KATHLEEN HYNDMAN
Nature+Maths=Art
27 February – 4 October 2025 at the Mathematical Institute, University of Oxford
KATHLEEN HYNDM AN Nature+Maths=Art
By Professor Martin Kemp, FBA
(Compiled from various statements in the archive) (all works by Kathleen Hyndman unless otherwise noted)
In Her Own Words
My paintings are often sparked off by something that strikes me visually. Without a visual stimulus, the result seems arid. I think some mathematicians believe maths needs a link with reality. I use mathematical sequences and geometry to distribute motifs, shapes, colours; e.g. Golden Section, prime and Fibonacci numbers and eccentric constructions. I make subjective decisions about which sequences and constructions to use. One idea can produce a series of works. Interrelations within the work and to the whole are aimed at a calm unity.
In my case, construction is not only an end in itself but is usually predominantly an objective means of expressing subjective feelings about a specific part of nature, e.g. the apparent interpenetration of sunlight through a blue sky and its intensification round a tree (fig 1); or the way sand is blown around stones: or a field of grass or dust rising. I make many rapid landscape, sea and other sketches and notes from nature and then search for the constructions (including colour tone constructions) that will carry the idea within the sketch, thus I go outside myself and theory to initiate a picture. The unexpected quirks - or rather - rules of geometry and number, the minor manifestations of catastrophe theory, the way numbers team up for or against one is most entertaining - and frustrating.
Fig 1. Sunshine and Tree, 1983, acrylic on canvas, 73 x 102 cm
I had to forget the initial stimulus to arrive at something pictorially satisfactory to me.
Before I really get going, I have to forget the realism in the sketches in order to define and refine the geometrical, arithmetical, colour and tone constructions. But during this process the original stimulus - or indeed other remembered stimuli come back to mind to help the picture towards its specificity. The geometry and arithmetic become the colour and tone, they relate before and/or during and/or even after with the specific things seen and, hopefully, through time, effort, doubt and confusion arrive at a visual symbiosis. The process is mainly the subjectively judged use of construction and sequence for expressive purposes but some of the work is almost pure construction and sequence (usually a spin off from the previously related process): even then it seems to have a relation to known natural phenomena like molecular movement; an example is “Spinoff, Movement and Vertical Stasis” - a regular pattern of sequential rotated bi-coloured dots which give the effect of movement (fig 2). Though not an aim, optical effects occur, or can be made or manipulated and add another interest.
A satisfactory system has often led to more ideas based on variations of it. In these cases, the memory of things seen seemed to attach itself to the system variation. This feedback became incorporated in terms of colour, tone values, disposition of units etc.
For the earlier work in acrylic on canvas I looked for large geometric systems of shapes and developed arithmetical sequences of colour and tone (fig 3). These systems and sequences were related to the visual stimulus but underwent change as colour and shape values took over.
For the acrylic paintings on paper, again, arithmetical sequences and geometrical constructions that expressed something of the initial stimulus were looked for. When found, the initial seen idea had to be largely forgotten so that it did not obstruct the feedback from the purely abstract use of the sequences and constructions: the disposition of units, their exact shapes, the positioning and sequences of colour and tone (fig 4). The systems used gave a discipline within which to work. Concentric curves, Fibonacci numbers, Golden Section proportions, prime numbers, eccentric constructions etc. were used; they are the underlying structure of the work.
I think everything is interdependent, a unity, like a stone causing ripples to the edge of a pool. I can only express this by bringing it down to manageably human scale, by trying to make small unities where I attempt to relate everything. Number, sequence, construction have a logic that might be a metanym [sic] for universal logic. [metanym here means a term that stands figuratively for something else.]
Fig 2. Spin Off Movement and Vertical Stasis, 1985, acrylic on canvas, 86 x 99.5 cm
Fig 3.
Radiate / Glow, 1975, acrylic on canvas, 122 x 114 cm
Fig 4
Raiate Tetrad, 1997, acrylic on canvas, 69 x 69 cm
Her Maths
There have been many artists from the Renaissance onwards who exploited mathematical systems. This has for the most part involved the description of space according to the geometrical optics of perspective, and to a lesser extent the visual music of proportions. In the 20th century geometrical form gained prominence in its own right as the primary feature of the artwork, most conspicuously in Constructivism and Op Art. At first sight Hyndman’s art seems to fit quite happily within the former, while having definite affinities with the eye-catching compulsions of the latter. However, as her own accounts of her procedures stresses, she refines her subtle pictorial maths according to arithmetical systems in continuous and often unexpected dialogue with seen phenomena. The systems to which she looks, include prime numbers, the Fibonacci series and the incommensurable or irrational ratios of the so-called golden section. (Incommensurable or irrational means not capable of being expressed in whole numbers or fractions.)
