For a long time, MC Escher enjoyed little acclaim as an artist. Regarded, essentially, as a technician, the Dutch image-maker for many decades found his most passionate supporters came instead from within the mathematical community. Despite having received no training in the subject, in 1954 he curated a show for that year’s International Congress of Mathematicians. His reputation has held: the tiles outside my office are inspired by Escher’s work, and when I mentioned that I was going to Somerset House’s new exhibition on him, a colleague revealed his phone background was an Escher print.
While as recently as 2015 the mathematician Sir Roger Penrose had cause to lament that ‘strangely, he has often been overlooked by the art world’, it appears things are changing. Escher is now getting the critical appreciation that many felt he had been unjustly denied, treated as a unique bridge between mathematics and art. But just how can we evaluate him across this divide?
The mathematically inspired vein in Escher’s work dates back to the late 1930s. While his earlier stuff, consisting largely of landscapes and woodcut adverts, is more conventional, the printmaker had always been interested in replication. Disappointed with the tessellations he had attempted during the 1920s, Escher – drawing inspiration both from the tiling patterns of the Alhambra and the symmetries of mathematician George Pólya – set to work again on the same theme.
In some cases, the difference between those abortive earlier versions and the later ones reveals his newfound mathematical influences more as a shift in subject matter than form: instead of people, we see shapes or shape-like animals. In others, however, Escher does concern himself with the direct representation of mathematical phenomena. His ‘Circle Limit’ series (1958–60), for instance, realises a non-Euclidean geometry, with the image’s repeated pattern getting smaller as the tessellated motifs approach the circumference. The detail is incredibly fine, implying the infinite, while the properties of the geometry are preserved to the last.
At their most complex, these works earn their reputation for accurately reproducing mathematical phenomena – but it can be unclear what Escher’s role as an artist is within them; what separates the tessellations in kind from the mosaics they take after. The main event in ‘Circle Limit’ is Escher’s impressive representation of a model for hyperbolic geometry. But this is not something he created. His artistic contribution lies instead in the motifs he inserts – but, from kissing lizards to scowling bats, it can feel like these additions are accessories to, rather than part of, what makes the work compelling.
While popular among his fans, however, Escher’s tessellations are not his most famous works. In contrast to these faithfully rendered mathematical structures, the lithographs popularised in the 1960s – among the most reproduced pieces of 20th-century art – are built around human interaction with ‘impossible objects’, using them to explore how mathematics relates to and creates ideas of infinity and paradox. Escher’s most famous work, Relativity (1953), for instance, sees figures walk on the various sides of a Penrose Triangle staircase, the landings of which twist to extend, impossibly, up and up.
But in some of these blockbuster pieces, the expression of mathematical ideas is subordinated to an exploration of perception. Likely a product of their overproduction, Escher’s stylistic choices here – kings and queens in castles, serfs carrying sacks of grain, dragons eating themselves – can feel overwrought or even kitsch but, unlike in the tessellations, with the mathematics playing the accessory role. Hence, in Waterfall (1961) – where water flows up Penrose Triangle paths before falling down to its original level, and on and on – two compound polyhedra sit on top of the structure’s towers, below which Escher has scattered alien plants.
Stars (1948), meanwhile, looks like a tattoo. Two chameleons float in space, trapped in a cage shaped like another compound polyhedron, surrounded by, among other objects, the five platonic solids. In both cases, these shapes feel strangely inert, as though they are simply one of many signifiers – like being in space, or on another planet – that tell us we have entered the realm of the surreal.
At his best, Escher builds mathematics into his art. His 1958 lithograph Print Gallery, for instance, does not reproduce a mathematical idea or shape, but rather treats representation itself mathematically. The piece portrays a gallery-goer regarding a framed print which, as the warping perspective reveals, contains the very gallery he’s in. Unfinished by Escher, it was ‘completed’ by a mathematician in 2004, satisfying the artist’s goal of exactly recreating the image within itself. If even one of Escher’s paintings has a derivable mathematical solution, it would be a very impressive thing – but it does raise a question about the art. Is that solution the only way to fill in the blanks?
Escher once said: ‘My work is a game, a very serious game.’ At Somerset House, this quote is printed up on a wall and embodied by the surrounding show, which is packed with interactive exhibits, from an infinitely reflecting mirror installation to an Ames Room, a slanted space that makes you seem larger or smaller depending where you stand. In exploring mathematics as related to perception, reality and the absurd, the artist sought to comment on human experience and how it feels to acquire knowledge. Indeed, Escher did not invent many of the shapes that are attributed to him; often he was not even the first to represent them artistically. But while many of his most famous experiments were attempted before him by his contemporary Oscar Reutersvärd, the latter’s work is merely representational. Escher, by contrast, attempts to move from depicting mathematics to humanising it. Gimmicky or not, it is this that explains his widespread and enduring appeal.
‘MC Escher: The Exhibition’ runs at Somerset House until 6 Sep 2026. For more information, visit somersethouse.org.uk
