspective was encouraged by his friend and “kindred spirit”,[44] the art historian and artist Albert Flocon, in another example of constructive mutual influence. Flocon identified Escher as a “thinking artist”[44] alongside Piero della Francesca, Leonardo da Vinci, Albrecht Dürer, Wenzel Jamnitzer, Abraham Bosse, Girard Desargues, and Père Nicon.[44] Flocon was delighted by Escher’s Grafiek en tekeningen (“Graphics in Drawing”), which he read in 1959. This stimulated Flocon and André Barre to correspond with Escher and to write the book La Perspective curviligne (“Curvilinear perspective”).[45] Platonic and other solids Sculpture of a small stellated dodecahedron, as in Escher’s 1952 work Gravitation (University of Twente) The flat shape irritates me—I feel like telling my objects, you are too fictitious, lying there next to each other static and frozen: do something, come off the paper and show me what you are capable of! … So I make them come out of the plane. … My objects … may finally return to the plane and disappear into their place of origin.[46] Escher’s artwork is especially well-liked by mathematicians such as Doris Schattschneider and scientists such as Roger Penrose, who enjoy his use of polyhedra and geometric distortions.[34] For example, in Gravitation, animals climb around a stellated dodecahedron.[47] The two towers of Waterfall’s impossible building are topped with compound polyhedra, one a compound of three cubes, the other a stellated rhombic dodecahedron now known as Escher’s solid. Escher had used this solid in his 1948 woodcut Stars, which also contains all five of the Platonic solids and various stellated solids, representing stars; the central solid is animated by chameleons climbing through the frame as it whirls in space. Escher possessed a 6 cm refracting telescope and was a keen-enough amateur astronomer to have recorded observations of binary stars.[48][49][50] Levels of reality It is a neat depiction of one of Escher’s enduring fascinations: the contrast between the two-dimensional flatness of a sheet of paper and the illusion of three-dimensional volume that can be created with certain marks. In Drawing Hands, space and the flat plane coexist, each born from and returning to the other, the black magic of the artistic illusion made creepily manifest.[41] Infinity and hyperbolic geometry Doris Schattschneider’s reconstruction of the diagram of hyperbolic tiling sent by Escher to the mathematician H. S. M. Coxeter[34] Escher carefully studied Coxeter’s figure, marking it up to analyse the successively smaller circles[g] with which (he deduced) it had been constructed. He then constructed a diagram, which he sent to Coxeter, showing his analysis; Coxeter confirmed it was correct, but disappointed Escher with his highly technical reply. All the same, Escher persisted with hyperbolic tiling, which he called “Coxetering”.[34] Among the results were the series of wood engravings Circle Limit I–IV.[h][34] In 1959, Coxeter published his finding that these works were extraordinarily accurate: “Escher got it absolutely right to the millimeter”.[53] Legacy The Escher Museum in The Hague. The poster shows a detail from Day and Night, 1938 In art collections The primary institutional collections of original works by M.C. Escher are the Escher Museum in The Hague; the National Gallery of Art (Washington, DC);[56] the National Gallery of Canada (Ottawa);[57] the Israel Museum (Jerusalem);[58] and the Huis ten Bosch (Nagasaki, Japan).[59] Exhibitions Poster advertising the first major exhibition of Escher’s work in Britain (Dulwich Picture Gallery, 14 October 2015 – 17 January 2016). The image, which shows Escher and his interest in geometric distortion and multiple levels of distance from reality is based on his Hand with Reflecting Sphere, 1935.[60][23] In mathematics and science Wall tableau of one of Escher’s bird tessellations at the Princessehof Ceramics Museum in Leeuwarden The Pulitzer Prize-winning 1979 book Gödel, Escher, Bach by Douglas Hofstadter[69] discusses the ideas of self-reference and strange loops, drawing on a wide range of artistic and scientific sources including Escher’s art and the music of J. S. Bach. The asteroid 4444 Escher was named in Escher’s honor in 1985.[70] In popular culture See also |