Editing M. C. Escher

{{Short description|Dutch graphic artist (1898–1972)}}
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{{Infobox artist
| name          = M. C. Escher
| image         = Maurits Cornelis Escher.jpg
| caption       = Escher in 1971
| alt           = Black-and-white photograph of Escher in November 1971
| birth_name    = Maurits Cornelis Escher
| birth_date    = {{birth date|1898|6|17|df=y}}
| birth_place   = [[Leeuwarden]], Netherlands
| death_date    = {{death date and age|df=yes|1972|3|27|1898|6|17}}
| death_place   = [[Hilversum]], Netherlands
| resting_place = [[Baarn]], Netherlands
| education     = {{unbulleted list|[[Delft University of Technology|Technical College of Delft]]|[[Villa Welgelegen|Haarlem School of Architecture and Decorative Arts]]}}
| known_for     = {{hlist|Drawing|[[printmaking]]}}
| awards        = Knight (1955) and Officer (1967) of the [[Order of Orange-Nassau]]
| notable_works = {{unbulleted list|''[[Hand with Reflecting Sphere]]'' (1935)|''[[Relativity (M. C. Escher)|Relativity]]'' (1953)|''[[Waterfall (M. C. Escher)|Waterfall]]'' (1961)}}
| spouse        = {{marriage|Jetta Umiker|1924}}
| children      = 3
| father        = [[George Arnold Escher]]
| website       = {{URL|mcescher.com}}
}}

'''Maurits Cornelis Escher''' ({{IPAc-en|ˈ|ɛ|ʃ|ər}};<ref>[http://www.dictionary.com/browse/escher "Escher"]. ''[[Random House Webster's Unabridged Dictionary]]''.</ref> {{IPA|nl|ˈmʌurɪts kɔrˈneːlɪs ˈɛɕər|lang}}; 17 June 1898&nbsp;– 27 March 1972) was a Dutch graphic artist who made [[woodcut]]s, [[lithography|lithographs]], and [[mezzotint]]s, many of which were [[Mathematics and art|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 object]]s, explorations of infinity, [[reflection (mathematics)|reflection]], [[symmetry]], [[perspective (graphical)|perspective]], [[Truncation (geometry)|truncated]] and [[Stellation|stellated polyhedra]], [[hyperbolic geometry]], and [[tessellation]]s. Although Escher believed he had no mathematical ability, he interacted with the mathematicians [[George Pólya]], [[Roger Penrose]], and [[Harold Scott MacDonald Coxeter|Donald Coxeter]], and the [[Crystallography|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 [[lichen]]s, 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 [[Mosque–Cathedral of Córdoba|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 ==
[[File:Leeuwarden - Keramiekmuseum Princessehof.jpg|thumb|Escher's birth house, now part of the [[Princessehof Ceramics Museum]], in [[Leeuwarden]], [[Friesland]], the [[Netherlands]]]]
   
Maurits Cornelis{{efn|"We named him Maurits Cornelis after S.'s [Sara's] beloved uncle Van Hall, and called him 'Mauk' for short&nbsp;...", Diary of Escher's father, quoted in ''M. C. Escher: His Life and Complete Graphic Work'', Abradale Press, 1981, p. 9.}} 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.<ref name=Chronology>{{cite web |title=Chronology |url=http://www.worldofescher.com/reading/cronbib1.html |website=World of Escher |access-date=1 November 2015 |archive-url=https://web.archive.org/web/20150915212225/http://www.worldofescher.com/reading/cronbib1.html |archive-date=15 September 2015 |url-status=dead }}</ref><ref name=Paleis>{{cite web |title=About M.C. Escher |url=http://www.escherinhetpaleis.nl/about-escher-in-het-paleis/about-mc-escher/?lang=en |publisher=Escher in het Paleis |access-date=11 February 2016 |archive-url=https://web.archive.org/web/20160127100208/http://www.escherinhetpaleis.nl/about-escher-in-het-paleis/about-mc-escher/?lang=en |archive-date=27 January 2016 |url-status=dead  }}</ref> 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.<ref name="sundial">{{cite book |last=Bryden |first=Barbara E. |title=Sundial: Theoretical Relationships Between Psychological Type, Talent, And Disease |publisher=Center for Applications of Psychological Type |location=Gainesville, Fla |isbn=978-0-935652-46-8 |year=2005 }}</ref> Although he excelled at drawing, his grades were generally poor. He took [[carpentry]] and piano lessons until he was thirteen years old.<ref name=Chronology /><ref name=Paleis />

In 1918, he went to the [[Delft University of Technology|Technical College of Delft]].<ref name=Chronology /><ref name=Paleis /> From 1919 to 1922, Escher attended the [[Haarlem]] School of Architecture and Decorative Arts, learning drawing and the art of making [[woodcut]]s.<ref name=Chronology /> He briefly studied [[architecture]], but he failed a number of subjects (due partly to a persistent skin infection) and switched to [[decorative arts]],<ref name="sundial" /> studying under the graphic artist [[Samuel Jessurun de Mesquita]].<ref name="Locher 1971 5">{{harvnb|Locher|1971|p=5}}</ref>

== Study journeys ==
[[File:Alhambra-p3-closeup.jpg|thumb|[[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.<ref>{{harvnb|Locher|1971|p=17}}</ref>]]

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, Spain|Toledo]], and [[Granada]].<ref name=Chronology /> He was impressed by the Italian countryside and, in Granada, by the [[Moorish architecture]] of the fourteenth-century [[Alhambra]]. The intricate decorative designs of the Alhambra, based on [[Geometry|geometrical]] [[Symmetry|symmetries]] featuring interlocking repetitive patterns in the coloured tiles or sculpted into the walls and ceilings, triggered his interest in the mathematics of [[tessellation]] and became a powerful influence on his work.<ref>{{cite book |last=Roza |first=Greg |title=An Optical Artist: Exploring Patterns and Symmetry |year=2005 |publisher=Rosen Classroom |isbn=978-1-4042-5117-5 |page=20}}</ref><ref>{{cite book |last=Monroe |first=J. T. |title=Hispano-Arabic Poetry: A Student Anthology |url=https://books.google.com/books?id=3ZzXksIVQuYC&pg=PA65 |year=2004 |publisher=Gorgias Press LLC |isbn=978-1-59333-115-3 |page=65}}</ref>

[[File:Escher Alhambra Tessellation Sketch.jpg|thumb|left|upright|Escher's painstaking{{efn|The circled cross at the top of the image may indicate that the drawing is inverted, as can be seen by comparison with the photograph; the neighbouring image has a circled cross at the bottom. It is likely that Escher turned the drawing block, as convenient, while holding it in his hand in the Alhambra.}}<ref name=StAndrews /> study of the same Moorish tiling in the Alhambra, 1936, demonstrates his growing interest in tessellation.]]

