KATHLEEN HYNDMAN: a Mathematical Artist and her Lifelong Task

KATHLEEN HYNDMAN

A MATHEMATICAL ARTIST AND HER LIFELONG TASK

ABOVE Isthmus, 2002 Acrylic on canvas, 100 x 177cm.

COVER IMAGE Counterpoint, 1973 Acrylic on board, 83.5 x 114.1cm

Published to accompany the exhibition Kathleen Hyndman: a Mathematical Artist and her Lifelong Task at Clare Hall, Cambridge, 24 November 2023 to 11 January 2024.

For more about Clare Hall’s mostly modern and contemporary art collection, visit clarehall.cam.ac.uk/art/

INTRODUCTION

C

L A R E H A L L is proud to present the work of Kathleen Hyndman (1928-2022).

For the opportunity to do so, our thanks go to her husband and her daughter, Michael Hyndman and Sophie Hyndman Robertson. We are also indebted to Lizzie Collins, Founding Director of Zuleika Gallery, and her team, for their encouragement, support, and attention to detail. But the catalyst behind this event has been Professor Martin Kemp. His discernment of the importance of Kathleen Hyndman’s work, on first seeing it in the Zuleika Gallery at Woodstock, was communicated to us by letter and ignited our interest in this artist.

If Kathleen Hyndman’s name has been missing from artistic narratives in recent years, her art nevertheless continues to call for attention. It has appeared in a handful of Zuleika shows, including a solo exhibition, celebrating her 90th birthday in 2018, which was presented by Oxford University’s Saïd Business School. Clare Hall hopes to enhance further interest in her work with this memorial exhibition, which opens exactly a year after her death. We are pleased that Martin Kemp has gifted our catalogue with an original essay on the role of mathematics in Hyndman’s art. And we also welcome the short preface by the internationally renowned sculptor, Nigel Hall, in which he recounts his delight in the discovery of Kathleen Hyndman’s work.

She herself trained at Kingston-on-Thames School of Art, and afterwards pursued an active professional life as a painter. This began in the 1970s, and despite having a very full family life, involving two children, and working as a teacher of art, she managed to follow developments in abstract art, and exhibited in this country and abroad. She adopted a constructed and sequential approach, describing her method in simple terms: ‘My work often originates from natural effects: mountains or trees in the mist, shadows, movement of water, etcetera. I transpose theses visual stimuli into various geometrical and arithmatical sequences of tone, colour, rotations, interval and shape, and refine this until they seem right.’ As can be seen in the picture on the opposite page, one of her tools was the Fibonacci sequence. But all her pictures aim to achieve what Mondrian called a ‘dynamic equilibrium’, something calm and balanced but immensely alive, and with no false move in colour, tone or position. Following a conversation with the artist in her studio, the Zuleika Gallery discerned a search for an absolute or ‘truth’ in her exploration of the interrelation between mathematics and art.

She was grateful to David Elliott, Director of the Museum of Modern Art, Oxford, for his encouragement. He advised her to get into contact with the artist Jean Spencer. Kathleen had seen her work in ‘Colour Presentations’ at Swiss Cottage Library a year or two before. When writing to Jean she recollected: ‘Your work seemed very pure in its theoretical application of construction/ colour; mine is rather different, as you can see.’ She enclosed some slides of her work and then added: ‘I have been working in the constructivist sphere for many years and Richard Demarco, Annely Juda, Oliver Bevan and Peter Dormer have all seen recent actual work and much like it.’

As a result of this letter, Kathleen was invited to join a group of some ten constructivist artists who had formed a ‘Postal Academy’ for the sharing of texts and information. She accepted.

‘Thanks again,’ she replied to Jean, ‘for your energetic letter - it will be interesting to see how the “Academy” develops.’

Professor Frances Spalding, CBE, FRSL November 2023

3

RIGHT Ravensmere, Beccles, 1951 Oil on canvas, 39.7 x 32cm BELOW Sunshine and Tree, 1983 Acrylic on canvas 73 x 102cm

4

P R E FA C E

W

HE N I was first introduced to the work of Kathleen Hyndman by Lizzie

Collins I was astonished, partly by its freshness and invention but equally that she was a name quite unknown to me.

The two early works, Bomb Damage from 1949 and Ravensmere, Beccles from 1951, I find striking in their formal interpretation of a complex scene. She brings colour and beauty to unexpected subjects. Her incorporation of nature, the built environment and street furniture create a language that I understand and find echoes of in my own work.

As these early works evolve into abstraction, they carry with them the DNA of her formative years and keep her (and us) in touch with the world of observation. This shows strongly in the wonderful ‘weather’ paintings, ‘Sunshine and Trees’, Rain, Mist… and Snow Falling. They stand both as totally satisfying non-figurative works but also as true portraits of their subjects.

