कथा कौतुकम् - 12 - लीलावती
Bhāskara II’s Līlāvatī is presented both as a major Sanskrit mathematics text and as a work repeatedly addressing a girl named Līlāvatī with affection. The famous story of a pearl disrupting her marriage timing is identified as a later legend, while the surviving verses themselves demonstrate how mathematical problems, numerical encoding, and personal address were woven together in the text.
Article compiled by Harsha M Krishna
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अद्य गणितस्य कथा। किन्तु हृदयस्य अपि कथा। 💙 adya gaṇitasya kathā. kintu hṛdayasya api kathā. (Today, a story of mathematics. But also a story of the heart.)
द्वादशे शतके भास्कराचार्यः नाम गणितज्ञः आसीत्। dvādaśe śatake bhāskarācāryaḥ nāma gaṇitajñaḥ āsīt. (In the 12th century there was a mathematician named Bhāskarācārya.)
तस्य एका पुत्री आसीत् — लीलावती नाम। tasya ekā putrī āsīt — līlāvatī nāma. (He had a daughter — named Līlāvatī.)
तेन एकः गणितग्रन्थः लिखितः। तस्य नाम लीलावती। tena ekaḥ gaṇitagranthaḥ likhitaḥ. tasya nāma līlāvatī. (He wrote a mathematics book. Its name is Līlāvatī.)
तस्मिन् ग्रन्थे सः प्रश्नान् कस्मै पृच्छति? स्वपुत्रीम्। 🥺 tasmin granthe saḥ praśnān kasmai pṛcchati? svaputrīm. (In that book, whom does he ask the questions to? His own daughter.)
"हे बाले, हे मृगलोचने, लीलावति — वद।" "he bāle, he mṛgalocane, līlāvati — vada." ("O child, O deer-eyed one, Līlāvatī — tell me.")
कुतः? तत्र एका दुःखकथा अस्ति। 👇
In English — the legend 💔
Bhāskara II was the finest mathematician of the 12th century, head of the observatory at Ujjain — and, as scholars then were, also an astrologer.
He cast his daughter Līlāvatī's horoscope, and what he read frightened him: she would never marry, and never have children.
So he did what a father who believes in the stars would do. He calculated one single auspicious moment — the only instant at which her marriage could succeed.
To catch it exactly, he built a water clock: a cup with a tiny hole in its base, floating in a vessel of water. It would fill and sink precisely at that hour.
He placed it in a room and told her: do not go near it.
She went near it.
Leaning over to look — as any curious girl would — a pearl slipped from her bridal dress and fell into the cup.
It plugged the hole.
The cup never sank. The moment passed unmarked. The wedding never happened.
And then her father did something extraordinary 🌸
He could not give her a marriage. So he gave her the only thing he had — his work.
He named his greatest book after her, wrote her into it on nearly every page as the person being spoken to, and told her why:
a good name is a second life.
He was right. Nine hundred years later, we are saying her name in a WhatsApp group. 🙏
📖 श्लोकाः — Now let's actually read him
१. मङ्गलाचरणम् — The opening verse
प्रीतिं भक्तजनस्य यो जनयते विघ्नं विनिघ्नन् स्मृतम् तं वृन्दारकवृन्दवन्दितपदं नत्वा मतङ्गाननम् । पाटीं सद्गणितस्य वच्मि चतुरप्रीतिप्रदां प्रस्फुटाम् संक्षिप्ताक्षरकोमलामलपदैर्लालित्यलीलावतीम् ॥१॥
"Bowing to the elephant-faced Lord, whose remembrance destroys obstacles and whose feet the gods revere — I now set out the method of true mathematics: clear, delightful to the discerning, in words gentle and pure and few — graceful and playful."
⚠️ Look at the last word: लालित्यलीलावतीम्.
It means "graceful and charming." It is also her name.
