What started as a review of Tauba Auerbach’s current show at Paula Cooper led to the question of how indeed a successful work of art might engage with mathematics – what might be some approaches to visualising abstract and often inaccessible concepts?
Prior to seeing the New York exhibition, I visited the artist’s 2014 show at London’s ICA, The New Ambidextrous Universe. In London, Tauba Auerbach exhibited about 7 objects, made of plywood, glass, perspex, and powder-coated steel. The objects, smooth-surfaced and minimal, yet elaborately turned and possibly machine-made, looked sort of like useless furniture. Formally, they were united by a concern with chirality: some carried a right-handed orientation, others left, while (and here my memory may fail me) a glass piece demonstrated a similar idea through light-polarisation. Despite, or perhaps because of, the show’s sophisticated intellectual premise, I found myself oddly un-moved by it – there was no punch to the gut. All I saw was reasonably nicely-made objects on low long plinths, in designer colours – stuff that would look great at Heal’s or an expensive Knightsbridge condo, and definitely looked like what art is supposed to look like.
Reading interviews with the artist, it’s clear that she has a fascination with the idea of maths, and while that undoubtedly finds its way into the work, I felt her pieces added but little to my understanding, or even appreciation, of chirality or of the eponymous book by the late Martin Gardner.
Her current exhibition, Projective Instrument is also built around a book, this time by an eclectic American architect, Claude Bragdon, whose interests spanned higher-dimensional geometry through to Theosophy. The exhibition had a number of her trademark objects, made during a glass residency, as well as woven paintings. These, or similar, paintings unfortunately were displayed to much greater effect, alongside Charlotte Posenenske’s work, in the gorgeous rooms of Indipendenza Roma (2015). The Paula Cooper show also featured seductively-coloured paintings made with custom-made implements ‘inscribing patterns derived from chain-maille, fractal curves, and four-dimensional tilings into the paint’ (press release). At the end of the day, however, they were pretty simple, inoffensive wall decorations that neither illuminated the mathematics nor particularly pushed the boundaries of artistic practice. Auerbach’s imprint, Diagonal Press, was, if anything, more interesting, showing copies of Bragdon’s book, amongst others. I couldn’t tell if they were for sale, or if they’re thrown in gratis if one spends (apparently) $150,000 on a painting.
A second take on maths-in-art comes from Falke Pisano’s rather good show at Hollybush Gardens (London, 2015), entitled The Value in Mathematics. Pisano’s approach was more cerebral, less apparently infatuated with maths: in fact, there was very little about maths per se. It was more about the teaching of mathematics, and how the subject is presented in society. The exhibition consisted of a number of flat works, sculptures, and videos. The flat works seemed to be unified by descriptive texts or titles on the wall, while the sculptures had in common an open structure, relatively humble or light materials, and open plinths. For me, the overwhelming aesthetic was that of Modernism, of graphic design from a pre-computer era. However, on closer viewing, particularly of the prints, the organising principle revealed itself: the various prints described what could be characterised as systems of valuation or exchange. What animated the exhibition were the videos which, curiously, brought a more human and less conceptual feel to what could have been a cold and information-heavy exhibition. Only at the end did I read the press release, and worked out the political sub-text of the show: as I understand, it challenges the impression, apparently promulgated by mathematicians, that mathematics is somehow objective and ‘value-free’, whatever that means. The exhibition proposes that the teaching of mathematics makes it inherently political, context-dependent, and hierarchical. Whether one thinks Pisano’s particular programme is interesting or not, her handling of the material is deft, a collage of politics and the scientific, woven into a fictional system of thought, perhaps intentionally layered, obscure, even obtuse . I found Pisano much more convincing than Auerbach, where the maths seems just grafted onto a high-end design practice in order, one might surmise, to lend gravitas. At a presentational level, I liked the fact that Pisano’s show gave the impression that it could only be bought in its entirety, or even if bought piecemeal, the individual works would always be somehow connected to the installation. Auerbach’s were as distinct art-objects as they come: almost painfully asking to be collected.
Having looked at two artists working with maths, I wanted to highlight the counter-example: a mathematician attuned to visual aesthetics. Thomas Banchoff, a geometer at Brown University, pioneered the use of 3-D computer graphics to explore higher-dimensional geometries. In the old days, mathematicians used plaster Schilling models, such as those in the Harvard, MIT, or Oxford collections, to visualise complex geometric objects. Banchoff’s contribution was to use CGI to animate the shapes, allowing the viewer to perceive the model as it unfolds in time and thus form a mental image of what a 4-D object might look like and how it might behave. I would argue that, by allowing manipulation of the objects, the viewer could ‘fly’ around the shape in a way that simply wasn’t possible before, and intuition could be built directly from the image, rather than being mediated through the symbolic logic of the maths, or the drudgery and expense of finding physical models. Moreover, the physical models remain in a fixed 3-D configuration, whereas the digital allows for any 3 of the possible 4 (or higher) dimensions to be projected.