Escher returned to Italy and lived in [[Rome]] from 1923 to 1935. While in Italy, Escher met Jetta Umiker&nbsp;– a Swiss woman, like himself attracted to Italy<!--this probably needs a ref-->&nbsp;– whom he married in 1924. The couple settled in Rome where their first son, Giorgio (George) Arnaldo Escher, named after his grandfather, was born. Escher and Jetta later had two more sons&nbsp;– Arthur and Jan.<ref name=Chronology /><!--<ref>{{cite web |url=http://www.geom.uiuc.edu/~paul/escher.html |title=Escher |publisher=Geom.uiuc.edu |access-date=7 December 2013}}</ref>--><ref name=Paleis />

He travelled frequently, visiting (among other places) [[Viterbo]] in 1926, the [[Abruzzo|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:<ref name="Locher 1971 5" />

{{blockquote|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.<ref name=StAndrews />}}

The sketches he made in the Alhambra formed a major source for his work from that time on.<ref name=StAndrews /> He studied the architecture of the [[Mosque–Cathedral of Córdoba|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.<ref name="Locher 1971 5" /><ref name=StAndrews />

== Later life ==

In 1935, the political climate in Italy under [[Benito Mussolini|Mussolini]] became unacceptable to Escher. He had no interest in politics, finding it impossible to involve himself with any ideals other than the expressions of his own concepts through his own particular medium, but he was averse to fanaticism and hypocrisy. When his eldest son, George, was forced at the age of nine to wear a [[Opera Nazionale Balilla|Ballila]] uniform in school, the family left Italy and moved to [[Château-d'Œx]], Switzerland, where they remained for two years.<ref>Ernst, Bruno, '' The Magic Mirror of M.C. Escher'', [[Taschen]], 1978; p. 15</ref>

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.<ref name="hathaway1972">{{cite web |last=Hathaway |first=Dale K. |title=Maurits Cornelis Escher (1898–1972) |publisher=Olivet Nazarene University |date=17 November 2015 |url=http://web.olivet.edu/~hathaway/Escher_s.html |access-date=31 March 2016 |archive-url=https://web.archive.org/web/20160412192732/http://web.olivet.edu/~hathaway/Escher_s.html |archive-date=12 April 2016 |url-status=dead }}</ref>

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.<ref name=Chronology /><ref name=Paleis /> [[World War II]] forced them to move in January 1941, this time to [[Baarn]], Netherlands, where Escher lived until 1970.<ref name=Chronology /> 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.<ref name=Chronology /> 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,<ref name=Chronology /> but the illustrations and text for the lectures were later published as part of the book ''Escher on Escher''.<ref>{{cite book |author=Escher, M. C. |title=Escher on Escher: Exploring the Infinite |date=1989 |publisher=Harry N. Abrams |isbn=978-0-8109-2414-7}}</ref> He was awarded the Knighthood of the [[Order of Orange-Nassau]] in 1955;<ref name=Chronology /> in 1967 he was made an Officer.<ref>{{cite web |title=Timeline |url=https://www.escherinhetpaleis.nl/about-escher/timeline/?lang=en |website=Escher in het Paleis |access-date=14 March 2018 |archive-url=https://web.archive.org/web/20170915054022/http://www.escherinhetpaleis.nl/about-escher/timeline/?lang=en |archive-date=15 September 2017 |url-status=dead }}</ref>

In July 1969 he finished his last work, a large woodcut with threefold [[rotational symmetry]] called ''[[Snakes (M. C. Escher)|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.<ref>{{harvnb|Locher|1971|p=151}}</ref><ref>{{cite web |title=Snakes |url=http://www.mcescher.com/gallery/recognition-success/snakes/ |website=M. C. Escher |access-date=5 November 2015 |archive-url=https://web.archive.org/web/20151114122536/http://www.mcescher.com/gallery/recognition-success/snakes/ |archive-date=14 November 2015 |url-status=dead }}</ref><ref name="Cucker2013">{{cite book |last=Cucker|first=Felipe |title=Manifold Mirrors: The Crossing Paths of the Arts and Mathematics|url=https://books.google.com/books?id=_sxMbD_fiyIC&pg=PA107 |date=25 April 2013 |publisher=Cambridge University Press |isbn=978-0-521-42963-4 |pages=106–107}}</ref> The care that Escher took in creating and printing this woodcut can be seen in a video recording.<ref>{{cite web |title=M.C. Escher – Creating The "Snakes" Woodcut | date=16 February 2013 |url=https://www.youtube.com/watch?v=AmLaM6NkTDs | archive-url=https://ghostarchive.org/varchive/youtube/20211030/AmLaM6NkTDs| archive-date=30 October 2021|publisher=YouTube |access-date=5 November 2015}}{{cbignore}}</ref>

Escher moved to the [[Rosa Spier Huis]] in [[Laren, North Holland|Laren]] in 1970, an artists' retirement home in which he had his own studio. He died<!--see policy [[WP:V]] if adding anything--> in a hospital in [[Hilversum]] on 27 March 1972, aged 73.<ref name=Chronology/><ref name=Paleis/> He is buried at the New Cemetery in Baarn.<ref>[https://rkd.nl/nl/home/artists/26631 M.C. Escher] {{Webarchive|url=https://web.archive.org/web/20160308000518/https://rkd.nl/nl/home/artists/26631 |date=8 March 2016 }}, [[Netherlands Institute for Art History]], 2015. Retrieved 6 November 2015.</ref><ref>[http://www.vorstelijkbaarn.nl/zien-beleven/kaart/cultuur/escher/ M.C. Escher], Vorstelijk Baarn. Retrieved 6 November 2015.</ref>

== Mathematically inspired work ==

{{further|Mathematics and art}}

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.<ref name=Locher13/><ref name="Scotsman 2015"/> His originality and mastery of graphic techniques are respected, but his works have been thought too intellectual and insufficiently lyrical. Movements such as [[conceptual art]] have, to a degree, reversed the art world's attitude to intellectuality and lyricism, but this did not rehabilitate Escher, because traditional critics still disliked his narrative themes and his use of perspective. However, these same qualities made his work highly attractive to the public.<ref name=Locher13>{{harvnb|Locher|1971|pp=13–14}}</ref>

Escher is not the first artist to explore mathematical themes: J. L. Locher, a previous director of the [[Kunstmuseum Den Haag|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.<ref name="Locher11">{{harvnb|Locher|1971|pp=11–12}}</ref><ref name=NGA/> Another early artistic forerunner is [[Giovanni Battista Piranesi]] (1720–1778), whose dark "fantastical"<ref name=Carnegie/> prints such as ''The Drawbridge'' in his [[Imaginary Prisons|''Carceri'' ("Prisons")]] sequence depict perspectives of complex architecture with many stairs and ramps, peopled by walking figures.<ref name=Carnegie>{{cite web |last=Altdorfer |first=John |title=Inside A Fantastical Mind |url=http://www.carnegiemuseums.org/cmag/article.php?id=123 |publisher=Carnegie Museums |access-date=7 November 2015 |archive-url=https://web.archive.org/web/20100706192452/http://www.carnegiemuseums.org/cmag/article.php?id=123 |archive-date=6 July 2010 |url-status=dead }}</ref><ref>{{cite magazine |last=McStay |first=Chantal |title=Oneiric Architecture and Opium |url=http://www.theparisreview.org/blog/tag/giovanni-battista-piranesi/ |magazine=[[The Paris Review]] |access-date=7 November 2015 |date=15 August 2014}}</ref> Escher greatly admired Piranesi and had several of Piranesi's prints hanging in his studio.<ref>{{cite web |title=Giovanni Battista Piranesi |url=https://www.escherinhetpaleis.nl/escher-today/giovanni-battista-piranesi/?lang=en |website=Escher in het Paleis |access-date=6 August 2022 |date=14 November 2020}}</ref><ref>{{cite book |last=Hazeu |first=Wim |title=M.C. Escher, Een biografie |language=Dutch |publisher=Meulenhoff |year=1998 |page=175}}</ref>

