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Matematik Seçkileri
Sayılar Teorisi
Ziyaretçi defteri

Maurits Cornelius Escher

Born: 17 June 1898 in Leeuwarden, Netherlands
Died: 27 March 1972 in Laren, Netherlands

Maurits Escher was always referred to by his parents as Mauk. He was brought up by his father, George Escher, who was a civil engineer, and his second wife Sarah who was the daughter of a government minister. He lived with his four older brothers, Arnold, Johan, Berend, and Edmond. Maurits attended both elementary and secondary school in Arnhem between 1912 and 1918, where he failed to shine in many of his subjects, but exhibited an early interest in both music and carpentry.

People expressed the opinion that he possessed a mathematical brain but he never excelled in the subject at any stage during his schooling and treated the subject with some considerable unease. He wrote [7]:-

At high school in Arnhem, I was extremely poor at arithmetic and algebra because I had, and still have, great difficulty with the abstractions of numbers and letters. When, later, in stereometry [solid geometry], an appeal was made to my imagination, it went a bit better, but in school I never excelled in that subject. But our path through life can take strange turns.

Early reports detailed his methodological approach to life which was taken to be an unconscious reaction to his engineering family upbringing. As a child, Maurits always had an intensely creative side and an 'acute sense of wonder'. He often claimed to see shapes that he could relate to in the clouds.

Maurits, and his good friend Bas Kist both developed a deep interest in printing techniques as a consequence of receiving good reports from their respective art departments who had encouraged their student to experiment.

Family aspirations that Maurits would train as an architect were disappointed when he failed his final exams in history, constitutional organisations, political economies and book keeping, and as a result he never officially graduated. His family moved to Oosterbeek where a loophole in Dutch law allowed Maurits to enrol at the Higher Technical School in Delft (1918-1919) and thus allowed him to repeat some of the subjects he had failed. Unable and unwilling to catch up following poor health, Maurits decided to concentrate on his drawing and his woodcut techniques. He was influenced and initially trained by R N Roland Holst:-

He strongly advised me to do some woodcuts, and I immediately followed his advice ... It is wonderful work but far more difficult than working with linoleum.

In September 1920 Maurits moved to Haarlem in a final attempt to try follow his father's wish that he study architecture and he enrolled at the School for Architecture and Decorative Arts. A chance meeting with Samuel Jesserum de Mesquita, a graphic arts teacher, proved a landmark event in Escher's life and he became convinced that a graphic arts programme would be better suited to his skills. De Mesquita taught the eager Escher all he knew of woodcut printing techniques, gave him space to experiment, and encouraged him to experiment widely in order to develop his skills.

Escher was regularly heard to complain about his lack of natural drawing ability and as a result most of his pieces took a long time to complete, and required numerous attempts before he was completely happy. In his youth he concentrated on landscapes, many of which were drawn from unusual perspectives. He also made numerous sketches of plants and even insects, all of which regularly appear in his later work.

Travelling took up a large part of Escher's life from this point on. He made a trip with two friends to Florence in April 1922 and spent the whole time sketching and drinking. Escher then spent a further month travelling alone around Italy gathering material to use in his experimental woodcuts.

During his early drawing career Escher touched only briefly on the subject of 'filling the plane', signs of which had been visible from an early age. Many years later a lady [7]:-

... remembered the care with which this little boy [Escher] had selected the shape, quantity and size of his slices of cheese, so that, fitted one against the other, they would cover as exactly as possible the entire slice of bread. This particular trait never left him ...

His first work featuring regular division of the plane was named Eight Heads, and was completed in 1922.

Escher visited Spain in June 1922, making the voyage on a sea freighter, and there his interest in regular division was briefly revitalised. He travelled widely and visited many palaces and was inspired by a great number of both buildings and landscapes. One building which was to have an immense influence on his life was the Alhambra Palace in Grenada.

Escher was overwhelmed by the beauty of the 14th century Moorish palace and in particular, by the decorative majolica tilings which decorated many of the surfaces of the building. Unlike the Moors, Escher was both keen and permitted to use recognisable objects in his ad-hoc versions of the tilings. He made a number of attempts at using this style of artwork over the next couple of years but was unhappy about both the length of time this passion was taking (due to its trial and error nature) and the poor quality of his final work, and he left aside regular division for a number of years. We wrote that, in about 1924, [7]:-

... for the first time I printed on a cloth a single animal motif cut out of wood which repeats itself according to a certain system, thereby adhering to the principle that no blank spaces may occur. I needed at least three colours; with each in turn I rolled my stamping block in order to contrast one motif with its adjoining congruent repetitions. I exhibited this cloth together with my other work, but I did not have any success with it.

Following his return from Spain, Escher went to live in Italy. Again he travelled widely and in 1923, whilst staying in the town of Ravello, he met his future wife Jetta Umiker. They married on 12 June 1924 and made their home in Frascati, just outside Rome. They would have three children, George (born 23 June 1926 in Frascati), then Arthur (born 8 December 1928) and Jan (born 6 March 1938).