However, as Banchoff doesn’t reference the conventions of the Artworld, either by contextualising his images vis a vis Theory or presenting them in an arty way, perhaps he wouldn’t be thought of, nor call himself, a practicing artist . Yet, I feel his works are of far greater profundity than either Auerbach’s superficial approach or Pisano’s valid and interesting, sociological critique. They marry visual aesthetics with a potential for conceptual or perceptual access to a reality that lies beyond the mere image.
An artist whose approach parallels Banchoff, while acknowledging, and being acknowledged by, the Artworld, is Manfred Mohr. Still producing, with recent shows in London (Cubitt Gallery  and Carroll/Fletcher [2016/2014/2012]), he used some of the earliest plotters to produce works on paper, notably a series exploring views of the 4-D cube, a so-called hypercube or tesseract. Mohr’s work visually has an affinity to Minimalism’s serial tradition, but genealogically is better placed in relation to Concrete Art, particularly artists such as Jeffrey Steele and Anthony Hill. Mohr’s geometric focus, and a methodical exploration of all combinatorial alternatives, impacts the viewer through its sheer exhaustiveness and perceptual immersion. Some of his pieces, even more than Banchoff’s, imply the physically-impossible and the infinite. It is notable that he achieves this without colour, without any quasi-mystical or metaphysical twaddle, and his works are entirely governed by the internal logic of their generative rules.
The last, and potentially most interesting approach, is to view maths as an essentially performative practice. ‘Performative’, a over-used word in art-speak, is utilised in a specific sense here: the act of drawing a picture, handling a plaster model, manipulating a digital model, are ways of understanding, visually and haptically, how a given mathematical concept, for instance a multi-valued complex function, behaves: where are the zeroes, where lie the saddles and branches? This sense of the term ‘performative’ is taken up in the papers of Xin Wei Sha, a professor in Differential Topology who has sought to look at the practice of mathematics in light of analytical constructs used in art and critical theory.
In my view, what’s interesting about this approach is that it can be seen to break the understanding of a given mathematical problem into three levels: an intuitive grasp of the problem, let’s say the true knowledge; a symbolic quasi-linguistic analysis, such as a proof; and a graphical or haptic ‘feel for the thing’, which I equate with the performative. The actual drawing, digital image, physical model, blackboard scribbled with equations are residues of a symbolic or performative method. These physical residues can be put in a book, and indeed, if packaged a certain way and accepted as such by relevant competent judges, can be called art. But if the primary content of mathematical understanding is fundamentally intuitive, lying somewhere between the visual, the symbolic, and the physical, then it’s likely that a non-mathematician may never really access that content. Moreover, without facility with these tools, he/she is unlikely to communicate effectively with trained mathematicians operating in a network of peers . The most we can do is ‘poke’ at it, try to access it by manipulating the geometric objects, or, more interestingly, engage in a Wittgenstinian project of ’drawing connections’ between the mathematical objects and the world-at-large. To the extent these syntheses, these connections, are haunting and unexpected, we judge the success (or lack thereof) of art like Auerbach’s or Pisano’s.
I end with an analogy to Land Art. Certain artists such as Walter De Maria were concerned with documenting an ungraspable moment in time and space, or in the case of his Dia Beacon pieces, an apparently obvious yet subtle mathematical idea. Yet in the case of The Lightning Field, the primary aesthetic experience remained in him, and an element of it now invests the few viewers who can actually make it out to New Mexico. Similarly, Hamish Fulton and Richard Long made their experience, their walks, often in the countryside, the apparent content of their work, accessible substantially to themselves. The documentation is entirely secondary, from an aesthetic point of view, if not from a financial/re-sale perspective. It is as if, knowing they can never compete with the immensity of nature, they made minimal, repetitive but exquisitely calculated sculptural gestures: Et in Arcadia ego.
1 Fiduccia, Joanna Report: Bullshit ! Calling Out Contemporary Art, MAP Magazine, 1 June 2010, http://mapmagazine.co.uk/8981/report-bullshit-calling-out/ , accessed 23/12/15.
2 See Arthur Danto’s What Art Is (2013) for an introduction to how the late Danto analysed the perennially interesting question of what art is, and the circularity in art’s definition, particularly in the age of the ready-made.
3 Subject obviously to exceptions such as M.C. Escher, and his collaboration with Lionel & Roger Penrose.