M. C. Escher

Maurits Cornelis Escher (; ; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made woodcuts, lithographs, and mezzotints, many of which were inspired by mathematics. Despite wide popular interest, for most of his life Escher was neglected in the art world, even in his native Netherlands. He was 70 before a retrospective exhibition was held. In the late twentieth century, he became more widely appreciated, and in the twenty-first century he has been celebrated in exhibitions around 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, and Donald Coxeter, and the 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 for Douglas Hofstadter's Pulitzer Prize–winning 1979 book Gödel, Escher, Bach.

Early life

Maurits Cornelis Escher was born on 17 June 1898 in Leeuwarden, Friesland, the Netherlands, in a house that forms part of the Princessehof Ceramics Museum today. He was the youngest son of the civil engineer George Arnold Escher and his second wife, Sara Gleichman. In 1903, the family moved to Arnhem, where he attended primary and secondary school until 1918. Known to his friends and family as "Mauk", he was a sickly child and was placed in a special school at the age of seven; he failed the second grade. Although he excelled at drawing, his grades were generally poor. He took carpentry and piano lessons until he was thirteen years old.

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.

In 1922, an important year of his life, Escher traveled through Italy, visiting Florence, San Gimignano, Volterra, Siena, and Ravello. In the same year, he traveled through Spain, visiting Madrid, Toledo, and Granada.

The Netherlands post office had Escher design a semi-postal stamp for the "Air Fund" (Dutch: Het Nationaal Luchtvaartfonds) in 1935, and again in 1949 he designed Dutch stamps. These were for the 75th anniversary of the Universal Postal Union; a different design was used by Suriname and the Netherlands Antilles for the same commemoration.

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. He was awarded the Knighthood of the Order of Orange-Nassau in 1955;

In July 1969, he finished his last work, a large woodcut with threefold rotational symmetry called Snakes, 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. The care that Escher took in creating and printing this woodcut can be seen in a video recording.

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.

Mathematically inspired work

Much of Escher's work is inescapably mathematical. This has caused a disconnect between his fame among mathematicians and the general public, and the lack of esteem with which he has been viewed in the art world.

Escher is not the first artist to explore mathematical themes: J. L. Locher, a previous director of the Kunstmuseum in The Hague, pointed out that 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. Escher greatly admired Piranesi and had several of Piranesi's prints hanging in his studio.

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.

<gallery mode=nolines widths=200px heights=200px caption="Forerunners of Escher identified by J. L. Locher">

Hexagonal tessellation with animals: Study of Regular Division of the Plane with Reptiles (1939). Escher reused the design in his 1943 lithograph Reptiles.

After his 1936 journey to the Alhambra and to La Mezquita, Cordoba, where he sketched the Moorish architecture and the tessellated mosaic decorations, Escher began to explore tessellation using geometric grids as the basis for his sketches. He then extended these to form complex interlocking designs, for example with animals such as birds, fish, and reptiles. One of his first attempts at a tessellation was his pencil, India ink, and watercolour Study of Regular Division of the Plane with Reptiles (1939), constructed on a hexagonal grid. The heads of the red, green, and white reptiles meet at a vertex; the tails, legs, and sides of the animals interlock exactly. It was used as the basis for his 1943 lithograph Reptiles.

His first study of mathematics began with papers by George Pólya and by the crystallographer Friedrich Haag on plane symmetry groups, sent to him by his brother Berend, a geologist.

In 1941 and 1942, Escher summarised 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"). The mathematician Doris Schattschneider unequivocally described this notebook as recording "a methodical investigation that can only be termed mathematical research."

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 Medieval 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", peopled with "jesters, knaves, and contemplators".

Escher was 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:

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.

Escher's interest in curvilinear perspective was encouraged by his friend and "kindred spirit", the art historian and artist Albert Flocon, in another example of constructive mutual influence. Flocon identified Escher as a "thinking artist"

Platonic and other solids

Escher often incorporated three-dimensional objects such as spheres, Platonic solids, including tetrahedrons and cubes, into his works, as well as mathematical objects such as cylinders and stellated polyhedra. In the print Reptiles, he combined two- and three-dimensional images. In one of his papers, Escher emphasized the importance of dimensionality:

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. For example, in Gravitation, animals climb around a stellated dodecahedron.

