In January 2014, mathematical enthusiasts will be celebrating the ninth centenary of Bhaskaracharya, an Indian scholar and astronomer who is recognised as a mathematical genius of his time.

Of the books Bhaskaracharya wrote on the pure aspects of mathematics as well as on its applications to astronomy, the most appealing is Lilavati. It is believed that the title of the book came from the name of his daughter. The book illustrates the use of algebra, geometry and trigonometry with the help of several exercises. Those who think of mathematics as a formal, colourless subject would surely have second thoughts on reading this book. Take for example the following problem in which Lilavati is challenged to find the answer to the posed question:
At the base of a pillar is a hole housing a snake. The pillar is nine-hands tall and a peacock is sitting on it. The peacock saw the snake heading for the safety of its hole. Travelling at the same speed as that of snake, but in an oblique direction, the peacock caught the snake before it could reach its hole. If the starting distance of the snake was three times the height of the pillar, tell me, what was its distance when it was caught by the peacock?
Very little is known about Bhaskaracharya’s family but, clearly, Lilavati must have been a very clever girl to be able to face such questions. Indeed, it will not be an exaggeration to say that she is the first woman mathematician on record. In a society dominated by male scholars, women scholars are a rarity and, surely, Lilavati was unique.
Several centuries separate the era of Lilavati from that of European women who contributed to mathematics. Though it was a male-dominated period, a name that stands out amongst these women mathematicians is of Sonya Kovalevskaya in the 19th century. What inspired her to choose mathematics as a career? It is worth recalling an incident narrated by her in her autobiography, A Russian Childhood. When she was eight years old, Sonya’s family moved from south of Moscow to the countryside. This involved getting the new house painted and decorated. It turned out that the wallpaper ordered from a city firm was inadequate — by the time the turn of children’s nursery came, no wallpaper was left. Sonya’s parents thought that the children would not care for anything fancy, so they took the pages of an old mathematics book, which contained advanced maths like calculus, lying in the attic for decoration.
So Sonya and her elder sister Aniuta had the pages of mathematics book covering the walls of their room to look at. Looking at the formulae, Sonya was intrigued as to what they stood for. Inadvertently, she got introduced to various mathematical symbols. This introduction stood her in good stead when she later went to study mathematics in college. She was familiar with mathematical symbols and hence learning about them was an easy task. Her teachers were astonished at how easily she picked up new ideas. Sonya made several important contributions to advanced mathematics and is counted amongst the leaders in her field.
Another famous woman mathematician was Emmy Noether, who was at her best in the first quarter of the 20th century. She faced difficulty in getting recognition in a male-dominated society; important posts in the academia were denied to her. David Hilbert, the great mathematician of her time, tried to get her an academic position in Germany, but there was too much opposition to appoint a woman mathematician. This provoked his outburst at a faculty meeting: “I do not see that the sex of the candidate is an argument against her admission as an academic staff member. After all we are a university, not a bathing establishment.” In 1919, she was recognised as a staff member with the honorary title of unofficial associate professor without a stipend. Although she was denied her rightful position, her research work in algebra was hailed as path breaking.
The prejudice against women was widespread in Europe including Britain. For example, the oldest universities in England, Oxford and Cambridge, admitted women undergraduates but did not give them degrees. A woman undergraduate would only receive a certificate that she fulfilled the requirements of a degree. Perhaps, the following event from the 19th century will highlight the irony behind this situation.
The toughest examination in mathematics was the Mathematical Tripos at Cambridge. Those who scored a first class were called “Wranglers’’ and the student who topped the entire list was called the “Senior Wrangler”. The Senior Wrangler was highly regarded and was the first to receive the degree at the annual congregation. But in 1890, the highest scorer was a girl, Phillipa Fawcett. She was bypassed in the above listing and a boy who scored the next highest marks was declared the Senior Wrangler. Phillipa had, in fact, scored 13 per cent more marks than the officially declared Senior Wrangler. She had a successful career as a maths teacher. She also had the satisfaction of seeing the day when her university recognised women as suitable for a Cambridge degree.
It is indeed surprising that in India women were treated at par with men in the first three universities set up in 1857 by the Britishers in Bombay, Calcutta and Madras, while their own premier universities were prejudiced in this respect. In fact, several examples can be found in other subjects besides mathematics where academia in the West followed such practices either openly or covertly. In an autobiographical article, the distinguished woman astronomer Margaret Burbidge recalls how she was denied observing privileges in the Palomar Observatories, which then housed the world’s largest telescope. The reason? The observatory did not have women’s toilet on the premises.

The writer, a renowned astrophysicist, is professor emeritus at Inter-University Centre for Astronomy
and Astrophysics, Pune University Campus