Al-Bīrūnī and Bhāskarāchārya

Abū Rayḥān al-Bīrūnī, a Persian scholar from Khwārizm (in today's Uzbekistan), was a mathematician, astronomer, geographer, historian and language expert all in one. He travelled widely and wrote, in Arabic and Persian, on almost every subject known in his time.

Around 1017, al-Bīrūnī came to India with Mahmūd's army. Instead of just looking on, he learnt Sanskrit, read Indian books and talked with Indian scholars.

The result was a huge survey of Indian religion, philosophy, literature, geography and science, often comparing them with Greek and Islamic ideas. He gathered what he could of the mathematics and astronomy of Āryabhaṭa, Varāhamihira and Brahmagupta, and translated Patanjali's Yogasūtras into Arabic.

He also recorded the damage the campaigns did. He wrote that Mahmūd 'utterly ruined the prosperity of the country' and scattered the people like dust, and that this is why Indian sciences had 'fled' from the lands 'conquered by us' to places 'which our hand cannot yet reach' — Kashmir, Varanasi and others. Notice he says 'us': he was on the invaders' side, and wrote it anyway.

Science did decline in north India a little later, but it kept flourishing elsewhere. Bhāskara II, better known as Bhāskarāchārya, born in 1114, probably in today's Maharashtra, was one of India's greatest mathematicians and astronomers, from a family of scholars.

His most famous works, all in Sanskrit:

• Līlāvatī — teaches basic mathematics through lively riddles and problems.
• Bījagaṇita — on more advanced algebra.
• Siddhāntaśhiromaṇi — 'Crown of Treatises' on mathematical astronomy.

Many later scholars wrote commentaries on his work, and some were translated into Persian in Mughal times, so his influence lasted long, in India and beyond. It took Europe a few centuries to rediscover some of his new methods.

Bhāskarāchārya was also a gifted poet who made his books fun, with clear examples, explanations and proofs; students loved them for centuries. One of his riddles: half of a herd of elephants and a third of that half went into a cave; a sixth, and a seventh of that sixth, drank at the river; an eighth, and a ninth of that eighth, played in a pond; and the king of the elephants led three females. How many elephants were in the herd?