Mathematics
Thomas Edwards Hankinson’s “Mathematics” is a brilliantly sustained comic complaint, but its wit should not obscure its genuine complexity. The poem stages an encounter with mathematics as though it were a reluctant courtship and, ultimately, an arranged marriage. The speaker is commanded by his father to “woo” a woman whom he finds aesthetically and temperamentally repellent, while being forced to abandon a former beloved whose beauty, musicality, and imaginative power have shaped his earliest happiness. At first glance, the premise appears merely playful: mathematical forms become bodily features, algebraic operations become social reconciliation, and the prospect of intellectual mastery turns into an absurdly ceremonial wedding. Yet the poem’s humor is inseparable from a serious meditation on education, obedience, desire, and the difficult relation between analytical discipline and imaginative freedom. Hankinson understands that the student’s resistance to an abstract subject can be emotional rather than merely intellectual. Mathematics is not simply difficult; she feels like an unwelcome demand upon the self.
The poem belongs to a long tradition of personifying knowledge. Classical and Renaissance writers frequently figured disciplines as women: Grammar, Logic, Rhetoric, Astronomy, and Music could appear as female allegorical figures in educational texts, paintings, and public architecture. Such figures were not intended as realistic women but as embodiments of distinct intellectual powers. Hankinson inherits this convention and gives it a sharply comic turn. Rather than representing Mathematics as a serene queen of the sciences, an elegant muse, or a majestic celestial intelligence, he makes her “peevish, cross, ill-natured,” squat, circular of face, and square of body. The description transforms the subject’s own visual vocabulary into caricature. Curves, circles, and squares do not remain neutral geometric properties; they become the supposedly ungainly anatomy of the speaker’s prospective bride. This is a schoolboy’s revenge upon a discipline that seems to demand more than it gives.
At the same time, the poem should not be reduced to a simple anti-mathematical statement. Its linguistic energy repeatedly demonstrates the speaker’s familiarity with mathematical terminology and his pleasure in making it serve poetic purposes. The speaker may resent Mathematics, but he is already thinking in her language. “Vinculum,” “extract,” “subtract,” and “equate” are not incidental technical flourishes; they organize the poem’s movement toward possible reconciliation. A vinculum, in mathematical notation, is a binding line or bar, as in a fraction or radical expression. To wish that two hostile parties might stand “beneath one vinculum” is therefore to imagine their relationship as something bound together by a shared sign. Likewise, to “extract each root,” “subtract our difference,” and “equate our hearts” converts operations of algebra into gestures of emotional repair. The speaker’s mockery becomes a form of mastery. He discovers, perhaps against his will, that the allegedly ungracious discipline can furnish a language for intimacy.
The historical setting implied by the poem is one in which education was closely tied to paternal authority, vocational expectation, and social advancement. The father’s command is absolute: “This is the wretch my father bade me woo.” The phrase compresses a familiar cultural pressure into the language of domestic obligation. A father’s instruction may represent literal parental authority, but it also suggests the broader authority of school, profession, and adult practicality. Mathematics was increasingly central to forms of education associated with navigation, engineering, commerce, surveying, military science, astronomy, and the expanding prestige of rational inquiry. Even for a student temperamentally drawn toward poetry, music, painting, or reverie, mathematics could appear as a necessary gatekeeper to adulthood. The speaker’s predicament thus extends beyond a private dislike of sums or diagrams. He confronts the question of whether one can remain faithful to youthful delight when social life requires useful knowledge.
The paternal command is particularly important because it casts study as a kind of marriage settlement. In the poem’s cultural imagination, marriage is not merely romantic fulfillment; it is also a contract, an obligation, and an arrangement that determines one’s future. To call Mathematics “the bride for me” means that the speaker is expected to bind himself to a subject he has not freely chosen. The language is deliberately exaggerated, but exaggeration clarifies the emotional stakes of compulsory study. A difficult discipline can seem to occupy all one’s time, command one’s loyalty, and estrange one from other pleasures. The joke works because an academic subject really can become a demanding companion: it insists upon repeated visits, punishes neglect, and yields affection only after labor.