Escher with his family took frequent holidays around Italy during the next decade. Years of sketching Italian landscapes, usually with impossible perspectives, followed before the family were forced to leave Italy as a result of the Fascist political uprising which developed in Italy during the summer months of 1935. They moved to the mountain village of Chateau-d'Oex in Switzerland but Jetta missed Italy and the high Swiss prices forced Escher to sell more prints.

The family was unhappy at first in their new surroundings and, lacking inspiration for his work, Maurits and Jetta set out on a Mediterranean excursion. Escher managed to negotiate a deal with the Adria Shipping Company which gave free passage and meals for himself and also a one way ticket for Jetta. He made payment with prints which he completed using sketches made on the journey. The trip began on the 26 April 1936, and during the next two months the pair made volumes of sketches from which to work from in the future.

Escher's fascination with order and symmetry took over his life after this Mediterranean journey in 1936 after he made his second visit to the Alhambra. Escher remarked that it was [7]:-

...the richest source of inspiration I have ever tapped.

Escher and his wife spent days on end working at the Alhambra Palace, where they sketched as much as they could, much to the amusement of the numerous tourists who visited each day. These sketches were to become a fundamental source for much of Escher's future work. After this trip Escher became obsessed with the concept of regular division of the plane. He wrote [7]:-

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.

Escher felt that he could improve upon the work of the Moorish artists and used his sketches as a geometric grid from which to design his own characters to fill the plane. He experimented with many different motifs such as birds, weightlifters and lions, all of which appear in many of his early designs. All of his work during this time period relied heavily on his own imagination along with his Spanish sketches, and was immensely time consuming.

In October 1937 Escher showed some of his new work to his brother Berend, by then a professor of geology at Leiden University, when both were visiting their parents home in The Hague. Recognising the connection between his brother's woodcuts and crystallography, Berend sent his brother a list of articles that he felt would be of assistance. This was Escher's first contact with mathematics.

Escher read Pólya's 1924 paper on plane symmetry groups. Although he did not understand the abstract concept of groups discussed in Pólya's paper he did understand the 17 plane symmetry groups described there. He subsequently taught himself the principles by which each of the 17 groups operated. Between 1937 and 1941 Escher worked on possible periodic tilings producing 43 coloured drawings with a wide variety of symmetry types. He adopted a highly mathematical approach with a systematic study using notation which he invented himself. Escher also studied an article written by F Haag in 1923 and he eventually challenged some of the views expressed in the literature following further research into the topic.

Near the end of 1937 the Escher family moved to Belgium which became their home until the 20 February 1941 when the invading German army forced them to flee to Baarn in Holland. World War II was a deeply emotional time for Escher and prevented him from concentrating on his work.

Over the years that followed Escher made numerous woodcuts utilising each of the 17 symmetry groups. With practice his skills naturally improved and as a result he could design and complete each piece far quicker than in his earlier years. His art formed an integral part of family life, and Escher would work in his study between 8 am and 4 pm every day. New concepts could take months or even years to come to fruition before the finished work was discussed and explained to the family. One of his children wrote [7]:-

The end of the cycle, making the first print, gave father a mixture of joy and sadness. It was exciting and satisfying to lift the paper from the inked wood for the first time, to see the finished print, crisp and immaculate, gradually appearing around the edge of the paper as it was carefully raised. But father had always a feeling of disappointment, of not having been able to depict adequately his thoughts. After all his efforts, how far short of the originally so lucid and misleading simple idea did this result fall!

Extensive research and investigation culminated in 1941 with his first notebook Regular Division of the plane with Asymmetric congruent Polygons. This notebook was extended and improved over the course of the following year, when the results obtained from extensive colour based division investigations were included. These books were never meant for publication - only for background information to allow him to continue as a visionary artist.

The notebooks were evidence of the fact that Escher had become a research mathematician of the highest order, regardless of his personal feeling of mathematical insecurity. He had developed his own categorisation system which covered all the possible combinations of shape, colour and symmetrical properties. As such he had unknowingly studied areas of crystallography years in advance of any professional mathematician working in this field. He wrote [7]:-

A long time ago, I chanced upon this domain [of regular division of the plane] in one of my wanderings... However, on the other side I landed in a wilderness.... I came to the open gate of mathematics. Sometimes I think I have covered the whole area ... and then I suddenly discover a new path and experience fresh delights.

Escher was inundated with requests to give lectures all over the world. In a lecture in 1953 Escher said [3]:-

... I have often felt closer to people who work scientifically (though I certainly do not do so myself) than to my fellow artists.

By around 1956 Escher's interests changed again taking regular division of the plane to the next level by representing infinity on a fixed 2-dimensional plane. Earlier in his career he had used the concept of a closed loop to try to express infinity as demonstrated in Horseman.

