A Mathematical Problem by Samuel Taylor Coleridge (Poem, Summary, & Analysis)

 

A Mathematical Problem

by Samuel Taylor Coleridge

(Poem, Summary, & Analysis) 

A Mathematical Problem

This is now--this was erst,

Proposition the first--and Problem the first.

 

I.

On a given finite Line

Which must no way incline;

To describe an equi--

--lateral Tri--

--A, N, G, L, E.

Now let A. B.

Be the given line

Which must no way incline;

The great Mathematician

Makes this Requisition,

That we describe an Equi--

--lateral Tri--

--angle on it:

Aid us, Reason--aid us, Wit!

 

II.

From the centre A. at the distance A. B.

Describe the circle B. C. D.

At the distance B. A. from B. the centre

The round A. C. E. to describe boldly venture.

(Third Postulate see.)

And from the point C.

In which the circles make a pother

Cutting and slashing one another,

Bid the straight lines a journeying go,

C. A., C. B. those lines will show.

To the points, which by A. B. are reckon'd,

And postulate the second

For Authority ye know.

A. B. C.

Triumphant shall be

An Equilateral Triangle,

Not Peter Pindar carp, not Zoilus can wrangle.

 

III.

Because the point A. is the centre

Of the circular B. C. D.

And because the point B. is the centre

Of the circular A. C. E.

A. C. to A. B. and B. C. to B. A.

Harmoniously equal for ever must stay;

Then C. A. and B. C.

Both extend the kind hand

To the basis, A. B.

Unambitiously join'd in Equality's Band.

But to the same powers, when two powers are equal,

My mind forbodes the sequel;

My mind does some celestial impulse teach,

And equalises each to each.

Thus C. A. with B. C. strikes the same sure alliance,

That C. A. and B. C. had with A. B. before;

And in mutual affiance,

None attempting to soar

Above another,

The unanimous three

C. A. and B. C. and A. B.

All are equal, each to his brother,

Preserving the balance of power so true:

Ah! the like would the proud Autocratorix do!

At taxes impending not Britain would tremble,

Nor Prussia struggle her fear to dissemble;

Nor the Mah'met-sprung Wight,

The great Mussulman

Would stain his Divan

With Urine the soft-flowing daughter of Fright.

 

IV.

But rein your stallion in, too daring Nine!

Should Empires bloat the scientific line?

Or with dishevell'd hair all madly do ye run

For transport that your task is done?

For done it is--the cause is tried!

And Proposition, gentle Maid,

Who soothly ask'd stern Demonstration's aid,

Has prov'd her right, and A. B. C.

Of Angles three

Is shown to be of equal side;

And now our weary steed to rest in fine,

'Tis rais'd upon A. B. the straight, the given line.

 

Summary

Samuel Taylor Coleridge’s poem “A Mathematical Problem” is a satirical and humorous take on the world of mathematics and its perceived complexity. In this poem, Coleridge weaves together nonsensical imagery, technical mathematical jargon, and a touch of absurdity to critique and mock the abstract and often incomprehensible nature of advanced mathematics.

The poem starts with an ironic tone, presenting the structure of a mathematical problem using formal propositions and problems. Coleridge begins with phrases such as "Proposition the first--and Problem the first," evoking the style of geometric proofs from Euclid’s Elements. However, as the poem progresses, it becomes clear that Coleridge is not genuinely exploring mathematical theory but rather parodying its intricacies and the ways in which it can alienate the layperson.

 

Throughout the poem:

Complex Language: Coleridge employs technical and pseudo-mathematical language that intentionally confuses the reader. By doing so, he mirrors the bewilderment people often feel when confronted with complex mathematics.

Absurd Imagery: The poet introduces surreal and nonsensical elements, such as references to imaginary lines and points, abstract shapes, and improbable scenarios, to highlight the detachment of theoretical mathematics from everyday life.

Satirical Undertone: Coleridge uses irony to suggest that mathematics, while logical and rigorous, can also become a meaningless exercise if not grounded in practical application or human understanding.

Mockery of Overcomplication: The poem subtly critiques the tendency of mathematicians or intellectuals to overcomplicate simple concepts. Coleridge implies that such over-intellectualization can turn something as beautiful as mathematics into an inaccessible and sterile pursuit.

 

Themes:

The Complexity of Knowledge: The poem explores the tension between specialized knowledge and its accessibility to ordinary people.

