After a conversation with Hans de Rijk, the friend of the artist and author of the book The magic mirror of M.C. If the art gallery where the young man is standing is reproduced again inside the painting, the same thing should happen within the white blob. To decipher it, Professor Lenstra identified what is known as the Droste effect, named in honour of a famous advertising image of Dutch chocolate. In the lithograph, Escher defies the laws of perspective by creating an infinite and distorted repetition for which he had neither the means nor the calculations to complete. This intersection between mathematics and the arts crystallizes in Print Gallery. Intersection between mathematics and the arts From that time on, the dialogue that he maintained with mathematicians and crystallographers was a source of inspiration for his impossible compositions, his optical illusions and his representations of infinity. In 1954, some of his engravings were exhibited at the International Congress of Mathematicians in Amsterdam.
In the next phase, his compositions began to explore errors of perspective in structures that, at first glance, seemed plausible, but upon closer inspection were impossible to create in reality. From these scientific investigations -of which the artist himself acknowledged that he did not understand all concepts- Escher developed a knowledge of mathematics largely visual and intuitive. Coxeter: Crystal Symmetry and Its Generalizations.
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The solution of how to carry out these compositions was found in the mathematical article by H.S.M. Later on, Escher wondered if it would be possible to go a step further and fill the image with figures that, while keeping their shape and remaining fastened to each other, would change in size in a regular way. Escher reflected in his “Hand with Reflecting Sphere”. Dozens of his engravings are filled with repetitions of animated figures whose spaces create new shapes.
The Dutchman was so interested in concepts such as tessellation and the regular division of the plane -which he discovered in 1936 at the Alhambra in Granada, where he spent days carefully copying the geometric designs that decorate the palace- that they would become a central element of his work.
Despite this theoretical deficiency, mathematics and geometry are key elements of his work. He began studying architecture, but left to focus on his career as a graphic artist. Maurits Cornelis Escher was never an outstanding student and his formal mathematical knowledge was limited to what he received in secondary school.
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“More generally, I also wondered what the structure is behind the picture: how would I, as a mathematician, make a picture like that?” The answer to these questions did not come during the hours of the flight, so Lenstra decided to embark on a two-year investigation, in which he discovered that unravelling the empty patch of Print Gallery was also to decipher Escher himself. “I wondered whether if you continue the lines inward, if there’s a mathematical problem that cannot be solved?” he explained in an interview with The New York Times. Lenstra took advantage of the trip to try to find the solution to the centre of the puzzle. The first time that Professor Hendrik Lenstra came across Escher’s lithograph was in the inflight magazine on a flight from San Francisco to Amsterdam. Almost fifty years would pass before a mathematician from the University of Leiden in Holland would manage to complete the work. The impact of the work would be perfect were it not for the white circular patch in the centre of the image, between the Mediterranean-style buildings and the gallery windows, a blank spot onto which Escher stamped his signature. Escher also distorts this endless repetition, which bulges and twists, acquiring impossible shapes. This infinite composition called Print Gallery is from the Dutch artist M. Among the buildings in the painting appears the art gallery in which the young man is standing, with the youth again looking at a picture of that same Mediterranean quay, in which, once again, the buildings appear with the art gallery and the young man. A young man inside an art gallery is gazing at a picture of the seaport of Senglea, Malta.
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