The eccentric engineer: M.C. Escher’s mathematical arty adventures

Maurits Cornelis (M.C.) Escher, known as ‘Mauk’ to his friends, grew up in an engineering family in the Netherlands. His father George was a well-respected civil engineer who had travelled to Japan to oversee the restoration of the Yodo river and the building of the Mikuni harbour.

His mother was the daughter of a government minister who had fulfilled George’s eccentric requirements for marriage, fulfilling the equation v = 1/2m + 10, where v was the age of the woman and m the age of the husband.

Mauk himself wanted to be an architect but wasn’t a healthy child and fell behind in school. Having failed his second grade, he was sent to the Technical College of Delft and then managed to secure a place at the Haarlem school of Architecture and Decorative Arts.

In Haarlem, Mauk found his real love, drawing and making woodcuts, and he switched to decorative arts. After graduating in 1922, he set out on a tour through Italy and Spain, sketching the countryside as he went. It was on this trip that he first visited the Moorish place of the Alhambra in Granada, a place that would change his life.

However, for now it was the clear Italian light that attracted Mauk, along with a young Swiss Italophile, Jetta Umiker, whom he married in 1924, setting up home with her in Rome.

Yet all was not well in Italy, with the rise of Mussolini, and when Mauk’s son was forced to wear a fascist youth uniform to school he decided to move the family, first to his wife’s home of Switzerland and then on to Brussels in 1937.

By the time he arrived, his whole artistic direction had changed. The year before, he had persuaded the Adria shipping line to give him and Jetta free passage to Spain in return for prints of the sketches he made on the voyage and, to his enormous surprise, they accepted.

He returned to the Alhambra to marvel at the intricately tessellated tiles that decorated the interiors, which they both sketched continuously for three days. As he later wrote, it was “the richest source of inspiration I have ever tapped”. Further tiling treasures awaited at the ancient mosque in Córdoba and with that everything changed.

Mauk, or M. C. Escher as he is more commonly known to us now, began experimenting with unusual tessellations, often featuring animals and birds, all intricately drawn and printed. From now on his travels were over; he had his inspiration.

At this point a fortunate meeting with his brother, geologist Berend Escher, led Escher to mathematics. Berend noticed the connection between Escher’s tessellated woodcuts and crystallography, so sent him Pólya’s 1924 paper on plane symmetry groups. Although the maths seemed beyond him, he drew his way to an understanding of this complex mathematical concept.

With the German invasion of Belgium in 1941, Escher and his family moved to Baarn in the Netherlands, where he would spend most of the rest of his life. Here under the cold, wet skies of Northern Europe he began exploring the bright uplands of geometry: “A long time ago, I chanced upon this domain 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.”

Soon Escher was in demand as a speaker, not among artists, but among mathematicians. By 1956, he was experimenting with representing infinities on a two-dimensional plane, working on hyperbolic tessellations described by his friend, the mathematician Harold Coxeter. Correspondence with leaders in the new field of topology, particularly Roger Penrose, led to further explorations of space, inspired by his fascination with the Möbius strip.

It is perhaps from these etchings that we know him best, and there can be few engineers who have not at some point had an Escher drawing on their wall.

Yet for all his mathematical renown, Escher was not lauded by the art establishment, his first retrospective only occurring three years before his death. Indeed, his first exhibition in 1954 at Amsterdam’s Stedelijk Museum was only organised on the initiative of the International Mathematical Congress then meeting in the city.

Perhaps he will always be the mathematicians’ artist and while his works now command huge premiums, he would undoubtedly be happier with his old friend Coxeter’s 1995 proof of the mathematical perfection of one of his etchings (Circle Limit III) rather than the plaudits of the art establishment.