The golden section (alternatively, the divine proportion, or extreme and mean ratio) is constructed when a line is cut asymmetrically so that the ratio of the whole to the larger proportion is equal to that of the larger proportion to the smaller portion. The ratio is incommensurable. In the 19th century it was progressively realised that the golden ratio was present in a number of phenomena. Not least, it corresponds to the increasing volume inside a sea shell shaped as a logarithmic or equiangular spiral, and to the numbers in the Fibonacci series, named after the mediaeval mathematician, Leonardo Fibonacci. His series was expounded by imagining generations of reproducing (and immortal!) rabbits. Each breeding pair mates at the age of one month, and at the end of their second month they always produce another pair of rabbits. The sequence, in which each element is the sum of the two elements that precede it, begins: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… As it progresses, so the ratio of each successive term more closely approximates that of the golden section. Prime numbers, still the subject of intense arithmetical interest, are those that can only by divided by themselves and 1. Their obstinate individuality granted them a special status for Hyndman.
Hyndman’s collection of books testifies that she undertook a process of self-education in maths beyond that required for passing a school O-level examination. At her death, she owned the 5 volumes of H. W. Clayton’s and D. N. Straker’s, A Natural Approach to Mathematics, in the metric edition of 1972 (fig 5). A series of pencil marks on the list of contents and elsewhere record chapters that had been read or were planned to be read. For instance, she might well have been drawn in volume 3 to demonstrations like, “AB, Fig. 2, has to be rotated about P through an angle of 180. A rotates to A, where APA, is a straight line and PA, = PA. B rotates to B, where BPB, is a straight line and PB, = PB. Note that A,B, is parallel to AB but the direction is reversed.” (fig 6). She was much concerned with compound rotations (fig 7 and 8). Hyndman uses all four of the basic mathematical translations: position, rotation, reflection and enlargement.
5
H.W. Clayton and D. N. Straker, A Natural Approach to Mathematics, 1972
Fig 6
Drawing the transformation of a figure after rotation, in Clayton and Straker, vol 3, p. 94
Fig
Fig 7 Rotation, 1987, acrylic on canvas, 76.5 x 76.5 cm
Fig 8
Straight Line Rotation, White on Black. Forest, 1986, acrylic on canvas, 76.5 x 76.5 cm
These books were used solely by her and not by her children, and they were housed with her books on art.
Hyndman’s rotations go far beyond a simple turning of a composition or its elements. The triangles on one of a preliminary study for a series of rotations on a 10 x 24 grid (fig 9) are assigned numbers, which helps us deconstruct what is happening – at least to some extent. Importantly, the triangles vary in darkness from 1 to 6. The 2x2 squares have various triangles and many of the moves are clockwise pivots of the triangle (marked red), around the centre of the 2x2 square to give the next 2x2 square (fig 10). There are also many anticlockwise pivots of the triangle (marked blue) around the centre of the 2x2 square to give the next 2x2 square. In the centre, there are either 180-degree rotations or no rotations. The pattern goes snakes-and-ladders style around the grid. There may be other ways of analysing or generating the pattern but this appears the most accessible. The effect is to balance repetition and variety – order and disorder – in a systematic way. The mode of composition is akin to Serialism in music, in which recurrent series of ordered elements are manipulated to give an internal unity. That she was consciously creating a form of visual music is confirmed by her series of 10 overtly musical paintings. In Clarinet a row of circular motifs are rotated as they progress across a bar (fig 11).
When we turn to her other books, we can be certain that Hyndman was the reader of the well-thumbed copy of H.E Huntley’s The Divine Proportion. A Study in Mathematical Beauty in the Dover edition of 1970. Pasted inside the front cover are two sheets of her notes on paper torn from the magazine, Oxford Today (fig 12). Huntley produces a great historical parade of thinkers, in and beyond mathematics, to demonstrate the ubiquity of the golden or divine ratio in nature and art. Those quoted, often ecstatically, belong to the worlds of philosophy, psychology, science, poetry, art, music and virtually all sectors of human creation in which aesthetics can be claimed to operate. The witnesses stretch from ancient Greece (inevitably, Pythagoras) to the twentieth century. We can imagine that Hyndman was particularly drawn to famous number arrays such as Pascal’s triangle and the Chinese triangle (known to Fibonacci) (fig 13). Such mathematical patterns that are discernible on a wide basis lie behind her deep conviction that “everything is interdependent, a unity.”
Fig 9
Study for Rotations and Pivots of Triangles on a 10 x 24 grid
Fig 10
Diagram of Rotations and Pivots of Triangles on a 10 x 24 grid (courtesy of Jonathan Kemp)
Fig 11
Clarinet, 1994, Acrylic on board, 36 x 36 cm
Fig 12
Pasted Sheets on Inside Front Cover of H.E Huntley, The Divine Proportion. A Study in Mathematical Beauty, 1970
Fig 13
Pascale’s Triangle and the Chinese Triangle, from H.E Huntley, The Divine Proportion. A Study in Mathematical Beauty, Pages 132-133, 1970
Fig 14
Visiting Fibonacci Monument and Square, 1999, acrylic on board, 27 x 31 cm
Other artists
Hyndman keenly sought out works by artists with whom she sensed an affinity, particularly those Constructivists involved in abstraction of a systematic and geometrical kind. Prominent amongst them were Jean Spencer and her husband, Malcolm Hughes. Hyndman exchanged letters with Spencer who was not only active as an abstract painter but also in the organising of groups of artists committed to promoting Constructivist theories. In a letter to an unknown recipient, Hyndman mentions,
1 The Colour Presentations booklet written by Bernard Harrison of Brighton University showing constructed colour areas by Jean Spencer and others.