Only with 20th century movements such as [[Cubism]], [[De Stijl]], [[Dada]]ism, and [[Surrealism]] did mainstream art start to explore Escher-like ways of looking at the world with multiple simultaneous viewpoints.<ref name=Locher13 /> However, although Escher had much in common with, for example, [[Magritte]]'s surrealism and [[Op art]], he did not make contact with any of these movements.<ref name="Scotsman 2015">{{cite news |last=Mansfield |first=Susan |title=Escher, the master of impossible art |url=http://www.scotsman.com/lifestyle/arts/visual-arts/escher-the-master-of-impossible-art-1-3815073#axzz3qnqdWYGr |newspaper=[[The Scotsman]] |access-date=7 November 2015 |date=28 June 2015| archive-url=https://web.archive.org/web/20150701214226/http://www.scotsman.com/lifestyle/arts/visual-arts/escher-the-master-of-impossible-art-1-3815073#axzz3qnqdWYGr | archive-date=July 1, 2015}}</ref><ref name="Marcus 2022">{{cite news |last=Marcus |first=J. S. |author-link=J. S. Marcus |title=M.C. Escher's illusionist art has long been ignored by the establishment due to its mass appeal. A Houston show hopes to correct that |url=https://www.theartnewspaper.com/2022/03/11/mc-escher-poster-boy-of-illusionist-art |access-date=7 August 2022 |work=[[The Art Newspaper]] |date=11 March 2022 |quote=the art world proper has [been] inclined to regard Escher, whose finished prints share formal qualities with Surrealism and Op art, as somewhat derivative or merely decorative.}}</ref>

<gallery class=center mode=nolines widths=200px heights=200px caption="Forerunners of Escher identified by J. L. Locher">
File:Parmigianino Selfportrait.jpg|Forerunner of Escher's [[Curvilinear perspective|curved perspectives]], geometries, and reflections: [[Parmigianino]]'s ''[[Self-portrait in a Convex Mirror]]'', 1524<ref name="Locher11"/>
File:William Hogarth - Absurd perspectives.png|Forerunner of Escher's impossible perspectives: [[William Hogarth]]'s ''[[Satire on False Perspective]]'', 1753<ref name="Locher11"/>
File:Giovanni Battista Piranesi - The Drawbridge - Google Art Project.jpg|Forerunner of Escher's fantastic endless stairs: [[Giovanni Battista Piranesi|Piranesi]]'s ''[[Imaginary Prisons|Carceri]]'' Plate VII&nbsp;– The Drawbridge, 1745, reworked 1761<ref name="Locher11"/>
</gallery>

=== Tessellation ===

{{further|Tessellation}}

In his early years, Escher sketched landscapes and nature. He sketched insects such as ants, bees, grasshoppers, and mantises,<ref>{{harvnb|Locher|1971|pp=62–63}}</ref> which appeared frequently in his later work. His early love of [[Ancient Rome|Roman]] and Italian landscapes and of nature created an interest in tessellation, which he called ''[[Regular Division of the Plane]]''; this became the title of his 1958 book, complete with reproductions of a series of woodcuts based on tessellations of the plane, in which he described the systematic buildup of mathematical designs in his artworks. He wrote, "[[Crystallography|crystallographer]]s have opened the gate leading to an extensive domain".<ref name="Peterson's2012">{{cite book | last=Guy | first=R.K. | last2=Woodrow | first2=R.E. | title=The Lighter Side of Mathematics: Proceedings of the Eugene Strens Memorial Conference on Recreational Mathematics and Its History | publisher=Mathematical Association of America | series=Spectrum | year=2020 | isbn=978-1-4704-5731-0 | url=https://books.google.com/books?id=FsH2DwAAQBAJ&pg=PA92 | access-date=16 June 2024 | page=92}}</ref>

[[File:Study of Regular Division of the Plane with Reptiles.jpg|thumb|right|Hexagonal tessellation with animals: ''Study of Regular Division of the Plane with Reptiles'' (1939). Escher reused the design in his 1943 lithograph ''[[Reptiles (M. C. Escher)|Reptiles]]''.]]

After his 1936 journey to the [[Alhambra]] and to [[Mosque–Cathedral of Córdoba|La Mezquita]], [[Córdoba, Andalusia|Cordoba]], where he sketched the [[Moors|Moorish]] architecture and the tessellated mosaic decorations,<ref>{{harvnb|Locher|1971|pp=17, 70–71}}</ref> 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.<ref>{{harvnb|Locher|1971|pp=79–85}}</ref> 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 (M. C. Escher)|Reptiles]]''.<ref>{{harvnb|Locher|1971|p=18}}</ref>

His first study of mathematics began with papers by [[George Pólya]]<ref>{{cite journal |author=Pólya, G. |author-link=George Pólya |title=Über die Analogie der Kristallsymmetrie in der Ebene |journal=Zeitschrift für Kristallographie |volume=60 |year=1924 |issue=1–6 |pages=278–282 |language=de |doi=10.1524/zkri.1924.60.1.278|s2cid=102174323 }}</ref> and by the crystallographer [[Friedrich Haag]]<ref name=Haag>{{cite journal |author=Haag, Friedrich |title=Die regelmäßigen Planteilungen |language=de |journal=Zeitschrift für Kristallographie |volume=49 |year=1911 |issue=1–6 |pages=360–369 |url=https://zenodo.org/record/1448954 <!--open access--> |doi=10.1524/zkri.1911.49.1.360 |s2cid=100640309 }}</ref> on plane [[symmetry group]]s, sent to him by his brother [[Berend George Escher|Berend]], a geologist.<ref name=MathSide /> He carefully studied the 17 canonical [[wallpaper group]]s and created periodic tilings with 43 drawings of different types of symmetry.{{efn|Escher made it clear that he did not understand the abstract concept of a [[group theory|group]], but he did grasp the nature of the 17 wallpaper groups in practice.<ref name=StAndrews />}} 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 polygon]]s into regular patterns in a plane to form a human motif. He extended the approach in his piece ''[[Metamorphosis III]]'', which is almost seven metres long.<ref name=StAndrews /><ref>{{harvnb|Locher|1971|p=84}}</ref>