Every work is filled with vibrancy, rhythm and a delight in the world. They seem to express a perfect synthesis of head, heart and eye. How wonderful to have this late introduction to such a

ABOVE Bomb Damage, Schooner St, Isle of Dogs, London, 1949 Oil on canvas, 35 x 35.7cm

profound body of work.

Nigel Hall, RA October 2023 5

RIDDLES OF FORM A PRELIMINARY LOOK AT KATHLEEN HYNDMAN’S ART OF MATHEMATICS

BY MARTIN KEMP, FBA

G

ALILEO famously said, “the book of nature is written in the language of

mathematics”; or rather, in Il Saggiatore (1623), he wrote that Philosophy is written in this grand book — I mean the Universe — which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics.

The same philosophy permeates key aspects of Renaissance and post-Renaissance art, most notably the Euclidian geometry of perspective. In the 20th century, the naturalistic basis of perspective was largely abandoned by mathematically-minded artists in favour of geometrical abstraction. We might think most obviously of Piet Mondrian – or closer in space and time, of Bridget Riley, with whom Hyndman was in touch. Looking at the evolution of Mondrian’s art, we witness his progressive geometricising of nature – typically, skeletal trees with pronounced patterns of branching – to the point of total abstraction. But a specific sensory stimulus can still reassert its presence, as when he responds to New York in his masterpiece of pictorial jazz, Broadway Boogie Woogie in 1942.

Yet Hyndman’s paintings, drawing and prints have a different look and feel from Mondrian, Riley and other committed practitioners of pictorial mathematics. The prime reason is that she founded her abstractions on numbers as much as geometry. As Hyndman wrote, she “explored arithmetical sequences and geometry as a means of distributing motifs, shapes, colours. Golden Section proportions and angles, prime numbers, Fibonacci numbers and eccentric constructions”.

The golden section arises 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. In the 19th century it had been shown that the golden ratio has wide resonances. For instance, it corresponds to the increasing volume inside a spiral sea shell and to the numbers in the Fibonacci series, named after the mediaeval mathematician, Leonardo Fibonacci. His series was envisaged across 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 begins: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… As the sequence progresses, so the ratio of each successive term more closely approaches that of the golden section. Prime numbers, still

PIET MONDRIAN Broadway Boogie Woogie, 2022 Oil on canvas, 127 x 127cm.

Museum of Modern Art, New York.

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.

Arithmetical and geometrical series, beloved of Hyndman, could be understood as imminent across the whole spectrum of nature. This was the vision of the great Scottish biologist and man of letters, D’Arcy Wentworth Thompson in his On Growth and Form in 1917, the supreme text on the mathematics of natural processes and configurations. Thompson was well regarded by British artists, particularly with those associated with St Ives. This embeddedness in nature and its science distinguishes British painterly abstraction from that practised in the USA.

OPPOSITE Abstract – UNTITLED, c. 1998 Acrylic on canvas, 38.5 x 20.7cm.

7

Hyndman’s works often begin from a compelling perception in nature, such as her observation of “the light of an early morning hazy sun around apple tree twigs”. The branching patterns were synthesised into right angles and then Y shapes, “which are used in various formats of prime numbers”. The Ys are standardised within rectangles twice as high and as wide. One series places them in the positions of prime numbers on a 5 x 9 grid reading from left to right. They await her creative manipulation, which they duly receive here, dancing with each other.

We gain insight into her instinctive interventions and rational thought if we read Kathleen Hyndman’s own descriptions of her work. For instance, on Visiting Fibonacci Monument and Square (Fig.1) she writes: Pyramid of eight layers of vertical lines starting with one and continuing downwards through the succession of Fibonacci numbers to 34. Then halving the height of the verticals repeating the succession of Fibonacci numbers in reverse down to one. The halving of the height of the vertical lines gives a different slope to the lower part of the pyramid. Two colours used in Fibonacci sequence starting with 2 at the top so avoiding perfect symmetry.

Untitled (Y reverse), c. 1988 Acrylic on paper, 63 x 15cm.

Fig. 1 Visiting Fibonacci Monument and Square, 1999 Acrylic on board, 27 x 31cm.

And of Gulls and Flags (Fig. 2), with its improvised music, she writes: In centre area each prime number quadrilateral is marked with a smallish rectangle (flag) in pink, pale pink, mid-pink or orange; a quadrilateral adjacent to each flag is black, within it is a white arrow (gull) pointing towards nearest flag. All flags have lines linked vertically with colour of flag above the link, the lines do not pass through the black areas. Where the lines Fig. 2 OPPOSITE Gulls and Flags, 2003-2010 Acrylic on canvas, 123 x 70cm.