He signed his daughter into the opening verse of the book, where it reads as an ordinary adjective. Nobody but the two of them would have noticed. 🥹
(Metre: शार्दूलविक्रीडित)
२. The addition problem — verse 13
अये बाले लीलावति मतिमति ब्रूहि सहितान् द्विपञ्चद्वात्रिंशत्त्रिनवतिशताष्टादश दश । शतोपेतानेतानयुतवियुतान् चापि वद मे यदि व्यक्ते युक्तिव्यवकलनमार्गेऽसि कुशला ॥१३॥
"Ah, child Līlāvatī, clever girl — tell me the sum of 2, 5, 32, 193, 18, 10 and 100; and tell me also what remains when that is taken from ten thousand — if you are skilled in the ways of addition and subtraction."
Answer: the sum is 360; 10,000 − 360 = 9,640.
(Metre: शिखरिणी. He changed the metre between problems — arithmetic in different music.)
३. The multiplication problem — verse 17
बाले बालकुरङ्गलोलनयने लीलावति प्रोच्यताम् पञ्चत्र्येकमिता दिवाकरगुणा अङ्काः कति स्युर्यदि । रूपस्थानविभागखण्डगुणने कल्पासि कल्याणिनि छिन्नास्तेन गुणेन ते च गुणिता जाताः कति स्युर्वद ॥१७॥
"O child, O Līlāvatī with the restless eyes of a fawn — tell me: the number measured five-three-one, multiplied by the sun — how much is it? If you are able, auspicious girl, do it by splitting into places and parts; then split by that same multiplier and tell me what results."
Answer: 135 × 12 = 1,620.
🔍 Where are the numbers? Look again: पञ्च-त्र्येक-मिता → five, three, one → read right to left → 135 दिवाकर → "the sun" → the Ādityas are twelve → 12
The numbers are hidden as words — exactly the bhūtasaṃkhyā system we saw on Day 4. A mathematics problem written so that it reads as poetry.
And notice: he doesn't just want the answer. He asks her to solve it three different ways and check that all three agree.
That's not a father being sentimental. That's a teacher.
He even hid his own birthday 🎂
रसगुणपूर्णमहीसम शकनृपसमयेऽभवन्ममोत्पत्तिः । रसगुणवर्षेण मया सिद्धान्तशिरोमणी रचितः ॥
रस = 6 (the six tastes) · गुण = 3 (sattva, rajas, tamas) · पूर्ण = 0 (the full circle) · मही = 1 (there is one earth)
Read right to left: 1036 — in the Śaka era → 1114 CE. His birth year.
And रसगुण = 36 → "I composed the Siddhānta Śiromaṇi at thirty-six." ✨
Why it matters beyond the story 📐
Līlāvatī is no lightweight. It is the first volume of the Siddhānta Śiromaṇi — "Crest-Jewel of Accuracy" — with 272 verses across 15 topics, including an entire section on the rules of zero.
It gives the first full systematic treatment of the decimal system, names place values up to 10¹⁷, and approximates π ≈ 3.141666 using polygons of up to 384 sides.
It was India's standard mathematics textbook for roughly 800 years.
In 1587, Emperor Akbar ordered his poet laureate Faizi to translate it into Persian — and it is in Faizi's preface that the pearl-and-water-clock story first appears.
India's national award for excellence in communicating mathematics to the public is the Leelavati Award, presented at the International Congress of Mathematicians.
⚠️ Honest note: the water-clock story surfaces first in that 16th-century Persian translation — some 400 years after Bhāskara's death. Historians treat it as legend.
But this part is not legend. Open the book and the verses really are addressed to a girl, again and again, with tenderness: बाले (child), कल्याणिनि (auspicious one), मतिमति (clever one), मृगलोचने (deer-eyed).
Whatever happened with the pearl, a 12th-century master spent his life's work talking to his daughter. 🌸
नाम्नः एव द्वितीयं जीवनम्। A good name is itself a second life. 🙏
अद्य कः श्लोकं १३ गणयति? 🐝 Answers below — and whoever spots the hidden name in verse 1 first, take a bow. 👇