Hankinson’s personification also needs to be read with historical care. The poem uses a comic convention in which an abstract noun is feminized and evaluated through the language of courtship, beauty, and marriage. Modern readers may reasonably notice that its descriptions rely on dismissive assumptions about women’s appearance and temperament. Mathematics is made grotesque by being imagined as a woman who fails conventional ideals of delicacy, grace, and beauty, while the preferred “airy spirit” embodies idealized feminine charm. The poem’s humor therefore draws upon gendered stereotypes embedded in its literary inheritance. Yet the allegory is more revealing than it is simply insulting. The “female” figures are not portraits of actual women but competing models of intellectual experience: one is angular, demanding, and disciplinary; the other is graceful, sensuous, and imaginative. Recognizing the convention allows readers to appreciate the poem’s ingenuity while also seeing how its inherited metaphors limit the human realities they invoke.
The contrast between the two feminine figures supplies the poem’s emotional center. Mathematics is characterized by weight, fixity, and visible form. She is “squat,” “stumpy,” circular, and square: a creature made from the solid shapes of elementary geometry. The language has a heavy, blunt physicality. Even the succession of adjectives seems to stumble forward, as if imitating the awkward gait that the speaker attributes to her. The other beloved, by contrast, is “bright and airy,” associated with voice, cloud, rainbow, sunbeam, and waves at evening. She moves rather than stands; she “steals softly” over the heart; she paints the heavens; she joins light to water. Hankinson thus establishes an opposition between the hard-edged world of measurable form and the mutable world of sensation and art. The first figure is defined by body and outline; the second by atmosphere, color, music, and touch.
The unnamed “airy spirit” is best understood not as one narrowly identifiable subject but as a composite emblem of imaginative delight. She may represent poetry, art, music, fancy, or the undivided playfulness of childhood itself. The poem intentionally leaves her broad enough to gather these associations. Her “rainbow-touch” recalls the painter’s art, while her “voice” suggests song or lyric poetry. Her marriage of “the sunbeam to the waves at even” evokes the visual splendor of sunset but also the poet’s power to make unlikely elements harmonize. This beloved is not merely attractive; she is creative. She turns perception into beauty and allows the speaker to experience the natural world as emotionally alive. If Mathematics is a subject to be learned through effort, the airy spirit is a mode of delight that seems to arrive spontaneously.
Childhood gives this second figure a special poignancy. The speaker calls her his “first” and “dearest joy,” “Youth’s fond companion,” and “childhood’s early toy.” The sequence moves from emotion to companionship to play. In this sense, the poem expresses a familiar anxiety about maturation: the fear that formal education and adult usefulness will displace the imaginative games through which a child first experiences wonder. The word “toy” is especially suggestive. It does not trivialize the airy spirit; rather, it identifies play as the source of an early and essential education. Before the father’s command, before disciplined courtship, before the pressure to become competent, there was the free movement of imagination. The speaker’s sadness lies not simply in preferring one school subject to another but in feeling that growing up requires the dismissal of a beloved companion.
This tension recalls a broad Romantic and post-Romantic unease about the relationship between scientific explanation and beauty. Poets of the period often worried that analysis might flatten or “dissect” experiences that art perceives as unified and alive. The rainbow is a particularly resonant image in this tradition: it can be an object of optical explanation, but it can also remain a marvel of color, transience, and imaginative suggestion. Hankinson’s rainbow-touch does not argue against knowledge; it asserts the value of a knowledge that is felt, pictured, and sung. The poem does not present the mathematical and poetic temperaments as equally empowered. The father has chosen Mathematics, and the speaker must comply. Still, by making the abandoned muse so vivid, Hankinson grants imaginative perception a lasting authority. The speaker may chide her away, but he cannot make her disappear from the poem.
The poem’s opening insults are comic examples of hyperbole. “Peevish,” “cross,” and “ill-natured” pile up with such insistence that the speaker’s vehemence becomes amusing. He seems less like a calm critic than a child protesting an unpleasant assignment. The description of Mathematics as “a curious animal” heightens the absurdity: an abstract science becomes an awkward creature inspected at a distance. This vocabulary of ridicule enables readers to recognize the speaker’s frustration without requiring them to share his judgment. Mathematics is not actually malicious or ugly, of course; these qualities are projections of his resistance. The poem therefore dramatizes the psychological experience of difficulty. What one cannot yet understand may seem hostile. What one is compelled to study may appear cold, stubborn, and personally unkind.
There is a subtle irony in the claim that the speaker has repeatedly tried “to win her kindness or awake her love.” Mathematics is conventionally imagined as impersonal: its truths do not yield to charm, pleading, or romantic effort. The student’s language misreads the discipline precisely because he desires a more reciprocal relation to it. He wants Mathematics to respond as the airy spirit does, with voice, tenderness, and beauty. But mathematics demands another kind of courtship. It requires patience, attention, repeated practice, and acceptance of rules that do not bend to mood. The speaker’s comic language reveals a serious educational insight: learning often begins with the wish that a subject might be easier, kinder, or more intuitively responsive than it is. Maturity may involve discovering forms of attachment that are not immediately pleasurable.
