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Leelavati looked entranced at the water-clock her father had brought home. Its movements were fascinating. She had a slight feeling of guilt, for her father had told her never to enter that room. But because it was forbidden territory, its exploration gave her a sense of adventure. And she continued looking at the clock.
Then came disaster, though she was never to know about it. A tiny pearl slipped out of her nose-ring and fell into the clock. She was so alarmed that she fled. And in the excitement of the arrangements being made for her wedding the next day she forget all about the clock and the pearl. Which was not surprising for she was only six years old.
Leelavati was married, but a week later her husband fell off a cliff and died. This was what her father, Bhaskara, a great mathematician and astrologer, had feared. Astrological calculations had shown Bhaskara that, if the marriage of his daughter was not performed at a particular hour on that particular day, she would become a widow. And he had bought the water-clock to ensure that he would know the right time. He did not know that the pearl in it had made the clock inexact. And, going by that clock, he had made an error. Bhaskara thought that it was his astrological calculations that had gone wrong and blamed himself for the tragedy.
In those days, widowed girls were not allowed to marry again. Bhaskara, therefore, began to try to arouse her interest in mathematics, so that she would forget her grief. It is not known how good a mathematician she turned out to be, but he made her immortal in the history of mathematics in India by titling after his daughter a chapter of the book Siddhantasiromani that he wrote when he was only 30 years old. At one time there was even a popular saying: “Whosoever is well-versed with Leelavati can tell the exact number of leaves on a tree.”
The part of the book titled Leelavati dealt essentially with arithmetic. The other three parts were on different aspects of mathematics: Bijaganita dealt with algebra, Coladhyaya with spheres and Grahaganita with planetary mathematics. Basically the book was a text-book, a collection of the works of some eminent scholars like Brahmagupta, Mahavira and Sridhara, after they had been simplified to help students. The book contained problems presented in such a way as to stimulate the student’s interest. It was so popular and authoritative that four to five centuries later it was translated twice into Persian.
Bhaskara was an original thinker, too. He was the first mathematician to declare confidently that any term and infinity is infinity.
In algebra, Bhaskara considered Brahmagupta his guru and mostly extended Brahmagupta’s work. But his introduction of Chakrawal, or the cyclic method, to solve algebraic equation is a remarkable contribution. It was only after six centuries that European mathematicians like Galois, Euler and Lagrange rediscovered this method and called it “inverse cyclic". Determination of the area and volume of a sphere in a rough integral calculus manner was also mentioned for the first time in his book. It contained some important formulas and theorems in trigonometry and permutation and combination.
Bhaskara can also be called the founder of differential calculus. He had conceived it several centuries before Isaac Newton and Gottfried Leibniz, who are considered in the West to be the founders of this subject. He had even given an example of what is now called “differential coefficient” and the basic idea of what is now known as “Rolle’s theorem". Although Bhaskara attained such excellence in calculus, no one in the land took any notice of it.
As an astronomer Bhaskara is renowned for his concept of Tatkalikagati, which means instantaneous motion. This enables astronomers to determine the motion of the planets accurately.
Bhaskara was born in 1114 at Bijjada Bida (Bijapur, Karnataka) in the Sahyadri Hills. He learnt mathematics from his saintly father. Later, the works of Brahmagupta inspired him so much that he devoted himself entirely to mathematics. At the age of 69 he wrote his second book, Karanakutuhala, a manual of astronomical calculations. Though it is not as well known as his other book, it is still referred to in making calendars.
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