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").<ref>{{cite book |title=What's Happening in the Mathematical Sciences, Volume 4 |last=Cipra |first=Barry A. |author-link=Barry Arthur Cipra |editor=Paul Zorn |publisher=American Mathematical Society |page=103 |year=1998 |isbn=978-0-8218-0766-8}}</ref> The mathematician [[Doris Schattschneider]] unequivocally described this notebook as recording "a methodical investigation that can only be termed mathematical research."<ref name=MathSide/><ref name="Schattschneider  2010">{{cite journal |last=Schattschneider |first=Doris |author-link=Doris Schattschneider |date=June–July 2010 |title=The Mathematical Side of M. C. Escher |journal=[[Notices of the American Mathematical Society]] |volume=57 |issue=6 |pages=706–18 |url=https://www.ams.org/notices/201006/rtx100600706p.pdf}}</ref> She defined the research questions he was following as

{{blockquote|(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?<br />(2) Moreover, in what ways are the edges of such a tile related to each other by [[Isometry group|isometries]]?<ref name=MathSide />}}

=== Geometries ===

{{further|Perspective (geometry)|Curvilinear perspective}}

[[File:The Artist - Maurits Cornelis Escher - working at his Atelier (50385403156).jpg|thumb|Escher at work on ''Sphere Surface with Fish'' (1958) in his workshop, using a [[mahlstick]] for support, late 1950s]]
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Although Escher did not have mathematical training – his understanding of mathematics was largely visual and intuitive – his [[mathematics and art|art had a strong mathematical component]], and several of the worlds that he drew were built around impossible objects. After 1924 Escher turned to sketching landscapes in Italy and [[Corsica]] with irregular [[perspective (geometry)|perspectives]] that are impossible in natural form. His first print of an impossible reality was ''[[Still Life and Street]]'' (1937); impossible stairs and multiple visual and gravitational perspectives feature in popular works such as ''[[Relativity (M. C. Escher)|Relativity]]'' (1953).{{efn|See [[Relativity (M. C. Escher)]] article for image.}} ''[[House of Stairs]]'' (1951) attracted the interest of the mathematician [[Roger Penrose]] and his father, the biologist [[Lionel Penrose]]. In 1956, they published a paper, "Impossible Objects: A Special Type of Visual Illusion" and later sent Escher a copy. Escher replied, admiring the Penroses' [[Penrose stairs|continuously rising flights of steps]], and enclosed a print of ''[[Ascending and Descending]]'' (1960). The paper contained the tribar or [[Penrose triangle]], which Escher used repeatedly in his lithograph of a building that appears to function as a [[perpetual motion]] machine, ''[[Waterfall (M. C. Escher)|Waterfall]]'' (1961).{{efn|See [[Waterfall (M. C. Escher)]] article for image.}}<ref name=Seckel2004>{{cite book |last=Seckel |first=Al |title=Masters of Deception: Escher, Dalí & the Artists of Optical Illusion |url=https://archive.org/details/mastersofdecepti00alse |url-access=registration |year=2004 |publisher=Sterling |isbn=978-1-4027-0577-9 |pages=[https://archive.org/details/mastersofdecepti00alse/page/81 81]–94, 262}} Chapter 5 is on Escher.</ref><ref>{{cite journal |last1=Penrose |first1=L.S. |last2=Penrose |first2=R. |title=Impossible objects: A special type of visual illusion |journal=[[British Journal of Psychology]] |year=1958 |volume=49 |issue=1 |pages=31–33 |doi=10.1111/j.2044-8295.1958.tb00634.x | pmid=13536303}}</ref><ref>{{cite book | last1=Kirousis | first1=Lefteris M. | last2=Papadimitriou | first2=Christos H. | title=26th Annual Symposium on Foundations of Computer Science (SFCS 1985) | chapter=The complexity of recognizing polyhedral scenes | author2-link=Christos Papadimitriou | doi=10.1109/sfcs.1985.59 | pages=175–185 | year=1985| isbn=978-0-8186-0644-1 | citeseerx=10.1.1.100.4844 }}</ref><ref>{{cite book | last=Cooper | first=Martin | title=Inequality, Polarization and Poverty | contribution=Tractability of Drawing Interpretation | doi=10.1007/978-1-84800-229-6_9 | isbn=978-1-84800-229-6 | pages=217–230 | publisher=Springer-Verlag | year=2008}}</ref>

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 [[Middle Ages|Mediaeval]] woman in a two-pointed headdress and a long gown in his lithograph ''[[Belvedere (M. C. Escher)|Belvedere]]'' in 1958; the image is, like many of his other "extraordinary invented places",<ref name=Poole>{{cite news |last1=Poole |first1=Steven |title=The impossible world of MC Escher |url=https://www.theguardian.com/artanddesign/2015/jun/20/the-impossible-world-of-mc-escher |newspaper=The Guardian |access-date=2 November 2015 |date=20 June 2015}}</ref> peopled with "[[jester]]s, [[wikt:knave|knaves]], and contemplators".<ref name=Poole /> Thus, Escher not only was interested in possible or impossible geometry but was, in his own words, a "reality enthusiast";<ref name=Poole /> he combined "formal astonishment with a vivid and idiosyncratic vision".<ref name=Poole />

Escher worked primarily in the media of [[Lithography|lithographs]] and [[woodcut]]s, although the few [[mezzotint]]s 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.<ref>{{cite web |url=http://www.mcescher.com/Biography/biography.htm |title=The Official M.C. Escher Website – Biography |access-date=7 December 2013 |archive-url=https://web.archive.org/web/20130702184317/http://www.mcescher.com/Biography/biography.htm |archive-date=2 July 2013 |url-status=dead }}</ref>

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:<ref name=NGC>{{cite web |title=Möbius Strip II, February 1963 |url=https://www.gallery.ca/en/see/collections/artwork.php?mkey=21164 |website=Collections |publisher=National Gallery of Canada |access-date=2 November 2015 |archive-url=https://web.archive.org/web/20150719142225/http://www.gallery.ca/en/see/collections/artwork.php?mkey=21164 |archive-date=19 July 2015 |url-status=dead }} which cites {{cite book |last1=Escher |first1=M. C. |title=M. C. Escher, the Graphic Work |date=2001 |publisher=Taschen}}</ref>

{{blockquote|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.<ref name=NGC />}}

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 Sea|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".<ref name=StAndrews>{{cite web |last1=O'Connor |first1=J. J. |last2=Robertson |first2=E. F. |title=Maurits Cornelius Escher |url=http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Escher.html |website=Biographies |publisher=University of St Andrews |access-date=2 November 2015 |date=May 2000 |archive-url=https://web.archive.org/web/20150925235220/http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Escher.html |archive-date=25 September 2015 |url-status=dead }} which cites {{cite news |author=Strauss, S. |title=M C Escher |work=The Globe and Mail |date=9 May 1996}}</ref>