2 An issue of ‘Constructivist Forum’ with instructions for constructions, diagrams and reliefs.
3 Sundry items from Exhibition Space including mention of both Jean Spencer and Malcolm Hughes.
All three publications are very pure in their constructivist theory – they are to a lesser extent sequential – I think I would be on the margins of this.
In a letter to an unidentified contact, she recalled “looking through books and catalogues of mine in search of Jean Spencer. You suggested I might contact her at Bulmershe” [the College of Higher Education where Spencer was teaching].
She wrote a long letter to Spencer at the Constructivist Group of Women Artists on 31st January 1990, explaining her “method of transposing a seen thing geometrically and numerically.” She had reservations about the “purism” of the British Constructivists.
There is a theoretical cold quality that is only attractive to one part of what I am trying to do. But their work seems to adhere strictly to related broad colour stripes so I may be considered frivolous. However, Ex. Space favours J. S. Bach and so do I.
Kathleen’s correspondence with other artists characteristically emphasises her highly personal methods but betrays an anxiety about her own status and how she might be regarded by the clubbish artists in the metropolis. Theirs was an inner circle to which she did not obviously belong.
Series of her notebooks and diaries are devoted to a large number of artworld contacts, actual and prospective (fig 15). Two pages in a notebook apparently dating from 1995 contains a series of aide-memoires and contact details (fig 16). Rather unusually for a notebook, the left-hand page also contains a sketch for Two Trees. In the notes, she mentions amongst others, Peter Reddick, printmaker, Chris Mercier, artist and printmaker, Sylvie Turner, art historian expert on papers, who rang back, Advanced Graphics (with specific mention of Patrick Caulfield), Nicholas Sinclair, photographic portraits of artists, Peter Rhoades, natural history photographer (“unable to help until late in the year”), and Kip Gresham, printmaker to whom she sent a letter and photos. The notebook also contains numerous notes about print-making techniques, with which she was much concerned. There is distinct anxiety in her concern to network with artists and art organisations.
Fig 15
Kathleen Hyndman’s studio with folders of correspondence and clippings from exhibitions.
In her statements and letters, the one artist immune from her critical eye was Piet Mondrian, the magisterial Dutch painter of geometrical abstractions. She recorded that:
My wish to try to relate everything rather than to express self directly, to try to make a non- aggressive whole started around 1964 and was confirmed by reading and looking at [Michel] Seuphor’s large book on Mondrian (Piet Mondrian Life and Work, New York, 1956).
She well knew that Mondrian’s square and rectangular planes of colour had been progressively abstracted from his experiments with the depiction of natural forms, most notably in his paintings of rectilinear trees. Hyndman’s own explorations of branching involved “Ys” and related shapes, distributed across grids according to various formats of prime numbers (fig 17).
Hyndman, Notebook 1995, Study for Two Trees, with Colour Notes, Lists of Contacts etc., pp, 38-9
Fig 16
Kathleen
Fig 17
Riverweed, 1988, acrylic on paper, 31.5 x 56.5 cm
Of the contemporary British painters, she most admired Bridget Riley, the great practitioner of Op Art. Hyndman owned a copy of the exhibition catalogue, Bridget Riley, Paintings and Drawings, Arts Council 1973-4. She almost certainly saw the show in London. Riley invited Kathleen to her studio, but there is no sign of their enjoying any kind of sustained relationship.
There was in fact a key difference in what the two painters were doing. For Riley, the painting was a painting was a painting was a painting. It consisted of “simple forms without any pretentions” and was “not demonstrating any scientific principle, not perceptual, arithmetical or geometrical”. The painting is an autonomous ocular event of a non-referential kind. For Hyndman, perception of seen things generally provided the underlying basis for the motif of the painting. Additional perceptions might arrive at any stage. That Hyndman was interested in the latest thinking about perception is confirmed by her copy of an article by Bernard Dixon about Colin Blakemore, the distinguished neuroscientist, who was exploring “The Mind’s Eye” in the BBC Horizon programme on 28 January 1980.
Hyndman did express reservations about Riley:
I have long admired B. Riley (though I found her Artist’s Eye picture at the N. Gallery [in 1989] somewhat bleak and disappointing as are, to me, some of her later stripy works).
There then follows a quartet of non-British Constructivists and Op Artists:
Vasarely, Uecker’s nails, Castellani, De Soto. Pure British constructivists do seem to me limited, but who am I to say?
Some other British abstract artists attracted her attention.
I saw Tess Jaray’s work at the Ashmolean [in 1984] – I have always liked her work, the restraint and tension of geometry plus intimations of nature or buildings [fig 18]. Kenneth and Mary Martin also seem more human – less theorising and more straightforward descriptions of method and philosophy. A quote from an Arts Council exhibition ‘Working Methods’ – text by Michael Harrison; “…this century…much art has been preoccupied with examining the nature of art itself and, all too often, an ever more self-referring and sterile reductionism has resulted. Martin however has sought to use the physical nature of art, as he grows to understand it, to achieve an abstract equivalent and emotive expression of the universal laws which he and we experience.” And by K. Martin. “The shape of the bird is the result of its desire to do certain things, to fly at certain altitudes and at certain speeds. So the shape of the mobile (in this case) is the result of its dynamic attributes. The subjective will of bird or animal has affected its shape and colour (a process over innumerable generations), that of the artist gives form to his work.” [Kenneth Martin undertook a series of “Screw Mobiles” of a mathematical-organic kind].
