The enduring enigmas of Albrecht Dürer’s ‘Melencolia I’

That’s Maths: The engraving is filled with symbols that show the artist’s interest in maths

Melencolia I by Albrecht Dürer: behind the main figure is a four-by-four grid. This is the first occurrence in western art of a magic square

Albrecht Dürer, a master painter and engraver of the German Renaissance, made his Melencolia I in 1514, just over five centuries ago. It is one of the most brilliant engravings of all time, and among the most intensively debated works of art.

The winged figure, Melancholy, sits in a mood of lassitude and brooding dejection, weighed down by intellectual cares. Her head rests on her left hand while her right hand holds a mathematical compass, one of many symbols and motifs in the work that reflect Dürer’s interest in mathematics. This allegorical work is full of enigmas. It might depict Melancholy as the inevitable counterpart of creativity. Some art experts have described it as a spiritual self-portrait of Dürer.

The artists of the early Renaissance strove to understand the natural world that they were depicting. With the primitive state of science, they were driven to develop knowledge of anatomy, geometry and optics. Indeed, some profound scientific advances were initiated by the investigations of visual artists.

Dürer was conversant with the principles of perspective; this is clear from St Jerome in His Study, an engraving made in the same year as Melencolia.

He wrote The Painter’s Manual to guide young artists in the geometric principles underlying representational art.

Behind the main figure is a four-by-four grid, with the first 16 counting numbers. Each row and each column sums to 34, as do the diagonals. This is the first occurrence in western art of a magic square.

It has many other interesting mathematical symmetries. A curious aspect of the square is the appearance of the numbers 15 and 14 in the centre cells of the bottom row, corresponding to 1514, the year the engraving was made. On the left side of Melencolia we see a strange-looking rainbow above a marine horizon, and off-centre behind it a comet with blazing rays. This might have been inspired by the comet observed at Christmas 1471, the year of Dürer’s birth.

The rainbow cuts the horizon vertically, implying that the source of light is near the horizon. It is narrower than a real rainbow and has no striped pattern: it may be a moon-bow, as the comet suggests a nocturnal scene.

Ghostly image

The large polyhedron at centre left has four visible faces: three pentagons and an equilateral triangle. Assuming that the hidden side of the polyhedron is of similar form, we have six pentagons and two triangles. It is a truncated rhombohedron, like a stretched cube with two corners clipped off, but just what inspired Dürer to draw it is a mystery. On the front of the polyhedron, the ghostly image of a face can be seen.

At bottom left is a spherical ball. Its illumination indicates the source of light, behind and to the right of the viewer. Some carpenter’s or wood-turner’s tools lie on the floor. On the wall behind the figures hang a balance, an hour-glass, a sun-dial and a bell.

Examination of the high-resolution image of the engraving, available on Wikipedia, is a rewarding experience and will reveal a wealth of interesting details. There are many other enigmas in Melencolia and you may discover something new or dream up a novel theory about meanings hidden in the work. Perhaps you can explain the shadowy figure on the face of the polyhedron.

• Peter Lynch is emeritus professor of meteorology at University College Dublin. He blogs at thatsmaths.com
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