Absurdity and Humor: By employing nonsensical constructs and playful language, Coleridge emphasizes the humor in the overly serious treatment of abstract concepts.

Critique of Intellectual Elitism: The poem challenges the exclusivity of academic disciplines like mathematics, suggesting a disconnect between theory and practical value.

 

Conclusion:

In “A Mathematical Problem,” Coleridge blends wit and satire to critique the abstract nature of mathematics and its potential to confuse rather than enlighten. While the poem is not a literal engagement with mathematics, it serves as a commentary on the ways intellectual pursuits can sometimes lose sight of their purpose and become esoteric. Through his playful tone and imaginative approach, Coleridge invites readers to reflect on the balance between complexity and clarity in human thought.

 

Analysis

Samuel Taylor Coleridge’s A Mathematical Problem is a satirical and humorous work that reflects his skepticism about the rigid and overly abstract nature of mathematics. Through absurd imagery, playful language, and a critical tone, the poem delves into themes of intellectual elitism, the disconnection of theory from reality, and the role of creativity in human understanding.

 

1. Structure and Form

The poem mimics the style of a formal mathematical problem or proof, adopting phrases such as "Proposition the first" and "Problem the first." This structure mirrors the logical format of Euclid’s Elements, but Coleridge uses it to humorous effect by introducing nonsensical and absurd content. The formal tone juxtaposed with ridiculous scenarios creates a comedic contrast that underscores the poem's satirical nature.

 

2. Use of Language

Coleridge employs both mathematical jargon and nonsensical phrases to parody the exclusivity of mathematical language. For example:

The deliberate mixing of technical and absurd terms reflects the alienation many feel when confronted with advanced mathematics.

The mock-seriousness in tone highlights the irony of presenting an inherently ridiculous "problem" as though it were profound.

This approach suggests that mathematics, while valuable, can become inaccessible and impractical if it prioritizes abstraction over clarity.

 

3. Satirical Critique

Coleridge critiques intellectual elitism through his playful dissection of mathematical problems:

Overcomplication of Simple Concepts: The poem lampoons the tendency of mathematicians or scholars to over-intellectualize straightforward ideas, making them unnecessarily complex.

Disconnect from Practicality: By presenting problems that are absurd or irrelevant to real life, Coleridge highlights how excessive focus on theoretical concepts can lead to a lack of practical utility.

This critique aligns with Romantic ideals, which emphasize intuition, imagination, and human experience over cold rationality.

 

4. Romantic Perspective

As a Romantic poet, Coleridge often championed creativity and imagination. In A Mathematical Problem, he implicitly contrasts the rigid, formulaic nature of mathematics with the fluid, intuitive qualities of poetry and art. By highlighting the absurdity of purely logical pursuits, he reinforces the Romantic belief in the importance of balancing reason with emotion and creativity.

 

5. Themes

The poem addresses several key themes:

Intellectual Alienation: The technical jargon and abstract ideas in mathematics can create a barrier between experts and laypeople.

Absurdity of Over-Intellectualization: Coleridge suggests that excessive abstraction can render even the most logical discipline absurd.

The Limits of Reason: By parodying mathematics, Coleridge critiques the Enlightenment ideal that reason alone can explain everything, a common Romantic stance.

Imagination vs. Logic: The poem celebrates the unpredictability and whimsy of imagination, contrasting it with the rigidity of logical thought.

 

6. Tone and Humor

The poem’s tone is lighthearted and mocking, with an undercurrent of serious critique. The humor comes from Coleridge's ability to mimic the precise, dry language of mathematics while simultaneously subverting it with absurdity. This approach engages the reader, inviting them to question the seriousness of disciplines that take themselves too seriously.

 

7. Broader Implications

Coleridge’s playful yet critical tone reflects broader Romantic concerns about the increasing dominance of science and rationalism during his time.

The poem serves as a reminder that knowledge should remain accessible and relevant, and that creativity and practicality should not be sacrificed in the pursuit of intellectual rigor.

 

Conclusion

In A Mathematical Problem, Samuel Taylor Coleridge uses satire and humor to critique the abstract nature of mathematics and its potential to alienate rather than enlighten. By blending absurd imagery with a formal structure, he underscores the limitations of logic and reason when divorced from imagination and practical relevance. The poem is not just a playful dig at mathematics but also a broader commentary on the need for balance between intellectual pursuits and human experience