The two towers of Waterfall 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 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.

Levels of reality Escher's artistic expression was created from images in his mind, rather than directly from observations and travels to other countries. His interest in the multiple levels of reality in art is seen in works such as Drawing Hands (1948), where two hands are shown, each drawing the other. The critic Steven Poole commented that

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. He sent Escher a copy of the paper; Escher recorded that Coxeter's figure of a hyperbolic tessellation "gave me quite a shock": the infinite regular repetition of the tiles in the hyperbolic plane, growing rapidly smaller towards the edge of the circle, was precisely what he wanted to allow him to represent infinity on a two-dimensional plane.

Escher carefully studied Coxeter's figure, marking it up to analyse the successively smaller circlesSchattschneider notes that Coxeter observed in March 1964 that the white arcs in Circle Limit III "were not, as he and others had assumed, badly rendered hyperbolic lines but rather were branches of equidistant curves."

Legacy

The Escher Museum in The Hague. The poster shows a detail from Day and Night, 1938.

In art collections

The Escher intellectual property is controlled by the M.C. Escher Company, while exhibitions of his artworks are managed separately by the M.C. Escher Foundation.

The primary institutional collections of original works by M.C. Escher are exhibited at the Escher Museum in The Hague (which are part of the large collection of the Kunstmuseum there ); the National Gallery of Art (Washington, DC); the National Gallery of Canada (Ottawa); the Israel Museum (Jerusalem); and the Huis ten Bosch (Nagasaki, Japan).

Exhibitions

In 2023, the Kunstmuseum in the Hague created a large retrospective of Escher, entitled 'Escher – Other World'.

In mathematics and science

Doris Schattschneider identifies eleven strands of mathematical and scientific research anticipated or directly inspired by Escher. These are the classification of regular tilings using the edge relationships of tiles: two-color and two-motif tilings (counterchange symmetry or antisymmetry); color symmetry (in crystallography); metamorphosis or topological change; covering surfaces with symmetric patterns; Escher's algorithm (for generating patterns using decorated squares); creating tile shapes; local versus global definitions of regularity; symmetry of a tiling induced by the symmetry of a tile; orderliness not induced by symmetry groups; the filling of the central void in Escher's lithograph Print Gallery by H. Lenstra and B. de Smit. 1979 book Gödel, Escher, Bach by Douglas Hofstadter discusses the ideas of self-reference and strange loops expressed in Escher's art. The asteroid 4444 Escher was named in Escher's honor in 1985.

In popular culture

Escher's fame in popular culture grew when his work was featured by Martin Gardner in his April 1966 "Mathematical Games" column in Scientific American. Escher's works have appeared on many album covers including The Scaffold's 1969 L the P with Ascending and Descending; Mott the Hoople's eponymous 1969 record with Reptiles, Beaver & Krause's 1970 In A Wild Sanctuary with Three Worlds; and Mandrake Memorial's 1970 Puzzle with House of Stairs and (inside) Curl Up. His works have similarly been used on many book covers, including some editions of Edwin Abbott's Flatland, which used Three Spheres; E. H. Gombrich's Meditations on a Hobby Horse with Horseman; Pamela Hall's Heads You Lose with Plane Filling 1; Patrick A. Horton's Mastering the Power of Story with Drawing Hands; Erich Gamma et al.'s Design Patterns: Elements of Reusable Object-oriented software with Swans; and Arthur Markman's Knowledge Representation with Reptiles. The "World of Escher" markets posters, neckties, T-shirts, and jigsaw puzzles of Escher's artworks. Both Austria and the Netherlands have issued postage stamps commemorating the artist and his works. In 2019, Robin Lutz wrote and directed the documentary film M.C. Escher: Journey To Infinity, telling the story of Escher's life and art.