I find Anthony Hill more accessible [than] Malcolm Hughes but I have only seen his work in magazine reproduction – he seems punctilious but also has a little more meaning.
Tess Jaray b. 1937 Minaret IV, 1984 etching, 49.5 x 43 cm
Courtesy of Tess Jaray RA
Fig 18
Tess Jaray b. 1937 Minaret, Outline (Blue), 1984 etching, 49.5 x 43 cm
Courtesy of Tess Jaray RA
Her Art
Kathleen Blomfield studied at Kingston-on-Thames School of Art. While a student, she produced an ambitious visual and written thesis on the war-battered Isle of Dogs, a lowlying land formed by a great loop of the Thames east of central London. It was a bombed land of massive docks, occasional parks, the homes of resilient dock-workers, shops and, it was said, 43 pubs. Completed during 1948-9, her thesis was taken up fifty years later and published by the Island History Trust as a handsome 25-page book.
The text and varied illustrations take us on her journey of discovery in an equally perceptive manner. She writes with skill and wit. Her visual records range from lively sketches of characterful residents to drawings of roads, domestic and commercial buildings, mighty docks etc, some with colour notes (fig 19). Detailed colour notes were often made later for her abstract compositions. Not a few of the Isle of Dogs illustrations already hint at her keen sense of the geometrical organisation of the space of a seen view and its transmission on to the flat surface of the page, (fig 20). She tells of her picturesque encounters with miscellaneous locals, including amused men who volunteered to be “photered.” I hope she received a good mark from her art school.
Her subsequent geometrical abstractions featured in a number of group exhibitions, including some at notable domestic and international galleries, including the Hayward Annual in 1982, the Kunstler Forum in Bonn in 1987, the Fourth International Triennale of Drawing in Wroclaw, Poland in 1988 (and the fifth one in 1992), the London Group Open Exhibition in the Norwich Gallery in 1990, the 3 Cities Art Show in Oxford and Birmingham in 1996, the Mondriaanhuis, Amersfoort in an exhibition of abstract geometrical art in 2000-1, and in 2003 in the same venue in an exhibition inspired by Pythagoras, and in 2007 at the Belgrave Gallery St. Ives. The full list of her exhibitions dispels any sense that she laboured without exposure and recognition, but there was no big breakthrough in which signs of admiration rose to widespread recognition, nationally and internationally. It may be that critics were unnecessarily deterred by her mathematics.
Fig 19
A Street Lamp and Cranes with Colour Notes, 1948-1949 from The Isle of Dogs, 1999, p. 21
Fig 20
Robin Hood Lane Flats, 1948-1949 from The Isle of Dogs, 1999, p. 10
Looking back over the spectrum of her paintings, we can detect an evolution from early works that featured large bands of rhythmic and geometrical colour (fig 21) to wonderfully delicate, energetic and suggestive sequences of smaller, linear marks that capture the inner organisation of nature (fig 22). But the development was not regular. Each work or series of works has its own rationale.
Fig 21 Damp Breeze, 1977, acrylic on canvas, 135.5 x 118 cm
Fig 22 Blue Green and Yellow Rhomboid (No.1), 1997
Looking at each refined and finished work, it is very difficult to “reverse engineer” her constructions; that is to say, working from their appearance to the decisions and “engineering” that lay behind them. Sometimes the starting point is no longer discernible. The initial observation of a potential subject is transformed into mathematical sequences which evolve as the process of invention proceeds, and are potentially changed by new or refreshed perceptions of things seen, which may themselves prove to be visually elusive. This is to say nothing of aesthetic choices. A few pages of preparatory maths survive (fig 23), but are difficult to follow in detail.
The best way of gaining some sense of how she creates is to quote extensively from a few surviving written statements about particular works or series she made in response to specific requests. The first, a printed account for a conference in Granada in 2003, (fig 24) starts with the sight of birds suddenly “escaping” from a tree, presumably in response to a frightening sound. This developed into a surprising series of geometrical transformations, which seem not to be obviously related to the starting point. The second account looks at the patterns assumed by windblown grasses. The fluidity of her visual thought and her propensity to relate what seem to us to be independent topics, defies our desire to follow what seems a logical sequence.
Fig 23
Studies of Number Sequences, Circles and Trajectories
Fig 24
Hyndman’s commentary on her use of Number Sequence and Geometry in Art
“Escape” (1) (fig 24a) Five ten-sided regular polygons are drawn concentrically. A Golden Section point on each polygon links it to the next. A space next to this allows the “bird” to escape outwards along a geometrical “trajectory”. Process repeated till “bird” outside the design. Base of “bird” starts at Golden Section point of the side where it lies.
