In her poem ‘A Woman in Love’, the mathematician and poet Sarah Glaz describes herself as seeing ‘a streak of mathematics/ in almost everything’. The title of her collection of mathematical poetry, Ode to Numbers, is taken from a poem by the Chilean poet Pablo Neruda which invokes the passion of mathematical curiosity, the urge to understand the mysteries of the universe in quantified terms, the desire ‘to know/ how many/ stars in the sky’(Neruda, 1999).
Ode to Numbers is divided into five sections, representing different stages of Glaz’s personal, emotional and intellectual development. The opening section draws on her childhood experiences. The second section, entitled ‘Pythagoras Plays His Lyre’, explores a number of mathematical topics, mainly from an historical perspective. ‘Serendipity’ focuses on her work and academic career as a mathematician, while the fourth section takes us on an intellectual and emotional journey through a range of locations. The final section, ‘Euclid’s 5th Postulate’, is both reflective and retrospective.
The starting point is ‘Close to the Origin’, in which the x and y axes of Cartesian geometry denote the endless potential of childhood:
‘The day stretches its lazy golden arms interminably long and elegant like x and y axes.’
A ‘band of gold’ suggests the O that mathematicians place at the axes’ intersection to denote the origin, but also invokes a wedding ring, a symbol of union, ‘the source from which everything springs’. The staggered layout and short, uneven stanzas have the effect of slowing the poem down, delicately conveying a child’s perception of time.
‘Trains’ is addressed to a ‘you’ who, we assume, is Glaz’s childhood self, setting out on a train journey. Perhaps this was the emigration with her parents from Romania, where she was born and spent the first few years of her life, to Israel. The train ‘chugging along as if there is no tomorrow’ serves as an objective correlative that represents a journey from the known to the unknown, a metaphor for the process of mathematical discovery as well as for life’s trajectory. Sensory details are vividly described, with deft use of poetic devices such as consonance, assonance and onomatopoeia: ‘iron spokes/ clang-strike sparks/ on steel tracks in your brain’. As the child presses her face against the windowpane she observes how geometric patterns are formed by the condensation of her breath.
‘You correct their shape
with one finger: star,
octagon, circle, flat helix.’
This is a tender, touching image of how the child turns to geometry to keep her emotions in check, to impose some sense of order in a disordered world.
The image of a journey (often, but not always, a train journey) recurs throughout the collection. It forms the subject of a poem at the heart of the book (‘The Journey’) that describes the process of doing mathematics and, like ‘Trains’, addresses the second person. The poem’s opening line – ‘You wait till the unconscious makes the unknown known’ – could apply equally well to writing poetry as it does to doing mathematics. The creative process is envisaged as a fantastic landscape in which mathematical formulations appear as colourful flowers: ‘blue is for lemmas, orange for corollaries’. It is, as Daniel May notes, ‘a beautiful, synesthetic depiction of mathematics’.
There is a marked shift in tone as we progress through the collection. ‘Late Arrival’ also features a train, but instead of the youthful intellectual drive expressed in ‘Trains’ there is a sense of regret, of failed ambition: ‘The train lost its axle,/ the tracks derailed the engine’. In the eponymous poem of the final section, ‘Euclid’s 5th Postulate’ Glaz invokes an axiom of classical geometry to develop a striking image of her dual preoccupations, words and numbers, as trains that initially run smoothly on parallel tracks (neatly represented by the use of couplets). Ill health and life’s ups and downs drain her of energy and she is obliged to become an observer rather than a participant in mathematics:
‘Today I only drive the engine of words, and it is getting harder to watch neglected numbers jump over tracks and barriers like wooly sheep and let the whoosh of passing trains brush their coats.’
Many of the poems in the second and third sections of the collection are overtly mathematical in content. ‘The Enigmatic Number e’ is a tour de force, summarizing with great clarity and succinctness the history of our understanding of one of the most significant numbers in mathematics. Boldly, Glaz uses mathematical formulae, so that this is very much a poem by a mathematician for mathematicians:
‘In retrospect, following Euler’s naming,
e lifted its black mask and showed its limit:
𝑒 = lim𝑛→∞(1+1/𝑛)𝑛
Bernoulli’s compound interest for an investment of one.’
‘What Can We Do If We Crave Certainty in Mathematics?’ explores the impact of Gödel’s Incompleteness Theorem, which essentially demolished the accepted understanding of mathematics as a complete and logically consistent system. Glaz captures the sense of despondency among mathematicians as they considered the implications of Gödel’s result:
‘Nothing was pure logic. Pure logic was nothing. We could not even count on knowing what truth can be proved. Uncertainty permeated everything.’