Escher's interest in [[curvilinear perspective]] was encouraged by his friend and "kindred spirit",<ref name=ErnstinEmmerSchattschneider2007>{{cite book |last1=Emmer |first1=Michele |last2=Schattschneider |first2=Doris|last3=Ernst |first3=Bruno |title=M.C. Escher's Legacy: A Centennial Celebration |url=https://books.google.com/books?id=5DDyBwAAQBAJ&pg=PA16 |year=2007 |publisher=Springer |isbn=978-3-540-28849-7 |pages=10–16}}</ref> the art historian and artist Albert Flocon, in another example of constructive mutual influence. Flocon identified Escher as a "thinking artist"<ref name=ErnstinEmmerSchattschneider2007 /> alongside [[Piero della Francesca]], [[Leonardo da Vinci]], [[Albrecht Dürer]], [[Wenzel Jamnitzer]], [[Abraham Bosse]], [[Girard Desargues]], and [[Père Nicon]].<ref name=ErnstinEmmerSchattschneider2007 /> Flocon was delighted by Escher's ''Grafiek en tekeningen'' ("Graphics and Drawings"), 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]]").<ref>{{cite book |author1=Flocon, Albert |author2=Barre, André | title=La Perspective curviligne |publisher=Flammarion |year=1968}}</ref>

=== Platonic and other solids ===
[[File:Universiteit Twente Mesa Plus Escher Object.jpg|thumb|left|Sculpture of a [[small stellated dodecahedron]], as in Escher's 1952 work ''[[Gravitation (M. C. Escher)|Gravitation]]'' ([[University of Twente]])]]

Escher often incorporated three-dimensional objects such as the [[Platonic solid]]s such as spheres, tetrahedrons, and cubes into his works, as well as mathematical objects such as [[cylinder (geometry)|cylinders]] and [[Stellation|stellated polyhedra]]. In the print [[Reptiles (M. C. Escher)|''Reptiles'']], he combined two- and three-dimensional images. In one of his papers, Escher emphasized the importance of dimensionality:

{{blockquote|The flat shape irritates me — I feel like telling my objects, you are too fictitious, lying there next to each other static and frozen: {{em|do}} something, come off the paper and show me what you are capable of!&nbsp;... So I make them come out of the plane.&nbsp;... My objects&nbsp;... may finally return to the plane and disappear into their place of origin.<ref name=OutOfPlane>{{cite book |last1=Emmer |first1=Michele |last2=Schattschneider |first2=Doris |title=M.C. Escher's Legacy: A Centennial Celebration |url=https://books.google.com/books?id=5DDyBwAAQBAJ&pg=PA183 |year=2007 |publisher=Springer |isbn=978-3-540-28849-7 |pages=182–183}}</ref>}}

Escher's artwork is especially well-liked by mathematicians such as [[Doris Schattschneider]] and scientists such as [[Roger Penrose]], who enjoy his use of [[Polyhedron|polyhedra]] and [[geometry|geometric]] distortions.<ref name=MathSide>{{cite journal |last1=Schattschneider |first1=Doris| volume=57 |issue=6 |pages=706–718 |journal=Notices of the AMS |title=The Mathematical Side of M. C. Escher |url=https://www.ams.org/notices/201006/rtx100600706p.pdf |date=2010}}</ref> For example, in ''[[Gravitation (M. C. Escher)|Gravitation]]'', animals climb around a [[stellation|stellated]] [[dodecahedron]].<ref name="Hargittai2014">{{cite book |last=Hargittai |first=István |title=Symmetry: Unifying Human Understanding |url=https://books.google.com/books?id=vXTiBQAAQBAJ&pg=PA128 |date=23 May 2014 |publisher=Elsevier Science|isbn=978-1-4831-4952-3 |page=128}}</ref>

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 [[Compound of three octahedra|Escher's solid]]. Escher had used this solid in his 1948 woodcut ''[[Stars (M. C. Escher)|Stars]]'', which contains all five of the [[Platonic solid]]s and various stellated solids, representing stars; the central solid is animated by [[chameleon]]s climbing through the frame as it whirls in space. Escher possessed a 6&nbsp;cm [[refracting telescope]] and was a keen-enough amateur [[astronomer]] to have recorded observations of [[binary star]]s.<ref>{{harvnb|Locher|1971|p=104}}</ref><ref name=Beech>{{cite journal |title=Escher's ''Stars'' |last=Beech |first=Martin |journal=Journal of the Royal Astronomical Society of Canada |year=1992 |volume=86 |pages=169–177|bibcode=1992JRASC..86..169B }}</ref><ref name=CoxeterReview>{{cite journal |last=Coxeter |first=H. S. M. |author-link=Harold Scott MacDonald Coxeter |doi=10.1007/BF03023010 |issue=1 | journal=The Mathematical Intelligencer |pages=59–69 |title=A special book review: M. C. Escher: His life and complete graphic work |volume=7 |year=1985|s2cid=189887063 }}</ref>

=== 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.{{efn|See [[Drawing Hands]] article for image.}} The critic Steven Poole commented that

{{blockquote|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.<ref name=Poole />}}

=== Infinity and hyperbolic geometry ===

[[File:Schattschneider Reconstruction of Escher's Coxeter Diagram.jpg|thumb|left|upright=1.4<!--size for very low image-->|[[Doris Schattschneider]]'s reconstruction of the diagram of hyperbolic tiling sent by Escher to the mathematician [[Harold Scott MacDonald Coxeter|Donald Coxeter]]<ref name=MathSide />]]

In 1954 the International Congress of Mathematicians met in Amsterdam, and N. G. de Bruin organised a display of Escher's work at the Stedelijk Museum for the participants. Both Roger Penrose and [[Harold Scott MacDonald Coxeter|H. S. M. Coxeter]] were deeply impressed with Escher's intuitive grasp of mathematics. Inspired by ''Relativity'', Penrose devised his [[Penrose tribar|tribar]], and his father, Lionel Penrose, devised an endless staircase. Roger Penrose sent sketches of both objects to Escher, and the cycle of invention was closed when Escher then created the [[perpetual motion]] machine of ''Waterfall'' and the endless march of the monk-figures of ''Ascending and Descending''.<ref name=MathSide />
In 1957 Coxeter obtained Escher's permission to use two of his drawings in his paper "Crystal symmetry and its generalizations".<ref name=MathSide /><ref>{{cite journal |last=Coxeter |first=H. S. M. |title=Crystal symmetry and its generalizations |journal=A Symposium on Symmetry, Transactions of the Royal Society of Canada |volume=51 |issue=3, section 3 |date=June 1957 |pages=1–13}}</ref> 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 [[Models of the hyperbolic plane|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.<ref name=MathSide /><ref>{{cite web |last=Malkevitch |first=Joseph |title=Mathematics and Art. 4. Mathematical artists and artist mathematicians |url=https://www.ams.org/samplings/feature-column/fcarc-art4 |publisher=American Mathematical Society |access-date=1 September 2015}}</ref>