“Exit” (2) (fig 24b ) Five – seventeen sided polygons are drawn concentrically. Each starts with one radius. Succeeding radii are drawn at the Golden Section angle. Outer ends of radii are joined giving irregular polygons. Succeeding polygons start at the G.S. point on a side of previous polygon.
Birds process between polygons to exit – marked by two radii across all polygons. The colour processes from green to pale green to pale blue to blue gradually. The bird colours and the exit demarcation lines are the reverse of this. 22 variations.
Each work has a regular pentagon or heptagon. One side of each is missing; adjacent sides to this are shortened by G.S. proportion. Lines are drawn at a G.S. angle from shortened points to edge. The polygons relate differently in each work. This one is ‘Moon Buggy’(fig 25/25a).
Fig 24a Escape, 1992, acrylic on paper, 29.7 x 30.5 cm
Fig 24b
Exit (a seventeen sided work), 1993, acrylic on board, 105 cm diameter
Fig 25a
Glowing Stone (landing meteorite), 1996, acrylic on board, 57 x 57 cm
Fig 25 Moon Buggy, 1996, acrylic on board, 57 x 57 cm
Why the title, Moon Buggy? It does look somewhat like a moon lander, but other titles in the series do not consistently rely upon such descriptive names. In this series of 22 variations in 1996, she uses varied types of titles, for example: Newspaper Reading Traveller; Jellyfish; Water Flea; Water Tower; Smile; Exits Together; Cactus; Toothless and Glowing Stone (landing meteorite), 1996. What unites them is their basis in three regular polygons.
It is worth looking briefly at her melange of types of titles, which is typified by a shorter series of three 3 curved pyramids, amongst which we encounter Hot Breeze (fig 26), which is similar to five closely related images that bear psychological titles: Early Excursion (fig 27), with an implicit father, mother and child. There is also a Late Excursion, in evening colours, and 2 Depressed Adults and One Less Depressed Young Person. Caring involves elided curves, while Look Out is a tower of nine bent pyramids. There is an instinctive wit even cuteness in her titles, but in a sense her specific observations have been so abstracted into universals that almost any engaging title would suffice.
Fig 26
Hot Breeze, 1994, acrylic on canvas, 114.5 x 109 cm
Fig 27
Early Excursion, 1993 acrylic on canvas, 94 x 133 cm
The heat of Hot Breeze also serves to remind us that colour is a vibrant component in many of her paintings (fig 28). A very attractive series of more than a dozen colour experiments survives for the print, Two Trees (fig 29/29a). She views the surface of the image as an interactive whole, in which vividly coloured shapes provide key elements of the pictorial structure. She is tuning her colours like a composer of music.
Returning one more time to the Exit series, altogether she creates 22 variations on the geometrical “escapes”. A substantial set of drawings survive, including one that lays out the basic pentagon, hexagon and heptagon (fig 30), with a note to indicate which is the “top” of the drawing.
Unexpectedly, the Fibonacci series intervenes in her Granada agenda. It seems not to belong, but it appears thus in the printed document of the agenda for her talk. This is the course we are pursuing here, even if I cannot smoothly integrate the changes in direction that she takes. She tells us that “this idea evolved further”. The “idea” may be the conjunction of the Fibonacci series and the golden section that plays such an active role in the Exit series.
Fig 28 Purple Cloud and Reflection, 1978, acrylic on canvas, 151.4 x 93 cm
Fig 29 Colour Studies for “Two Trees”
Fig 30
Two sets of Inscribed Pentagons, Hexagons and Heptagons, pencil on A4 paper
Fig 29a
Two Trees, circa 1995, screenprint, 51 x 46 cm. Edition of 35 plus 1 Artist’s proof
I made Fibonacci units: 9 strips of Fibonacci numbers (155); no.1 line is tallest, succeeding strips (2-55) each include and adjoin the previous strip but are reduced in height by one ninth. Height of no.1 line is equal to width of 55 strip. These units can interlock when reversed, transposed, rotated to make big pictures. The two colours in each separate line use Fibonacci sequences contrapuntally.
An example is New York (fig 31). Her drawings testify that she placed a good deal of emphasis upon colour stripes, seemingly in the form of linear vibrations. One colour study is executed on the reverse of a canvas which she had abandoned and cut up (fig 32). The Fibonacci series played an increasing role in her later works.
Fig 31
New York, 2001, acrylic on canvas, 90.5 x 106.5 cm
Fig 32
Colour Studies for a Fibonacci Series, acrylic on canvas
The second account is a direct response to Jean Spencer in a letter of 31st January 1990 (fig 33).
Dear Jean,
You asked me to let you know more of my method of transposing a seen thing to a geometrically and numerically based work. An actual example seems to be the best way…
Large area of grass is the starting point. The end point is to try to express this in an interesting format that is not regular but controlled by a system.
We should realise that she is not looking at the botanical formation of grass, but at the swirling patterns made by long grass in the wind. Her text is cast as an abrupt series of notes.
The intersections of concentric curves with parallel straight lines to be the springing point for the “blades” of grass. Intersections too unevenly distributed.
She continues.
Concentric curves, each one nearer to one side of previous curve, parallel lines over now make a more interesting distribution of intersections.
