There are works of art –in music, films, or paintings– that only a few can unravel and understand. These works resemble convoluted puzzles and each piece is a unique element that shines a light on the underlining meaning. Da Vinci or Dalí, for example, didn’t only create beautiful and extravagant pieces, but also their paintings were based on mathematical and symmetrical principles. Besides them, there are other artists whose paintings are almost indecipherable puzzles. Escher is usually associated to the field of mathematics, while Magritte to semiotics.
Take a look at these masters and the complexity of their work.
Leonardo da Vinci
The Renaissance genius excelled in many disciplines besides art. He devoted himself to the study of the human anatomy, as well as other subjects such as aerodynamics, hydraulics, botanicals, architecture, anatomy, among others. He applied maths and geometry into his works and experiments, but where he really stood out was in painting, becoming one of the most representative artists of his time.
For example, he painted The Last Supper following the basic principles of symmetry and perspective. Jesus appears at the center of the painting, and from his position, one could trace two imaginary lines that create a pyramid where the other elements of the image appear. The apostles are positioned in two of the thirds that divide the image.
In the same way, The Mona Lisa was created under the same principle. It was composed following the “rule of thirds.” Her face is situated in the middle of one of the thirds while her right eye –the first thing one notices– and her hand are located over one of the intersection points. The “golden ratio” starts also in her right eye and finishes in her hands. If we cut out her face, the symmetry, the rule of thirds, and the golden ratio would still be there.
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René Magritte
This Belgian painter based his work on the oneiric. The first phase of his artistic life was influenced by the work of Giorgio De Chirico, so it has futuristic and rational elements included. The second phase was more related to surrealism, an artistic trend of his time. As a result of this combination, Magritte developed a unique style in which he introduced symbols representing the dreamscape.
In Magritte’s work, the puzzles belong to the conceptual field instead of da Vinci’s use of geometry. Despite this, the painter thought spectators would form their own analysis based on their own perspectives and contexts. He portrayed his dreams or the things he imagined so that, later on, spectators would read it using their own imagination.
Magritte inserted language into his pieces; he used metaphors, hyperboles, and other figures of speech to add layers of mystery and depth to his paintings. His work aims to make spectators question their preconceived ideas about life and art.
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Georges Seurat
When he was still very young, Seurat started working at Pablo Lehmann’s workshop, where he learned some techniques about light and color that later on he would apply in his work. He became an expert in impressionism and later on revolutionized it by creating neo-impressionism.
He was a pioneer in pointillism, a technique based on the use of small dots and primary colors to create different perspectives and color intensities. His work was so groundbreaking that even many composers transferred his principles into the field of music. Just as with paintings, listeners would recognize basic, separated sounds, but once they were together, they would perceive intense melodies.
Seurat used the golden radio to create lines and geometrical shapes. Inspired by cubism, he created distorted versions of society, endowed with his own emotions.
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Salvador Dalí
The eccentric Spanish painter was so influenced by surrealism that he soon became its most important representative. Dalí didn’t have a set esthetic ideology, on the contrary, his vision would wander across many art rules and movements, creating a symbolic, dream-like universe. This is now called the “paranoiac-critical method.”
This method consists of a game of words related to jokes, dreams, and paranoia. Dalí’s paintings insert conventional images into abstract settings, which represent the irrational, as Freud termed it.
With this method, Dalí proved that nonsensical figures are not indispensable to represent the irrational. Actually, through common images recognized by the mind you can create visual games capable of distorting perception.
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Maurits Cornelis Escher
Escher’s paintings and drawings became extremely popular within the international mathematic community despite the fact that the Dutch artist always said he was not an expert on the subject. He only depicted what his imagination dictated and, as strange as this may seem, it was always related to mathematics and geometry. Optical illusions became essential to his work, and he created many symmetrical mosaics.
His symmetric images broke all the rules written by Euclid, father of geometry. Using the basic principles of geometry, he created tridimensional images that distorted conventional perspectives.
Another mathematical element used by Escher was the “Moebius strip”: a half-twisted paper strip with united ends. This is a game of perception, since it would seem like we’re looking at both sides of the strip at the same time.
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Translated by María Isabel Carrasco Cara Chards
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