Escher carefully studied Coxeter's figure, marking it up to analyse the successively smaller circles{{efn|Schattschneider 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."<ref name=MathSide />}} 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".<ref name=MathSide /> Among the results were the series of wood engravings ''Circle Limit I–IV''.{{efn|See [[Circle Limit III]] article for image.}}<ref name=MathSide /> In 1959, Coxeter published his finding that these works were extraordinarily accurate: "Escher got it absolutely right to the millimeter".<ref name=StAndrewsCoxeter>{{MacTutor|title=Maurits Cornelius Escher|id=Escher|mode=cs1}} which cites {{cite book |author=Schattschneider, D. |contribution=Escher: A mathematician in spite of himself |title=The Lighter Side of Mathematics |editor1=Guy, R. K. |editor2=Woodrow, R. E. |publisher=The Mathematical Association of America | location=Washington |year=1994 |pages=91–100}}</ref>

== Legacy ==

[[File:Gevel Escher in Het Paleis 300 dpi.jpg|thumb|The [[Escher Museum]] in [[The Hague]]. The poster shows a detail from ''[[Day and Night (M. C. Escher)|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.{{efn|In 1969, Escher's business advisor, Jan W. Vermeulen, author of a biography on the artist, established the M.C. Escher Foundation, and transferred into this entity virtually all of Escher's unique work as well as hundreds of his original prints. These works were lent by the Foundation to the Hague Museum. Upon Escher's death, his three sons dissolved the Foundation, and they became partners in the ownership of the art works. In 1980, this holding was sold to an American art dealer and the Hague Museum. The Museum obtained all of the documentation and the smaller portion of the art works. The copyrights remained the possession of Escher's three sons&nbsp;– who later sold them to Cordon Art, a Dutch company. Control was subsequently transferred to The M.C. Escher Company B.V. of Baarn, Netherlands, which licenses use of the copyrights on all of Escher's art and on his spoken and written text. A related entity, the M.C. Escher Foundation of Baarn, promotes Escher's work by organizing exhibitions, publishing books and producing films about his life and work.<ref>{{cite web |title=Copyrights&Licensing |url=http://www.mcescher.com/licensing/ |website=M.C. Escher |access-date=2 November 2015 |archive-url=https://web.archive.org/web/20151108203426/http://www.mcescher.com/licensing/ |archive-date=8 November 2015 |url-status=dead }}</ref><ref>{{cite web |title=M.C. Escher Foundation |url=http://www.mcescher.com/foundation/ |website=M.C. Escher |access-date=2 November 2015 |archive-url=https://web.archive.org/web/20151107185518/http://www.mcescher.com/foundation/ |archive-date=7 November 2015 |url-status=dead }}</ref>}}

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<ref>{{Cite web |title=Escher |url=https://www.kunstmuseum.nl/en/collections/escher |access-date=2025-03-11 |website=www.kunstmuseum.nl |language=en}}</ref>); the [[National Gallery of Art]] (Washington, DC);<ref>{{cite web |title=Tour: M.C. Escher — Life and Work |url=https://www.nga.gov/collection/gallery/ggescher/ggescher-main1.html |publisher=National Gallery of Art |access-date=4 November 2015 |archive-url=https://web.archive.org/web/20151223095836/http://www.nga.gov/collection/gallery/ggescher/ggescher-main1.html |archive-date=23 December 2015 |url-status=dead  }}</ref> the [[National Gallery of Canada]] (Ottawa);<ref>{{cite web |title=Collections: M.C. Escher |url=http://www.gallery.ca/en/see/collections/artist.php?iartistid=1655 |publisher=National Gallery of Canada |access-date=4 November 2015 |archive-url=https://web.archive.org/web/20150801122239/http://www.gallery.ca/en/see/collections/artist.php?iartistid=1655 |archive-date=1 August 2015 |url-status=dead }}</ref> the [[Israel Museum]] (Jerusalem);<ref>{{cite web|title=May 2013 (newsletter)|url=http://www.imj.org.il/news/eng/2013/May.html|publisher=Israel Museum Jerusalem|access-date=4 November 2015|archive-url=https://web.archive.org/web/20140705195240/http://www.imj.org.il/news/eng/2013/May.html|archive-date=5 July 2014|url-status=dead}}</ref> and the [[Huis Ten Bosch (theme park)|Huis ten Bosch]] (Nagasaki, Japan).<ref>{{cite web|title=M. C. Escher|url=http://www.huistenbosch.co.jp/event/escher/|publisher=Huis Ten Bosch Museum, Nagasaki|access-date=4 November 2015|language=ja|archive-url=https://web.archive.org/web/20151009075653/http://www.huistenbosch.co.jp/event/escher/|archive-date=9 October 2015|url-status=dead}}</ref>

=== Exhibitions ===

[[File:Escher Poster Dulwich Picture Gallery 2015.jpg|thumb|upright|Poster advertising the first major exhibition of Escher's work in Britain ([[Dulwich Picture Gallery]], 14 October 2015&nbsp;– 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.<ref name=Dulwich/><ref name=NGA/>]]