Straight uprights from the intersections each one not reaching the next parallel above, flanked by dots in varied sequence (seeds) – very literal. Boring overall effect –too insistently diagonally stripey. Variations, none worked. Seeds changed to a rotating quadrilateral on the top of each upright Eight positions (fig 34).
On the geometrical matrix, I related the position of the beginning of each rotational sequence numerically up the diagonal so many points and then across to the next diagonal via the appropriate curve. As the matrix is asymmetrical, so the relations vary over the surface, although their, as you might say, topological relationships remain the same.
Experimented with numerical variations, some were flat and boring. Found the most lively.
The rotation of the quadrilaterals varied the distances between the diagonal lines of units and gave rise to varied rhythms as the density of intersection points varied. I then had to decide thickness and length of lines and size of quadrilateral. So you see in this case I had to forget the initial stimulus to arrive at something pictorially satisfactory to me. En route to this conclusion I was reminded of a forest on a hill – a kind of feedback: so then I developed another similar picture based on early spring forest colours – but that is another story. I did also actually arrive at a grass picture later using a rhythm of 15 colours (fig 35).
Fig 34
Talking Afforested Hill, 1988, acrylic on paper, 55 x 75 cm
Fig 33
Letter from Kathleen Hyndman to Jean Spencer, 1990
In what is one of her later works, she was overtly concerned with eccentric constructions in what seems to be a delicate and elusive geometrical abstraction, but the title, Triple Eccentric Construction; Sun on Water (2) (fig 36), 1991 refracts back into an experience that entered her visual field at some stage. She always keeps us on our observational toes.
A great deal of effort was put into the eccentric motifs. Amongst a group of drawings on very different scales for the overlapping “suns”, is one drawn with a fine pen on draftsman’s film (fig 37). Whatever medium and instrument she was using throughout her career, her manual precision and concentration were extraordinary.
Fig 35
15 Grass Verge Colours, 1990, acrylic on paper, 55.2 x 75 cm
Fig 36
Triple Eccentric Construction; Sun on Water (2), 1991, pen and ink on paper, 48 x 48 cm
Fig 37
Studies of Eccentric Constructions, pen and ink on draftsman’s film
A related series, comprise sets of clustered circles, drawn with compasses, from which a dense and unexpected series of tangential lines radiate with penetrative energy across a dynamic space (fig 38). One in the series is entitled “burrs”, referring to the spikes on some seed-heads, most notably teasels. The result is an “all-over” and free-hand quality, in marked contrast to the sparse dispersal of the Exit series and its graphic precision. Is there a reflection here of American abstract expressionism? Another related set of drawings transform the overlapping circles of the Eccentric Construction into polygons of irregular side length, entitled Limpets (fig 39). From each centre, spokes are drawn at golden section angles and then joined at the tips. The six variants approximate how snow falls.
Over the course of her long career, Kathleen Hyndman created clusters of works in series, but looking at her vision as a whole, we witness a repeated desire to pursue new causes and effects. Hers is a sustained quest to evoke the mathematics of nature and the nature of mathematics. It is nice to see that the watery themes of her Isle of Dogs illustrations resonate as late as 2012 with Salt Weed (fig 40) which is inscribed on the reverse of the stretcher, “WHERE THE SALT WEED SWAYS IN THE STREAM”. In her book on the Isle in 1949 she had written about water of a very different colour: “a square inlet from the river with big barge boats drawn up – grey and rich green of mildew and water weed”.
Fig 38
Study of Circles with Tangential Trajectories, pen on paper
Fig 39
Study for Limpets, pen and pencil on paper
A Tail-Piece
None of this is easy. The procedures underlying her images are intense, complicated and personal. The relationship between the initial inspiration and the eventual work is often difficult to trace, initiating mathematical sequences of an oblique kind. Does she expect the viewer of her creations to master her maths and follow the diverse application of it to her pictures? I think the answer lies in her musical allusions, above all Bach. She is playing to our instinctive reaction to the pervasive order – themes and variations – that the lover of Bach can fully experience without a mathematical dissection of his musical means (fig 41). She intends that we should become aroused when looking at her paintings to sense the ubiquity of the mathematical harmonies that are built into nature, from the tiniest particle to the infinite grandeur of the cosmos. Music is never far away in her compositions. She aspires to extract timeless absolutes from the beauty of creation.
Fig 40
Salt Weed, c.2012, acrylic on canvas
Fig 41
Counterpoint, 1973 acrylic on board
83.5 x 114.1 cm
Personalia
Kathleen Hyndman (née Blomfield) was an art teacher, wife and mother based in an Oxfordshire village. Being a mother and an artist caused inevitable strain. She wrote to an unidentified correspondent:
Sorry about the coffee, I am really only writing this because I was such a wimp, physically and mentally while you were here; I put it down to the mere two hours sleep I had the previous night, the chaos of sorting the loft for boarding, my husband’s departure for Holland with B[ritish] R[ailways] complications etc. all happening at once! Last time someone came to see me about pictures, my son was ‘phoning Venezuela until 4 a.m.’
