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Above: Seville, Alcazar, entrance to the Sala de la Justica.
Right: Alhambra tiling depicted by M. C. Escher from The World of Patterns by Brian Wichmann

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Escher Maurits Escher was born in Leeuwarden, Holland in 1898. His father was an architect and his family had hoped that he would follow the same career, but he was not a successful student. However, his talent as an artist was evident from an early age and instead he became a graphic artist with a penchant for simple Mediterranean landscapes. Then, in October 1922, he visited the Alhambra Palace for the first time and was deeply impressed by what he saw.

Recalling that visit twenty years later, he wrote (see 'M.C. Escher, His Life and Complete Graphic Work') “The fitting together of congruent figures whose shapes evoke in the observer an association with an object or a living creature intrigued me increasingly after that first Spanish visit in 1922. And although at the time I was mainly interested in free graphic art, I periodically returned to the mental gymnastics of my puzzles.

In about 1924, I first printed a piece of fabric with a wood block of a single animal motif which is repeated according to a particular system, always bearing in mind the principle that there may not be any 'empty spaces'... I exhibited this piece of printed fabric together with my other work, but it was not successful. This is partly the reason why it was not until 1936, after I had visited the Alhambra a second time, that I spent a large part of my time puzzling with animal shapes.”

It was in 1936 that Escher's direction changed irreversibly. He made his second visit to Granada to see the Alhambra and he moved away from Italy where the subjects of his landscape works had been located. Believing that Northern Europe did not offer the scenes that he wished to paint he was searching for a new focus.

He was fascinated by the tilings and tessellations he found covering every piece of wall space, declaring them to be “the richest source of inspiration that I ever tapped”. After spending many days sketching the tiling patterns, Escher returned to Holland and began to explore the artistic possibilities of tiling and subdividing the plane. His first work was The Alhambra Sketch of 1936 and he believed that his new work was dedicated “to communicating a specific line of thought.

The ideas that are basic to them often bear witness to my amazement and wonder at the laws of nature which operate in the world around us. He who wonders discovers that this is in itself a wonder. By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I had made, I ended up in the domain of mathematics.”

Escher's work passed largely unnoticed until 1956 when his first exhibition was publicised by Time Magazine in the USA. Subsequently, his work has been a continual source of fascination for mathematicians and artists alike. Despite Escher's lack of any formal training in mathematics he managed to appreciate intuitively many of the important geometrical features of two- and three-dimensional surfaces on flat and curved surfaces.

There is probably no mathematics department in the world that lacks an Escher poster.

Text by John Barrow.
 

According to Doris Schattschneider, Escher “struggled for several years to produce animated interlocking designs, with very primitive results”. The key moment for Escher seems to have come through a paper by the Hungarian mathematician George Polya. Schattschneider goes on to say, “In examining Escher's notebooks, this author discovered that he copied in full the paper by G. Polya which outlines the important properties of each of the groups and includes a chart of illustrative designs.” It would appear that this was what allowed Escher's efforts to blossom and so we have an example of mathematics informing art not only in broad outline but in critical structural detail.

From 'Mathematics for the Imagination' by Peter M. Higgins. (OUP, 2002) pp 150 - 151.