Despite wide popular interest, Escher was for a long time somewhat neglected in the art world; even in his native Netherlands, he was 70 before a retrospective exhibition was held.<ref name=Poole />{{efn|Steven Poole comments "The artist [Escher] who created some of the most memorable images of the 20th century was never fully embraced by the art world."<ref name=Poole />}} In the twenty-first century, major exhibitions have been held in cities around the world.<ref name=ArtDaily /><ref name=NGAWhatson /><ref name=Treviso /> An exhibition of his work in Rio de Janeiro attracted more than 573,000 visitors in 2011;<ref name=ArtDaily>{{cite web |title=Exhibition of works by Dutch graphic artist M.C. Escher opens at Soestdijk Palace in Baarn |url=http://artdaily.com/index_iphone.asp?int_sec=2&int_new=57170#.VkstP-IvuHg |website=Artdaily |access-date=17 November 2015 |archive-date=19 November 2015 |archive-url=https://web.archive.org/web/20151119165631/http://artdaily.com/index_iphone.asp?int_sec=2&int_new=57170#.VkstP-IvuHg |url-status=dead }}</ref> its daily visitor count of 9,677 made it the most visited museum exhibition of the year, anywhere in the world.<ref>{{cite news |title=Top-attended museum show of 2011 is a surprise; also L.A. numbers |url=http://latimesblogs.latimes.com/culturemonster/2012/03/museum-attendance-2011.html |newspaper=[[Los Angeles Times]] |access-date=18 November 2015 |date=26 March 2013 |quote=The exhibition was ranked No. 1 based on daily visitors. It saw 9,677 visitors a day, according to the Art Newspaper.}}</ref> No major exhibition of Escher's work was held in Britain until 2015, when the [[Scottish National Gallery of Modern Art]] ran one in [[Edinburgh]] from June to September 2015,<ref name=NGAWhatson>{{cite web |title=The Amazing World of M.C. Escher |url=https://www.nationalgalleries.org/whatson/on-now-coming-soon/the-amazing-world-of-m-c-escher/ |publisher=[[National Galleries Scotland]] |access-date=1 November 2015 |archive-url=https://web.archive.org/web/20151118111315/https://www.nationalgalleries.org/whatson/on-now-coming-soon/the-amazing-world-of-m-c-escher/ |archive-date=18 November 2015 |url-status=dead }}</ref> moving in October 2015 to the [[Dulwich Picture Gallery]], London. The exhibition poster is based on ''[[Hand with Reflecting Sphere]]'', 1935, which shows Escher in his house reflected in a handheld sphere, thus illustrating the artist, his interest in [[semiotics|levels of reality]] in art (e.g., is the hand in the foreground more real than the reflected one?), [[perspective (graphical)|perspective]], and [[spherical geometry]].<ref name=NGA>{{cite web |title=M.C. Escher — Life and Work |url=http://www.nga.gov/content/ngaweb/features/slideshows/mc-escher-life-and-work.html#slide_11 |website=The Collection, National Gallery of Art |publisher=National Gallery of Art, Washington |access-date=1 November 2015 |quote=Escher and the interior of his studio in Rome are reflected in the mirrored sphere that he holds in his hand. Escher's preoccupation with mirrored reflections and visual illusion belongs to a tradition of northern European art established in the fifteenth century.}}</ref><ref name=Dulwich>{{cite web |title=The Amazing World of M.C. Escher |url=http://www.dulwichpicturegallery.org.uk/whats-on/exhibitions/2015/october/the-amazing-world-of-m-c-escher/ |publisher=Dulwich Picture Gallery |access-date=1 November 2015 |archive-url=https://web.archive.org/web/20151101033350/http://www.dulwichpicturegallery.org.uk/whats-on/exhibitions/2015/october/the-amazing-world-of-m-c-escher |archive-date=1 November 2015 |url-status=dead }}</ref><ref>{{cite web |title=Hand with Reflecting Sphere, 1935 |url=https://www.nga.gov/collection/gallery/ggescher/ggescher-47949.html |website=The Collection, National Gallery of Art |publisher=National Gallery of Art, Washington |access-date=1 November 2015 |archive-url=https://web.archive.org/web/20151225164242/http://www.nga.gov/collection/gallery/ggescher/ggescher-47949.html |archive-date=25 December 2015 |url-status=dead  }}</ref> The exhibition moved to Italy in 2015–2016, attracting over 500,000 visitors in Rome and Bologna,<ref name=Treviso>{{cite web |title=Escher. Santa Caterina Complex |url=http://www.italytravellerguide.com/evento/paese/treviso-467/escher-2144.aspx |website=Italy Traveller Guide|access-date=17 November 2015 |archive-url=https://web.archive.org/web/20151117134703/http://www.italytravellerguide.com/evento/paese/treviso-467/escher-2144.aspx |archive-date=17 November 2015}}</ref> and then [[Milan]].<ref name=Milan>{{cite web|url=http://www.mostraescher.it|title=Mostra Escher Milano}}</ref><ref>{{cite web |url=http://chiostrodelbramante.it/en/info/escher/ |title=Chiostro del Bramante, Rome |access-date=7 November 2015 |archive-url=https://web.archive.org/web/20141008212757/http://chiostrodelbramante.it/en/info/escher/ |archive-date=8 October 2014 |url-status=dead  }}</ref><ref>{{cite web |url=http://www.gallery.ca/en/see/exhibitions/current/details/m-c-escher-the-mathemagician-8228 |title=Exhibitions: M.C. Escher: The Mathemagician |publisher=[[National Gallery of Canada]] |access-date=7 November 2015 |archive-url=https://web.archive.org/web/20160304052313/http://www.gallery.ca/en/see/exhibitions/current/details/m-c-escher-the-mathemagician-8228 |archive-date=4 March 2016 |url-status=dead }}</ref>

In 2023, the [[Kunstmuseum Den Haag|Kunstmuseum]] in the Hague created a large retrospective of Escher, entitled 'Escher - Other World'.<ref>{{Cite web |date=2022-12-07 |title=Escher - Other World {{!}} Kunstmuseum Den Haag |url=https://www.kunstmuseum.nl/en/exhibitions/escher-other-world |access-date=2025-03-11 |website=www.kunstmuseum.nl |language=en}}</ref>

=== In mathematics and science ===

[[File:Leeuwarden - Tegeltableau Escher.jpg|thumb|Wall tableau of one of Escher's bird tessellations at the [[Princessehof Ceramics Museum]] in Leeuwarden]]

[[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 ([[Dichromatic symmetry|counterchange symmetry or antisymmetry]]); color symmetry (in [[crystallography]]); metamorphosis or [[topology|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 (M. C. Escher)|Print Gallery]]'' by H. Lenstra and B. de Smit.<ref name=MathSide />

The [[Pulitzer Prize]]-winning<ref>{{cite web | url=http://www.pulitzer.org/prize-winners-by-year/1980 | title=The Prizes | year=1980 | publisher=Pulitzer}}</ref> 1979 book ''[[Gödel, Escher, Bach]]'' by [[Douglas Hofstadter]]<ref>{{cite book | last=Hofstadter | first=Douglas R. |author-link=Douglas Hofstadter | title=Gödel, Escher, Bach: An Eternal Golden Braid | publisher=Basic Books | year=1999 | orig-year=1979 | isbn=978-0-465-02656-2 | url=https://archive.org/details/gdelescherbachet00hofs }}</ref> discusses the ideas of self-reference and [[strange loop]]s expressed in Escher's art. The [[asteroid]] [[4444 Escher]] was named in Escher's honor in 1985.<ref name="Schmadel2012">{{cite book |last=Schmadel |first=Lutz D.|title=Dictionary of Minor Planet Names |url=https://books.google.com/books?id=aeAg1X7afOoC&pg=PA359 |year=2012 |publisher=Springer |isbn=978-3-642-29718-2 |page=359}}</ref>

=== In popular culture ===

{{main|M. C. Escher 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|"Mathematical Games" column]] in ''[[Scientific American]]''.<ref>{{cite news |url=http://wordplay.blogs.nytimes.com/2014/10/27/stewart/?_r=0 |title=Ignited by Martin Gardner, Ian Stewart Continues to Illuminate |quote=It was Martin Gardner who was instrumental in spreading the awareness and understanding of Escher’s work |newspaper=[[The New York Times]] |date=27 October 2014 |access-date=2 December 2016 |archive-url=https://web.archive.org/web/20180121184322/https://wordplay.blogs.nytimes.com/2014/10/27/stewart/?_r=0 |archive-date=21 January 2018 |url-status=dead }}</ref>  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<!--sic--> Wild Sanctuary'' with ''Three Worlds''; and [[Mandrake Memorial]]'s 1970 ''Puzzle'' with ''House of Stairs'' and (inside) ''Curl Up''.{{efn|These and further albums are listed by Coulthart.<ref>{{cite web |last1=Coulthart |first1=John |title=MC Escher album covers |url=http://www.johncoulthart.com/feuilleton/2013/02/07/mc-escher-album-covers/ |access-date=2 November 2015 |url-status=live |archive-url=https://web.archive.org/web/20130217035851/http://www.johncoulthart.com/feuilleton/2013/02/07/mc-escher-album-covers/ |archive-date=17 February 2013|date=7 February 2013 }}</ref>}} His works have similarly been used on many book covers, including some editions of [[Edwin Abbott Abbott|Edwin Abbott]]'s ''Flatland'', which used ''Three Spheres''; [[Ernst Gombrich|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''.{{efn|These and further books are listed by Bailey.<ref>{{cite web |last1=Bailey |first1=David |title=M. C. Escher Miscellany |url=http://www.tess-elation.co.uk/m-c-escher-miscellany |url-status=live |archive-url=https://web.archive.org/web/20170508182728/http://www.tess-elation.co.uk/m-c-escher-miscellany |archive-date=8 May 2017}}</ref>}} The "World of Escher" markets [[poster]]s, [[necktie]]s, [[T-shirt]]s, and [[jigsaw puzzle]]s of Escher's artworks.<ref>{{cite news|title=M.C. Escher: An Artist for the Web|url=https://www.nytimes.com/2000/09/28/technology/28ESCH.html|newspaper=The New York Times|access-date=7 November 2015|date=28 September 2000}}</ref> Both Austria and the Netherlands have issued [[postage stamp]]s commemorating the artist and his works.<ref name="hathaway1972" />