Hyndman’s serenely orchestrated and unfailingly patient works bear witness to her success in navigating her careers. She could smile stoically at her situation. On three sheets of A4 on 3rd November 1989, she typed notes for a “fairly light-hearted talk ”. She listed almost fifty sources of professional and domestic stress. This is just a selection:
Artist as pain in the neck/ Manipulation of people and time…../Believing the books which say that one’s children need an afternoon rest – one can get another ½ hour of painting…/Using the living room as a studio./Cluttering every room with canvases./ Making sure that teaching is part time thus impoverishing the family.…/ Constant state of defensiveness against being used for odd jobs while working at home/ Constant battle of own conscience against this.…/Social life mostly confined to a walk to the P.O. after work for money and bread…./ So selfimposition of martyrdom for a cause nobody wants/ Guilt at working for self without money generation… /Stabs in the stomach when things seen./ Sense of loss and guilt when not noted…./Why should anyone want the product?/ Totally peripheral to most people’s lives…/ Do it for oneself./ Not owed a living..…/ So you might say that the artist is rightly an outcast or at the least, an embarrassment to non-art friends – and maybe even a perceived threat to art friends./ The artist to himself is then a complex mesh of compulsion, guilt, and cold planning.
All right I do not necessarily agree with all this!
Sources
The sources of quotations from Kathleen Hyndman, unless otherwise described, are papers held by the family.
Hyndman, Kathleen, “My Use of Number Sequence and Geometry in Art”, Granada, University of Alhambra, ISAMABRIDGES, 2003, ed. Barrallo, Javier et al., pp. 567-568 http://archive.bridgesmathart.org/2003/bridges2003567.html
Sharp, John, Kathleen Hyndman’s Sequence Paintings, Mathematics Teaching, 161, December 1997, n.p.
This may sound like a stance within modern feminism. However, Hyndman is not easily characterised. In a letter published in the Artists Newsletter in July 1985, she speaks as someone who has “painted, drawn, taught and reared a family over many years”. She allows that feminism is “probably a necessary political background against which women can see themselves as capable of anything”. But she insists,
art is art, not anything else; it is, I think, an individual pushing of abilities towards aesthetic spiritual integrity… Graft art onto ideas of feminism or any other moralising and the result is diluted sub-art propaganda. Art’s message can be implicit in its integrity; it can be, but does not have to be, overt.
Her beloved art manifests for her a truth that is absolute and lies beyond politics and social matters.
Whatever the political and social realities, Kathleen Hyndman somehow succeeded in excavating time and place for single-minded concentration on her deeply engrossing works of art. This is her enduring gift to all of us.
Interviewed by Lizzie Collins: https://www.youtube.com/watch?v=Q6cPEV_8Xtk
Kemp, Martin., “Riddles of Form”, A Preliminary Look at Kathleen Hyndman’s Art of Mathematics in Spalding, Frances, Kathleen Hyndman, A Mathematical Artist and Her Lifelong Task, 2003 cat. pp. 7-10
Zuleika Gallery website www.zuleikagallery.com
Kathleen Hyndman (1928-2022)
Kathleen Hyndman was born on 12th January 1928 to parents Lilian and Douglas Blomfield in Brentwood, Essex. She later moved to Dorking, where she became head girl at Dorking Grammar School, and then trained at Kingston School of Art. She was awarded a scholarship to the Slade but turned it down, stating she wanted to do “something useful for other people”, and instead, studied teaching at the Institute of Education in London. After a spell of teaching, she entered the London County Council, and did very well in their internal promotion exam. There she met her husband to be, Michael.
The Hyndmans, now with two young children, moved to Kingston Bagpuize in 1967, where Kathleen continued to paint as well as being a part-time art teacher in the local schools and the Further Education college. Throughout her life, Kathleen had the support of her family, which enabled her to develop her vision of depicting nature in geometrical patterns and mathematical sequences. She was intrigued by the work of Mondrian, the golden section, prime numbers, the Fibonacci sequence and eccentric constructions. Using these, she created compositions that strove for a calm and balanced unity.
In 1977, Kathleen won an Arts Council Award and her work toured throughout the South East. In 1982, her work was selected for the Hayward Gallery Annual Exhibition, and in 2000, she was awarded a Millennium Fellowship for her early work about the Isle of Dogs. This was published as a special narrative and observation of life in the post-Blitz docklands; in addition, she was given a solo exhibition at The Space, a gallery on the Isle.
Throughout the ‘80s, ‘90s and ‘00s, Kathleen exhibited, both in the UK and internationally, in group and solo shows. More recently, in early 2022, the Zuleika Gallery presented Hyndman and Riley: The Rhythm of Life, and in 2023, Professor Frances Spalding curated Kathleen Hyndman: A Mathematical Artist and Her Lifelong Task at Clare Hall in Cambridge, a show dedicated to exploring her legacy and unique talent.
Martin Kemp, Emeritus Professor in the History of Art, University of Oxford
He was trained in Natural Sciences and Art History at Cambridge University and the Courtauld Institute, London. His books include The Science of Art. Optical Themes in Western Art from Brunelleschi to Seurat. He has published and broadcast extensively on Leonardo da Vinci. He wrote regularly for Nature, and his essays have been published as Visualizations and developed in Seen and Unseen (both Oxford). Recent books are Heavenly Visions. Dante and the Art of Divine Light’ and Hockney’s Eye. He is now full-time speaking, writing and broadcasting. He has been a Trustee of the National Galleries of Scotland, The Victoria and Albert Museum and British Museum.
