"Having bowed to the deity, whose head is like an elephant; whose feet are adorned by gods; who, when called to mind, relieves his votaries from embarrassment; and bestows happiness on his worshipers; I propound this easy process of computation, delightful by its elegance, perspicuous with words concise, soft and correct, and pleasing to the learned."
So begins Bhaskara‘s Lilavati in Henry T. Colebrooke‘s classic 1817 translation. There’s an earlier Bhaskara, also famous, so Lilavati‘s Bhaskara is sometimes referred to as Bhaskara II or Bhaksaracharya. He was born in 1114 A.D. in Vijayapura (modern day Bijapur), India.
It was a quiet time. The quiet, that is, of a hurricane’s eye. In 1114 A.D., Angkor Wat was still an idea searching for its stone, but its future builder, King Suryavarman II, was already a year old. Genghis Khan was just fifty odd years away. The West hadn’t rediscovered Euclid and Aristotle yet, but Abelard of Bath and his students were in Syria, poring over the Arabic texts that would eventually ignite the Western renaissance. The Muslims had gained a foothold in Gujarat, and in the 13th through 15th centuries, they were to reinvigorate the subcontinent. And way north of Vijayapura, about 400 miles from Delhi, the last of the magnificent Khajuraho temples were being built.
Why did Bhaskara write the Lilavati? Simple. To teach duffers. As he concludes in the Bijaganita (one of his six works):
"A morsel of tuition conveys knowledge to a comprehensive mind; and having reached it, expands of its own impulse. As oil poured upon water, as a secret entrusted to the vile, as alms bestowed upon the worthy, however little, so does knowledge infused into a wise mind spread by intrinsic force….What is there unknown to the intelligent? Therefore for the dull alone it is set forth."
Almost 600 years later, in his Decline and Fall, Gibbons was even more pessimistic:
"The power of instruction is seldom of much efficacy except in those happy dispositions where it is almost superfluous."
And more recently, the late Richard Feynman– by all accounts, a great teacher– cites Gibbons with glum relish in the preface to his celebrated Lectures.
The Lilavati is a collection of worked out examples in algebra and geometry. The level of mathematics ranges between high school algebra and freshman pre-Calculus. In its time, it represented the height of 12th-century mathematics. The problems are generally addressed to one Lilavati, traditionally taken to be either his wife or his daughter. Tradition is as good a reason as any because there’s no other reason to support the claim. To modern ears, the phrasing of some of the problems is decidedly odd. Problem 2.2.16 begins with:
"Beautiful and dear Lilavati, whose eyes are like a fawn’s…."
Then there’s Problem 3.1.49 which begins:
"Pretty girl, with tremulous eyes, if thou know the correct method of inversion… "
And how can I overlook Problem 3.5.68?
"The square root of half the number of a swarm of bees is gone to a shrub of jasmine; and so are eight-ninths of the whole swarm: a female is buzzing to one remaining male that is humming within a lotus in which he is confined, having allured to it by its fragrance at night. Say, lovely woman, the number of bees."
Colebrooke, thorough as always, notes that the "jasmine" referred to is the "jasminum grandiflorum." And Ganesa, in his Buddhivilasini (1545 AD), supplies some context: "the lotus being open at night and closed in the day, the bee might be caught in it."
Indeed. The good professor’s concern is not misplaced. The hazards of being a bee are many. For poor Colebrooke, the text must have made many a warm Calcutta night even warmer.