Keats, with his belief in negative capability, would have rejoiced!
The poems in the second half of the collection tend to focus more on the process of doing mathematics than on the mathematics itself. Their emotional richness and depth belie the common perception of mathematics as dry. In ‘Commutative Coherent Rings’, addressed to an unspecified You, Glaz reflects on the source of inspiration for her seminal mathematical book on abstract algebra:
‘You bestowed on me the knowledge of Your secrets and let me play for You the music of the spheres.’
Elsewhere a new research project is compared to a newborn baby that ‘surprises you with the amount of work it asks/ for.’ Glaz is honest, too, about the sense of frustration and disappointment when research leads to a dead end: ‘Somewhere along the way,/ I took a wrong turn,/ and found confusion’ (from ‘No Matter What I Do’).
For me, the most striking poems are those that draw parallels between poetic and mathematical creativity. Daniel May observes that ‘To choose mathematics, or poetry, or both, is to choose a lifetime of searching, always chasing those few moments when everything falls into place like magic’. ‘Like a Mathematical Proof’ describes beautifully such a moment of inspiration, when one sets aside any ‘irritable reaching after fact & reason’.
‘A poem courses through me like a mathematical proof, arriving whole from nowhere, from a distant galaxy of thought.’
Given poetic forms such as the pantoum are defined by the mathematical combinations of lines within stanzas, and several are featured here. In ‘Mathematical Modeling’ the pantoum form elegantly suggests the iterative process used to develop and refine a mathematical model. This matching of content and form is a feature of Glaz’s work, particularly evident in some of her most adventurous and playful poems, those with a distinctively mathematical structure.
In ‘ln√2 = 1.41421’, the number of lines per stanza is determined by the successive digits of the decimal expansion in the title. The poem is a playful reimagining of the death of Hippasus, reputedly thrown overboard form a ship by his fellow Pythagoreans for proving that √2 is an irrational number (i.e. it cannot be expressed as a fraction).
‘13 January 2009’ is what is known as a factor poem, a form developed by Carl Andre (1978). A factor poem is structured according to the Fundamental Theorem of Arithmetic, with a particular phrase assigned to each prime number, and non-prime numbers expressed in terms of their prime factors. ‘13 January 2009’ applies this technique to the numbers 1 to 13 (in descending order) and the shifting combinations of repeated phrases give the poem a sonorous, bleak melancholy.
‘On the Way to New Jersey in Winter of 2000’ is a Fibonacci poem in which each stanza is a single line containing a Fibonacci number of syllables in sequential order. The final line extends to 144 syllables. The poem, describing yet another train journey, is a delightful interweaving of the mathematical and the visual. The ‘I’ persona observes a group of immense cylindrical oil containers from the train window and muses on how to model the pollution they might cause – yet she still finds them ‘beautiful beyond belief. All bathed in morning light, scrubbed pink and clean, powdered, disrobed and Rubenesque.’
The final poem in the collection, ‘Reflection about the t-Axis’, returns us neatly to the beginning, with its reference to coordinate geometry. Instead of the x and y axes of two-dimensional space, however, the poem is symmetrical about the origin of an imagined t-axis. The left segment of the poem stretches back into the past, the right segment into the future, and they meet at the origin, the present. Simply, concisely and poignantly, ‘Reflection about the t-Axis’ makes the point that as children we look forward to a future full of exciting possibilities whereas in the later stages of life we yearn for the past.
Glaz’s poetry is infused with warmth, wisdom and wry honesty. By the end of Ode to Numbers we feel that we know the author on a personal as well as an intellectual level. Through reading her poetry we can, as Eveline Pye observes, ‘experience some of the emotional aspects of studying mathematics; a huge leap of the imagination for many.’
Glaz, Sarah (2017) Ode to Numbers. Simsbury, Connecticut, Antrim House.
Selected poems from Ode to Numbers and other works can be read via Sarah Glaz’s personal page.
Andre, Carl (1978) “On the Sadness’, in Glaz, Sarah, and Growney, JoAnne (2008) Strange Attractors: Poems of Love and Mathematics, (eds) Wellesley, Massachusetts, A.K. Peters Ltd.
Neruda, Pablo (1999) ‘Ode to Numbers’ from Selected Odes of Pablo Neruda (translated by Margaret Sayers Peden). California, University of California Press.