Heat, 1976
acrylic on canvas
116 x 189 cm
Winter Afternoon, 1976
Acrylic on canvas
93.5 x 127 cm
Match Girl, 1976
acrylic on canvas
180 x 101 cm
Sand Shadow, Central Band, 1982
acrylic on canvas
74 x 117 cm
Lichen Covered Branches Over Stream, 1982
acrylic on canvas
133 x 79.5 cm
Stripe Shapes, c.1986 oil on board 84 x 50 cm
Long Triangle,1975
Acrylic on canvas
96.5 x 254 cm
List of Works
Riverweed, 1988
acrylic on paper
31.5 x 56.5 cm
12 ³₈ x 22 ¼ in
Visiting Fibonacci Monument and Square, 1999
acrylic on board
27 x 31 cm
10 ⁵₈ x 12 ¼ in
Counterpoint, 1973
acrylic on on board
83.5 x 114.1 cm
32 ⁷₈ x 44 ⁷₈ in
Purple Cloud and Reflection, 1978
acrylic on canvas
151.4 x 93 cm
59 ⁵₈ x 36 ⁵₈ in
Untitled (black and grey), 1989
acrylic on canvas
73.5 x 88 cm
29 x 34 ⁵₈ in
Hot Breeze, 1994
acrylic on canvas
114.5 x 109 cm
45 ¹₈ x 42 ⁷₈ in
Winter Afternoon, 1976
acrylic on canvas
93.5 x 127 cm
36 ¾ x 50 in
Sunshine and Tree, 1983
acrylic on canvas
73 x 102 cm
28 ¾ x 40 ¹₈ in
Stripe Shapes, c.1986
oil on board
84 x 50 cm
33 ¹₈ x 19 ¾ in
Rotation, 1987
acrylic on canvas
76.5 x 76.5 cm
30 ¹₈ x 30 ¹₈ in
Straight Line Rotation, White on Black Forest, 1986
acrylic on canvas
76.5 x 76.5 cm
30 ¹₈ x 30 ¹₈ in
Sand Shadow, Central Band, 1982
acrylic on canvas
74 x 117 cm
29 ¹₈ x 46 ¹₈ in
Exit (a seventeen sided work), 1993
acrylic on board
105 cm diameter
Match Girl, 1976
acrylic on canvas
180 x 101 cm
70 ⁷₈ x 39 ¾ in
Heat, 1976
acrylic on canvas
116 x 189 cm
45 ⁵₈ x 74 ³₈ in
Radiate/Glow, 1975
acrylic on canvas
122 x 114 cm
48 ¹₈ x 44 ⁷₈ in
Triple Eccentric Construction; Sun on Water (2), 1991
pen and ink on paper
48 x 48 cm
18 ⁷₈ x 18 ⁷₈ in
Long Triangle, 1975
acrylic on canvas
96.5 x 254 cm
38 x 100 in
Lichen Covered Branches
Over Stream, 1982
acrylic on canvas
133 x 79.5 cm
52 ³₈ x 31 ¼ in
Battersea - 4 Fibonacci Units; Counterpointed Colours, 2000
acrylic on canvas
96 x 82 cm
37 ¾ x 32 ¼ in
New York, 2001
acrylic on canvas
90.5 x 106.5 cm
35 ⁵₈ x 41 ⁷₈ in
Toothless, 1996
acrylic on canvas
57 x 57 cm
22 ½ x 22 ½ in
Glowing Stone (landing meteorite), 1996
acrylic on board
57 x 57 cm
22 ½ x 22 ½ in
Next to Short Ends and Tails Together, 1996
acrylic on board
57 x 57 cm
22 ½ x 22 ½ in
Smile, 1996
acrylic on board
57 x 57 cm
22 ½ x 22 ½ in
Exits Together, 1996
acrylic on board
57 x 57 cm
22 ½ x 22 ½ in
Extending the Points, 1996
acrylic on board
57 x 57 cm
22 ½ x 22 ½ in
Acknowledgements
I would like to thank the Mathematical Institute at the University of Oxford for hosting this exhibition. I would also like to thank Sarah Garwood for the beautiful graphic design for this catalogue and Tessa Jaray RA for her permission to use her images on page 10.
Thank you to Lizzie Collins whose unstinting advice has meant so much to me, and to co-curator Professor Martin Kemp whose research and essay has bought Kathleen’s work to a new audience.
Finally I would like to thank the family of Kathleen Hyndman, in particular Michael, Jim and Sophie and for their unwavering support in bringing this exhibition to fruition and honouring Kathleen in such a moving and meaningful way.
Maj (Retd) Philippa Phelan Curator, 2025
Front cover:
Detail: Radiate / Glow, 1975, acrylic on canvas, 122 x 114 cm
Inside front cover:
Detail: Exit (a seventeen sided work), 1993, acrylic on board, 105 cm diameter
Inside back cover:
Battersea - 4 Fibonacci Units; Counterpointed Colours,
2000 acrylic on canvas, 96 x 82 cm
Design by Sarah Garwood
