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.

Maurits Cornelis[a] Escher was born on 17 June 1898 in Leeuwarden, Friesland, the Netherlands, in a house that forms part of the Princessehof Ceramics Museum today.

[5] In 1922, an important year of his life, Escher traveled through Italy, visiting Florence, San Gimignano, Volterra, Siena, and Ravello.

The intricate decorative designs of the Alhambra, based on geometrical 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.

Escher and Jetta later had two more sons – Arthur and Jan.[2][3] 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.

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:[5] 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.

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.

When his eldest son, George, was forced at the age of nine to wear a Ballila uniform in school, the family left Italy and moved to Château-d'Œx, Switzerland, where they remained for two years.

[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.

[26][27] 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.

[32] 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.

[33] His first study of mathematics began with papers by George Pólya[34] and by the crystallographer Friedrich Haag[35] on plane symmetry groups, sent to him by his brother Berend, a geologist.

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 (1961).

[f][40][41][42][43] 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",[44] peopled with "jesters, knaves, and contemplators".

[44] Thus, Escher not only was interested in possible or impossible geometry but was, in his own words, a "reality enthusiast";[44] he combined "formal astonishment with a vivid and idiosyncratic vision".

[9] Escher's interest in curvilinear perspective was encouraged by his friend and "kindred spirit",[47] the art historian and artist Albert Flocon, in another example of constructive mutual influence.

Flocon identified Escher as a "thinking artist"[47] alongside Piero della Francesca, Leonardo da Vinci, Albrecht Dürer, Wenzel Jamnitzer, Abraham Bosse, Girard Desargues, and Père Nicon.

[49]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.

[g] 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.

[44]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.

[62] 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.

[74] 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.

[75] 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.

[l] 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.