The appearance of “Carus” expands the poem from private complaint into a social scene. The name is likely meaningful in its Latin sense of “dear,” making “dear friend” almost a translation and affectionate reinforcement of the address. It need not point to a specific classical writer or historical person. Carus is someone who has previously “bask’d” in Mathematics’ favorable smile and has promised to visit the speaker. This friend may be a tutor, a more capable classmate, or simply a companion already initiated into the discipline. His role is that of mediator. Where the speaker’s own courtship has failed, Carus may “smooth down old quarrels” and “set new ones right.” The idea is delightfully absurd, but it recognizes that intellectual progress is often social. Teachers and friends can translate what feels alien, encourage persistence, and show that an intimidating subject has another face.
The central cluster of mathematical puns gives the poem its most remarkable imaginative achievement. “Extract each root” refers to algebraic extraction, yet the phrase also evokes pulling up the buried causes of resentment. “Mutual hatred” grows into a “deadly flower,” a natural image that makes hostility seem organic and invasive. “Subtract our difference” cleverly turns a mathematical difference into interpersonal disagreement, while “equate our hearts” imagines equality not as a merely numerical condition but as emotional balance. These metaphors do more than decorate the poem. They enact its argument. The vocabulary initially used to make Mathematics seem alien gradually becomes the means through which reconciliation can be imagined. The speaker’s language learns to cross the boundary he has established between arithmetic and feeling.
That movement complicates the apparent opposition between reason and imagination. Mathematics, in Hankinson’s poem, is not confined to dry calculation; it supplies an unexpectedly fertile figurative resource. Conversely, the airy spirit is not simply irrational. Her artistry consists in relations: she paints clouds, joins sunbeam and wave, and creates harmonies among elements. Both figures, in different ways, make connections. Mathematics links quantities through operations and signs; poetry links sensations through image and metaphor. The poem’s deepest possibility is that these are not absolutely incompatible modes of thought. The speaker begins by seeing only ugliness and separation. By the end, he can imagine a “vinculum,” a binding relation, and can use mathematical language with playful elegance. His very complaint becomes evidence that the subject he resists has entered his imagination.
The final invitation to a wedding retains the tone of mock resignation, but it is warmer and more generous than the opening attack. The speaker promises Carus the first slice of cake and as many kisses as he chooses to take. Such extravagance makes the speaker’s acceptance comic: he is willing to celebrate his unwanted marriage with remarkable hospitality. Yet the ending also suggests a genuine shift from hostility toward accommodation. The bride has not become beautiful in the manner of the airy spirit, and the speaker has not repudiated his first love. Rather, he has accepted that the relationship deserves a trial. The phrase “as I hope we shall” preserves uncertainty. Mathematics cannot be mastered through declaration alone; the marriage remains a future possibility, dependent upon work, mediation, and a change of feeling.
The poem’s emotional force emerges from this mixture of resistance and hope. Readers may laugh at the circular face and square body, at the prospect of mathematical marital counseling, and at the ingenious deployment of “subtract” and “equate.” But laughter is joined by the ache of relinquishment. The speaker’s brightest attachment belongs to childhood, to an art that feels like a first joy. His situation is recognizable whenever practical demands seem to threaten the activities through which one experiences beauty most fully. The poem does not sentimentalize this conflict into a simplistic declaration that art is good and mathematics bad. Rather, it acknowledges the cost of discipline while allowing wit to make that cost bearable.
“Mathematics” is especially appealing because it refuses to let abstraction remain abstract. Hankinson turns intellectual frustration into a miniature drama of family command, thwarted affection, friendship, negotiation, and prospective union. His comic personification gives geometric and algebraic terms a memorable physical and emotional life, while his descriptions of the airy spirit preserve the splendor of imagination even under pressure. The poem belongs to the enduring conversation between practical learning and creative freedom, but it approaches that conversation with unusual lightness. Its lesson is not that one must choose permanently between calculation and poetry. Instead, it suggests that the mind can complain, joke, mourn, and learn at once. Even an unwanted subject may, through the transforming power of metaphor, become part of the imaginative world it seemed destined to oppose.