MC Escher: The intersection of Maths and Art

 by Sam Lewis

MC Escher has created some of the most recognisable works of art from the 20th century, and while his work can be seen everywhere from Doctor Strange to PGS’s very own maths department, few actually know his name. This is because while he has had a profound impact on the world of Mathematics and Optical Illusions, his impact as an artist has long gone unacknowledged. His most famous works such as ‘Ascending and Descending’ and ‘Relativity’ are instantly recognisable, but are also more likely to be seen in a Mathematician’s study than any art museum.

One reason for his relative obscurity is the fact that he was very reclusive. While studying Architecture in a technical college in the Netherlands, many of his teachers found him too philosophical to succeed in the increasingly scientific field, but noted his great skill at capturing perspective. After leaving college to pursue his own interests, however, Escher’s early work focused more on detailed observational drawing from nature than anything else, and he refined his precise craftsmanship.

This all changed, however, after Escher visited the Alhambra in Granada in 1936, and he was blown away by the Islamic patterns. The ‘order in chaos’ of the geometric patterns not only reignited his passion for architecture, but started his journey into ‘Tessellations’, a form of infinitely repeating pattern consisting of geometric shapes that can fit together like puzzle pieces, never overlapping or leaving gaps. Although his interest in the patterns was more from an artistic viewpoint, Escher had accidentally wandered into new regions of mathematical interest, ones that would greatly impact both Geometry and Crystallography.

It was these discoveries that also gained the attention of Sir Roger Penrose, a mathematician, who was exploring the ‘impossible’, most notably the ‘Penrose Triangle’. The impossible images (like this triangle that breaks the rules of geometry) deeply intrigued both men, and they became pen pals, collaborating on many of these impossible shapes. Penrose was excited that he could finally see his theories realised in art, while Escher was amazed his artworks had actual mathematical groundwork. This partnership inspired two of Escher’s most famous works, ‘Ascending and Descending’ and ‘Waterfall’.

‘Ascending and Descending’ shows the optical illusion of a paradoxical staircase, in which the continuous flight of stairs seems to lead both up and down forever, and you can see a reproduction in the PGS Maths block. It was directly influenced by Penrose’s ‘Penrose Stairs’, a concept of stairs that can only exist in 2D, and would break the laws of ‘Euclidean’ geometry (the geometry of 3-dimensional objects). Escher also combined both the Penrose triangle and the Penrose Stairs in ‘Waterfall’, where instead of the monks climbing the impossible shape it is the water. The towers of the waterfall are also topped by Polyhedra, showing Escher’s developing interest in Maths.

 Escher’s two most famous works, ‘Cycles’ and ‘Relativity’ can also be seen in the Maths block, ‘Cycles’ especially being the culmination of much of his work. The piece seems to be a continuation from the impossible staircase, with the monks falling from the staircase into a Tessellation pattern. This piece not only features his impossible perspectives, but also his infinite geometry and tessellations, with the pattern of the monks being inspired by the Islamic patterns of the Alhambra. His most influential piece ‘Relativity’ also plays on the impossible stair idea, with multiple staircases under their own source of gravity, and is his most well-known exploration of the impossible, being seen all across popular culture from Inception to Futurama.

On the topic of ‘the impossible’, Escher stated in a 1963 lecture that “If you want to express something impossible, you must keep to certain rules. The element of mystery to which you want to draw attention should be surrounded and veiled by a quite obvious, readily recognisable commonness.” This perfectly encapsulates why Escher has had such an impact on Optical Illusions and Geometry, exploring the impossible intersections of maths and art.