He had put his designs on to a variety of three-dimensional objects such as columns and spheres during the 1940s, again in an attempt to impart an endless perspective to his work. He later tried working with the concept of similarities, using identical motifs of diminishing size, arranged in a series of concentric circles, but as with much of his work, he was unhappy about the final quality.

In 1958 Escher met Coxeter and they became life-long friends. Escher came across an article written by Coxeter, and again whilst unable to understand the text, he was able to determine the rules regarding hyperbolic tessellations using only the diagrams in the paper. Escher paid thanks to Coxeter by sending him a copy of one of his new works Circle Limit I. Escher continued to develop and enhance this field and produced many more prints using both circles and squares as the frames for his works.

This style of artwork required enormous dedication because of the careful planning and trial sketches required, coupled with the necessary hand and carving skill, but was an enormous source of satisfaction to Escher. He wrote [7]:-

I discovered once again that the human hand is capable of executing small and yet completely controlled movements, on the condition that the eye sees sufficiently clearly what the hand is doing.

In 1995 Coxeter published a paper which proved that Escher had achieved mathematical perfection in one of his etchings. Circle Limit III was created using only simple drawing instruments and Escher's great intuition, but Coxeter proved that [8]:-

... [Escher] got it absolutely right to the millimetre, absolutely to the millimetre .... Unfortunately he didn't live long enough to see my mathematical vindication.


This proof serves to highlight Escher's amazing natural ability of being able to combine both his artistic skills and the techniques that he learned from others, into mathematically perfect designs.

By 1958 Escher had achieved remarkable fame. He continued to give lectures and correspond with people who were eager to learn from him. He had given his first important exhibition of his works and had also been featured in Time magazine. Escher received numerous awards over his career including the Knighthood of the Oranje Nassau (1955) and was regularly commissioned to design art for dignitaries around the world.

In 1958 he published Regular Division of the Plane and in this work he says:-

At first I had no idea at all of the possibility of systematically building up my figures. I did not know ... this was possible for someone untrained in mathematics, and especially as a result of my putting forward my own layman's theory, which forced me to think through the possibilities.

Again in Regular Division of the Plane Escher writes:-

In mathematical quarters, the regular division of the plane has been considered theoretically. ... [Mathematicians] have opened the gate leading to an extensive domain, but they have not entered this domain themselves. By their very nature they are more interested in the way in which the gate is opened than in the garden lying behind it.

Escher's work covered a variety of subjects throughout his life. His early love of portraits, Roman and Italian landscapes and of nature, eventually gave way to regular division of the plane. Many of his pieces were drawn from unusual perspectives thus creating enigmatic spatial effects. He was skilled in the art of a number of different printing techniques such as woodcuts, lithographs and mezzotints. Over 150 colourful and recognisable works testify to Escher's ingenuity and interest in regular division of the plane. He managed to capture the notion of hyperbolic space on a fixed 2-dimensional plane as well as translating the principles of regular division onto a number of 3-dimensional objects such as spheres, columns and cubes. A number of his prints combine both 2 and 3-dimensional images with startling effect as demonstrated for example in Reptiles.

He wrote [7]:-

When an element of plane division suggests to me the form of an animal, I immediately think of a volume. The "flat shape" irritates me - I feel as if I were shouting to my figures, "You are too fictitious for me; you just lie there static and frozen together; do something, come out of there and show me what you are capable of!" So I make them come out of the plane. But do they really do that? On the contrary, I am deliberately inconsistent, suggesting plasticity in the plane by means of light and shadow.

He was fascinated by topology, which only began to be studied during his lifetime, as illustrated by the Möbius strip. In his later years he learned much from the British mathematician Roger Penrose and used this knowledge to design many "impossible" etchings such as Waterfall or Up and down.

Escher used pictures to tell a story in his Metamorphosis series of designs. These designs brought together many of Escher's skills and show the transformation from one distinct object to another, by means of a series of slight changes to a regular pattern in the plane.

Metamorphosis 1 in particular, printed in 1933, yields an insight into the change of artistic style which occurred in Escher's life at this time. An Italian coastline is transformed through a series of convex polygons into a regular pattern in the plane until finally a distinct, coloured, human motif emerges, signifying his change of perspective from landscape work to regular division of the plane.

Escher fell ill initially in 1964 whilst delivering a series of lectures in North America. As a result he was forced to cut down his schedule substantially, later devoting most of his time to correspondence with friends. In [11] his last years are described as follows:-

When Escher's view of the world turned inward he produced his best known puzzling prints. which, art aside, were truly intellectually playful, yet he was not. His life turned inward, he cut himself off and he had few friends. ... He died after a protracted illness...

His final graphic work, a woodcut, Snakes took six months to complete and was finally unveiled in July 1969. This exceptional etching heads off to infinity at both the centre and the edges of the picture. Following further operations Escher moved to the Rosa Spier house in Laren and later died in hospital.


Article by: J J O'Connor and E F Robertson based on a project by Malcolm Raven.

May 2000

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