8

cut across a quad they turn it into two triangles, each triangle is treated as a whole unit in the sequencing of the colours. Five different blues, one green and one grey are sequenced. First sequence: saturated colours and grey rotate on the spaces adjacent to black squares – they

9

Fig. 3 OPPOSITE Narrow Zig Zag, 1998 Acrylic on canvas, 72.2 x 44.8cm.

sequence from right to left and back again alternately. They go from colour 1-7, 1-7 but leave out colours 6 and 7 on second and every alternate repeat. Then 1 to 5 missing 6 and 7 but adding green and grey. Second sequence: colours a little lighter. Similar sequences as first sequences but starting 7-1 etc. leaving out green and grey on 2nd and alternate sequences.

The role of the seen never becomes a set formula in the genesis of Hyndman’s patterns.

Sometimes, as in Narrow Zig Zag (Fig. 3), the process seems centred on what the picture itself is telling her: Three rhomboid units: one with red edges and yellow middle, one blue edges red middle and one black edges blue middle. These are strong primary colours plus black and where they partially overlap, give hints of secondary colours. Construction: red/yellow unit upright; blue/red unit has common top point but is swivelled from this so that bottom point is to the right; black/blue unit has common bottom point with blue/red unit but is swivelled out so that it is to the right of the previous top point.

Her ultimate choices are never slaves to the maths. The status of the maths and aesthetic choice is akin to the compositions of J. S. Bach. The Art of Fugue – relying upon a single subject varied in each canon and fugue – has both a remorseless structure and an insistent human dimension that are comparable to Hyndman’s mission. She sometimes used musical titles.

She insisted on the personal and intuitive as the final determinant.

Subjective choices are made as to which variety or conjunction of constructive ideas, and which colours, are used to parallel the initial visual perception. One idea can produce a series of work.

Interrelations within the work and to the whole aimed at achieving a calm balanced unity. So each work has a visual message only. It aims to be a visual version of “truth”; an attempt to make no false move – so colour, tone value, shape all belong together. This can be seen in the visual work of untutored young children.

A question.

Do we need to understand Hyndman’s mathematical procedures to appreciate her paintings?

The answer is that we do not need undertake mathematical analysis to appreciate the beauty of a turbinated sea shell or the packing of seeds in a sunflower head. The maths is necessary for nature’s operations, just as it is for Hyndman’s creative processes. It is not necessary for our acts of looking. But it is remarkable, as are the truly notable results.

I do not know if Hyndman knew D’Arcy Thompson’s book – it is difficult to think that she didn’t – but he provides what is the perfect quote for her enterprise. It is worth citing at some length.

The physicist proclaims aloud that the physical phenomena which meet us by the way have their manifestations of form, not less beautiful and scarce less varied than those which move us to admiration among living things. The waves of the sea, the little ripples on the shore, the sweeping curve of the sandy bay between its headlands, the outline of the hills, the shape of the clouds, all these are so many riddles of form, so many problems of morphology, and all of them the physicist can more or less easily read and adequately solve: solving them by reference to their antecedent phenomena, in the material system of mechanical forces to which they belong, and to which we interpret them as being due. They have also, doubtless, their immanent teleological significance; but it is on another plane of thought from the physicist’s that we contemplate their intrinsic harmony and perfection, and “see that they are good”

Martin Kemp, 2023 Further reading on Kathleen Hyndman’s use of mathematical sequences can be found in John Sharp, ‘Kathleen Hyndman’s Sequence Paintings’, Mathematics Teaching Nº 161, Dec. 1997 10

11

12

CLOCKWISE FROM LEFT Four Colour Triple Shift, 1998 Acrylic on canvas, 72.2 x 41cm.

Not Quite Reflections, c. 1999/2000 Acrylic on board, 23.5 x 33.5cm.

Roosting Starlings: Marazion: Meeting, 1999 Acrylic on board, 54 x 70cm.

13

ABOVE Winter Afternoon, 1976 Acrylic on canvas, 93.5 x 127cm.

RIGHT Two Trees, Screenprint 51 x 46cm OPPOSITE Stripe Shapes, c. 1 973 Oil on board, 84 x 50cm.

14

15

Water Garden, 1978 Acrylic on canvas, 139.7 x 83.8cm.

16

Purple Cloud and Reflection, 1978 Acrylic on canvas, 151.4 x 93cm.

17

Damp Breeze, 1977 Acrylic on canvas, 135.5 x 118cm.

18

City, 1966/7 Acrylic on board, 70.2 x 101.1cm.

19

Kathleen Hyndman 1928-2022

Snow Falling, 1989 Acrylic on paper, 60 x 40cm.

Herschel Road | Cambridge | CB3 9AL

T +44 (0) 1223 332 360 | E art@clarehall.cam.ac.uk DESIGNED BY WAYNE SUMMERS