M. C. Escher, was a Dutch graphic artist. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints. These feature impossible constructions, explorations of infinity, architecture, and tessellations.
He was a sickly child, and was placed in a special school at the age of seven and failed the second grade. Although he excelled at drawing, his grades were generally poor. Escher attended the Haarlem School of Architecture and Decorative Arts in Haarlem. He briefly studied architecture, but he failed a number of subjects (partly due to a persistent skin infection) and switched to decorative arts.
In 1922, an important year of his life, Escher traveled through Italy (Florence, San Gimignano, Volterra, Siena, Ravello) and Spain (Madrid, Toledo, Granada). He was impressed by the Italian countryside and by the Alhambra, a fourteenth-century Moorish castle in Granada. The intricate decorative designs at Alhambra, which were based on geometrical symmetries featuring interlocking repetitive patterns sculpted into the stone walls and ceilings, were a powerful influence on Escher's works. He returned to Italy regularly in the following years. When the political climate in Italy (under Mussolini) became unacceptable to Escher, he decided to move in Switzerland along with the family, but he was decidedly unhappy since he had been very fond of and inspired by the landscapes in Italy.
Maybe you know Escher for this famous work called " Ascending and Descending, in which lines of people ascend and descend stairs in an infinite loop, on a construction which is impossible to build and possible to draw only by taking advantage of quirks of perception and perspective.
Although Escher did not have mathematical training—his understanding of mathematics was largely visual and intuitive—Escher's work had a strong mathematical component, and more than a few of the worlds which he drew were built around impossible objects such as the Penrose triangle and the Penrose stairs.
His first study of mathematics, which later led to its incorporation into his art works, began with George Pólya's academic paper on planesymmetry groups sent to him by his brother Berend. This paper inspired him to learn the concept of the 17 wallpaper groups (plane symmetry groups). Using this mathematical concept, Escher created periodic tilings with 43 colored drawings of different types of symmetry.
Around 1956, Escher explored the concept of representing infinity on a two-dimensional plane. Discussions with Canadian mathematician H.S.M. Coxeter inspired Escher's interest in hyperbolic tessellations.
Overall, his early love of Roman and Italian landscapes and of nature led to his interest in the concept of regular division of a plane, which he applied in over 150 colored works. Other mathematical principles evidenced in his works include the superposition of a hyperbolic plane on a fixed 2-dimensional plane, and the incorporation of three-dimensional objects such as spheres, columns and cubes into his works.