== See also ==

* [[Escher sentence]]s, named after works like ''Ascending and Descending''
* [[Oscar Reutersvärd]]
* [[Victor Vasarely]]{{-}}

== Notes ==

{{notelist}}

== References ==

{{reflist|28em}}

== Further reading ==

=== Books ===

* {{cite book |author1=Ernst, Bruno |author2=Escher, M. C. |year=1995 |title=The Magic Mirror of M. C. Escher |publisher=Taschen America |isbn=978-1-886155-00-8 |ref=none}}
* {{cite book |author=Escher, M. C. |year=1971 |title=The Graphic Work of M. C. Escher |publisher=Ballantine  |ref=none}}
* {{cite book |author=Escher, M. C. |year=1989 |title= Escher on Escher: Exploring the Infinite|publisher=Harry N. Abrams |isbn=0-8109-2414-5 |ref=none}}
* {{cite book |last=Locher |first=J. L. |year=1971 |title=The World of M. C. Escher |publisher=[[Abrams Books|Abrams]] |isbn=0-451-79961-5<!--from rear cover-->}}
* {{cite book |author=Locher, J. L. |year=1981 |title=M. C. Escher: His Life and Complete Graphic Work |publisher=Abrams |isbn=978-0-8109-8113-3  |ref=none}}
* {{cite book |last=Locher |first=J. L. |title=The Magic of M. C. Escher |date=2006 |publisher=Thames & Hudson |isbn=978-0-500-51289-0 |ref=none}}
* {{cite book |author1=Schattschneider, Doris |author1-link=Doris Schattschneider |author2=Walker, Wallace |year=1987 |title=M. C. Escher Kaleidocycles |url=https://archive.org/details/mcescherkaleidoc00scha |url-access=registration |publisher=[[Pomegranate (publisher)|Pomegranate Communications]] |isbn=978-0-906212-28-8 |ref=none}}
* {{cite book |author=Schattschneider, Doris |year=2004 |title=M. C. Escher : Visions of Symmetry |url=https://archive.org/details/mceschervisionso0000scha |url-access=registration |publisher=Abrams |isbn=978-0-8109-4308-7 |ref=none}}
* {{cite book |editor=Schattschneider, Doris |editor2=Emmer, Michele |year=2003 |title=M. C. Escher's Legacy: a Centennial Celebration |url=https://archive.org/details/springer_10.1007-3-540-28849-X |publisher=Springer-Verlag |isbn=978-3-540-42458-1 |ref=none}}

=== Media ===

* Escher, M. C. ''The Fantastic World of M. C. Escher'', Video collection of examples of the development of his art, and interviews, Director, Michele Emmer.
* Phoenix Films & Video  ''[https://archive.org/details/adventuresinperception Adventures in Perception (1973)]''

== External links ==
{{Spoken Wikipedia |M. C. Escher.oga |date=8 May 2014}}
{{Sister project links |wikt=no |commons=Category:Maurits Cornelis Escher |b=no |n=no |q=M. C. Escher  |s=no |v=no |voy=no |species=no |d=no}}

* {{Official website}}
* {{cite web |url=http://mathcs.slu.edu/escher |archive-url=https://archive.today/20130419072917/http://mathcs.slu.edu/escher |url-status=dead |archive-date=19 April 2013 |title=Math and the Art of M.C. Escher |publisher=SLU }}
* {{cite book |url=https://www.ams.org/notices/200304/fea-escher.pdf |title=Artful Mathematics: The Heritage of M. C. Escher |publisher=AMS}}
* {{cite book |url=http://www.cgl.uwaterloo.ca/~csk/projects/escherization/ |title=Escherization problem and its solution |publisher=University of Waterloo |access-date=24 July 2005 |archive-date=27 January 2016 |archive-url=https://web.archive.org/web/20160127040921/http://www.cgl.uwaterloo.ca/~csk/projects/escherization/ |url-status=dead }}
* {{cite web |url=https://www.cs.technion.ac.il/~gershon/EscherForReal/ |title=Escher for Real |publisher=Technion |url-status=dead |archive-url=https://web.archive.org/web/20080120055138/https://www.cs.technion.ac.il/~gershon/EscherForReal/ |archive-date=20 January 2008}} — physical replicas of some of Escher's "impossible" designs
* {{cite web |url=http://www.nga.gov/collection/gallery/ggescher/ggescher-main1.html |publisher=NGA |title=M.C. Escher: Life and Work |url-status=dead |archive-url=https://web.archive.org/web/20090803124602/http://www.nga.gov/collection/gallery/ggescher/ggescher-main1.html |archive-date=3 August 2009 }}
* {{cite web |url=http://www.artquest.org.uk/articles/view/us-copyright-protection-for-uk-artists1 |title=US Copyright Protection for UK Artists |access-date=3 November 2011 |archive-url=https://web.archive.org/web/20111019103212/http://www.artquest.org.uk/articles/view/us-copyright-protection-for-uk-artists1 |archive-date=19 October 2011 |url-status=dead }} Copyright issue regarding Escher from the Artquest Artlaw archive.
*[https://www.gallery.ca/library/ngc010.html M. C. Escher Correspondence] at the [[National Gallery of Canada]], Ottawa, Ontario.

{{M. C. Escher}}
{{Mathematical art}}

{{Authority control (arts)}}

{{DEFAULTSORT:Escher, M. C.}}
[[Category:M. C. Escher| ]]
[[Category:1898 births]]
[[Category:1972 deaths]]
[[Category:Burials in Utrecht (province)]]
[[Category:Delft University of Technology alumni]]
[[Category:Dutch draughtsmen]]
[[Category:Dutch illustrators]]
[[Category:Dutch graphic artists]]
[[Category:Dutch male artists]]
[[Category:Dutch printmakers]]
[[Category:Dutch stamp designers]]
[[Category:Dutch wood engravers]]
[[Category:Mathematical artists]]
[[Category:Modern printmakers]]
[[Category:Officers of the Order of Orange-Nassau]]
[[Category:Artists from Leeuwarden]]
[[Category:People from Château-d'Œx]]
[[Category:20th-century Dutch engravers]]