Tell me, charming woman: the algebra textbook written as poetry (1150 CE)

# Tell me, charming woman: the algebra textbook written as poetry (1150 CE)

Here is problem 54 of a twelfth-century mathematics textbook, in Colebrooke's 1817 translation, lightly repaired from scan artifacts:

> Out of a swarm of bees, one-fifth part settled on a blossom of > kadamba; and one-third on a flower of śilīndhrī: three times the > difference of those numbers flew to the bloom of a kuṭaja. One > bee, which remained, hovered and flew about in the air, allured at > the same moment by the pleasing fragrance of a jasmine and > pandanus. **Tell me, charming woman, the number of bees.** > > — *Līlāvatī* §54, Bhāskara II (1150 CE)

Work it: x/5 + x/3 + 3(x/3 − x/5) + 1 = x. The fractions sum to 14x/15, the lone hovering bee is the missing fifteenth, and the swarm is 15. The text then shows the solution by its own method (false position: assume 30, correct by proportion) and moves on to the next poem.

This is the *Līlāvatī* — the arithmetic textbook of Bhāskara II, head of the Ujjain observatory and the most complete mathematician of medieval India. It teaches place-value arithmetic, fractions, interest, permutations, plane geometry, and shadow-reckoning, and every problem in it is a Sanskrit verse: bees among blossoms, a pearl necklace snapped in a lovers' quarrel with pearls scattering in fixed fractions, peacocks pouncing on snakes, elephants ambling off into the forest, arrows in flight. Problem §68 runs the game in reverse difficulty — "the square-root of half the number of a swarm of bees is gone to a shrub of jasmine…" — a quadratic, still in bee-and-jasmine dress.

Who is the charming woman?

Tradition says: Līlāvatī was Bhāskara's daughter. The story — told everywhere, so it belongs here with its provenance attached — goes that her horoscope promised no husband; Bhāskara computed one auspicious wedding hour; a pearl from her headdress fell unnoticed into the water clock and stopped it; the hour passed unmarked, the marriage was off, and her father wrote her a mathematics book so that her name, at least, would live forever.

Honesty about sources: that story is documented nowhere in the 12th century. It first appears in the preface Fyzī attached to his Persian translation of the *Līlāvatī* — made at Emperor Akbar's court in 1587, four hundred and thirty-seven years after the book. It may be true, it may be court-preface romance; the platform's job is to label it *legend*. What the text itself attests is the address: problem after problem turns to a woman — "charming woman," "fawn-eyed one," "friend" — as the student being taught. Whoever she was, the book is written *to* her, and a Sanskrit mathematics curriculum framed as conversation with a woman is itself a noteworthy artifact of 1150.

Why verse?

Not decoration — infrastructure. Sanskrit technical education ran on memorization, and meter is error-correcting: a dropped syllable breaks the scansion and announces itself, the way a checksum flags a corrupted file. A student who memorized the *Līlāvatī* carried the entire arithmetic curriculum, worked examples included, with no paper required. The poetry is also pedagogy in a second sense — the bees and necklaces make abstract quantity concrete, which is exactly the modern textbook's word-problem strategy, executed with considerably better prose.

The honest comparison: verse mathematics is not uniquely Indian. The Greek Anthology preserves arithmetic epigrams (Diophantus's own epitaph is a linear equation in disguise), Alcuin posed riddle problems for Charlemagne's court, and Chinese and Islamic traditions dressed problems in stories too. The Indian distinction is scale and institutional standing: the *Līlāvatī* is not a garland of puzzles appended to serious work — it *is* the serious work, a complete standard curriculum in poetic register, and it held that status across the subcontinent for roughly 700 years. Sanskrit colleges were still teaching from it in the 19th century when Colebrooke translated it; Fyzī had translated it into Persian three centuries before that.

Legacy

The *Līlāvatī*'s afterlife is the measure of the design. Hundreds of manuscript copies survive — among the most-copied scientific texts of the medieval world. Commentaries accumulated for centuries. Two Mughal-era Persian translations carried it into the Islamic world's curriculum. And when the East India Company's scholars went looking for Indian mathematics, this was the book everyone handed them — which is why Colebrooke's 1817 volume, the source text for this claim, pairs it with Bhāskara's algebra.

Bhāskara the poet and Bhāskara the mathematician were one working system: the same book that asks about bees also [divides by zero and names the result](/c/bc2f3ce7-9321-5405-8fae-9e56ff80f6b2), and its companion volume [solves equations Europe wouldn't crack for another five centuries](/c/e9b99c06-981f-5f4d-8628-0357df5417f0). The charm was never at the expense of the content. It was the delivery system — and it delivered for seven hundred years.

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Sources

- [Colebrooke, *Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara*, 1817](https://archive.org/details/1817-henry-colebrooke-algebra-with-arithmetic-and-mensuration-from-the-sanskrit-of-br) — Līlāvatī §54 and §68 cited. - Plofker, *Mathematics in India*, 2009, ch. 6 — Bhāskara II and the textbook tradition (secondary synthesis, for context). - Fyzī's Persian *Līlāvatī* preface (1587) — the source of the daughter legend (referenced to date the legend, not as fact).

Related claims

- [Bhāskara II divides by zero — khahara (1150 CE)](/c/bc2f3ce7-9321-5405-8fae-9e56ff80f6b2) - [Bhāskara II's chakravala method (1150 CE)](/c/e9b99c06-981f-5f4d-8628-0357df5417f0) - [Bhāskara's one-word Pythagorean proof: "Behold!" (1150 CE)](/c/5f7f63c3-d3b2-5e95-b44a-02eedd5073af)