In 2008, software company Infosys established a prize for outstanding mathematical research in India. It went to Manindra Aggarwal, a computer scientist at the Indian Institute of Technology ( IIT) in Kanpur, who had developed a sophisticated algorithm to quickly check whether a number is prime or not. Theoretical computer science and mathematics have fuzzy borders between them. Aggarwal’s work had solved a long-standing problem in mathematics.
Next year Infosys established the Infosys Science Foundation and expanded the awards to include the physical, social and biological sciences. For the mathematics prize the jury chose Ashok Sen, a brilliant physicist at the Harish Chandra Institute in Allahabad, who had made fundamental contributions to string theory.
Theoretical physics and mathematics also have fuzzy boundaries in many areas, and the jury had no qualms about awarding the mathematics prize to an outstanding physicist. No one would have grudged Sen a prize, but not everyone was sure his work was in mathematics.
In 2010 the jury could find no such people across the intellectual borders. So they travelled all the way to California in the US. The Infosys mathematics prize in 2010 went to Chandrasekhar Khare, professor of mathematics at the University of California in Los Angeles.
Khare had worked for some years at the Tata Institute of Fundamental Research (TIFR), and so he was not a pure foreign product. But the jury went to the US last year as well, awarding the prize to Kannan Soundararajan, professor of mathematics at Stanford University. Both Khare and Soundararajan are reputed number theorists.
In four years of awards, the jury could not find a pure mathematician under the age of 50 working in an Indian institution for an award. “My standards are high,” says the mathematics jury chair Srinivas Varadhan, professor of mathematics at the Courant Institute in New York. “I am not impressed by mathematics currently done here in India.”
The Infosys Science Foundation had set extraordinarily high standards of achievement as a condition for the award, and the jury would rather search for Indians abroad than lower their standards.
Varadhan is one of the most distinguished mathematicians in the world, having earned his PhD from the Indian Statistical Institute under CR Rao, arguably the finest living statistician. He had then moved to the famous Courant Institute where he became the director while making fundamental contributions to probability theory.
He had won several prizes including the Abel Prize, sometimes described as the mathematician’s Nobel Prize. The Indian government had honoured him with Padma Bhushan, and last year US president, Barack Obama, gave him the National Medal of Science, the highest honour bestowed on a scientist in the US.
Varadhan is probably the most well-known among a large number of contemporary mathematicians who had grown up in India but later moved to the US. They have made a big mark on the mathematics scene in the US, and they are now being joined by another set of Indian-origin mathematicians who have grown up in the US and are creating outstanding mathematics.
When Narasimhan and many of his colleagues at TIFR were in their prime in the 1960s and 1970s, going abroad was not in the air. The best mathematicians flocked to the TIFR and the ISI and remained there through most of their careers.
Rao worked in ISI for 40 years before retiring and moving to the US. Narasimhan, MS Raghunathan and CS Seshadri in TIFR were at one time known to be among the best mathematical minds in the world. Seshadri is now 80 and the others are in their late 70s. Subsequent generations of mathematicians did not quite reach this peak, and there is a general sense in the mathematical community that the subject has declined in India.
This fact is not easy to establish but there are indications that point to a decline. The opinion of the Infosys Prize jury is an indication and so is the absence of major prize winners in India. An Indian mathematician working in India is yet to win a major international mathematics prize like the Fields Medal, the Abel Prize or the Wolf Prize; the closest approach was made some time ago by the trio of Narasimhan, Seshadri and Raghunathan who were all elected Fellows of the Royal Society.
India is at the 14th place in the world pecking order in terms of the number of mathematics papers published in the past 10 years and 22nd in terms of citations in the same period. During the past decade, the Indian National Science Academy (INSA) has been struggling to get nominations for electing mathematics fellows, while it gets a large number of nominations for physics, chemistry and the biological sciences.
The interest of Indian students in participating in the International Math Olympiad has been declining over the years. “We are concerned at the state of mathematics in India,” says INSA president Krishan Lal.
It may be easy to pick holes in this argument. Many brilliant mathematicians finish their careers without getting a major award. Mathematicians form a small community, and so it is relatively more difficult to find nominations for fellowships.
Performance in the International Olympiad is not necessarily an indication of mathematical ability in a student. Mathematicians do not take citations in research papers as seriously as do the physicists and biologists. And so on. However, all these factors when combined tell one story: Mathematics in India has declined over the past three decades while Indian mathematicians performed extremely well abroad.
This decline has affected the development of science and technology in India. Large areas of mathematics go unrepresented in the country’s research landscape, and Indian R&D organisations use few mathematicians when compared to those in the developed countries. One glaring omission is applied mathematics, which has rapidly expanded in recent decades and widely used in many areas of industry.
At the time of independence, despite the tremendous reputation of Srinivas Ramanujam, mathematics in India was not in a state of good health. This was partly due to absence of quality institutions for mathematics education and research, with the possible exception of ISI. This situation had led Harish Chandra, India’s greatest modern mathematician (if you leave out Ramanujam), to leave the country in search of intellectual stimulation.
Nehru had perceived the vacuum as much as anybody and had pushed senior scientists and mathematicians to start new institutions. This led to the founding of the TIFR mathematics department in the 1950s and the creation of some outstanding mathematics for about three decades.
Aspiring mathematicians of high calibre in India sought out the TIFR for their research career. By the 1970s, however, a curious phenomenon started showing up. High-quality mathematicians began to leave the country to work in the US, both from ISI and the TIFR. These included Varadhan, VS Varadarajan, V Lakshmibai, Pavaman Murthy and others.
This effusion created a vacuum at the top in Indian mathematics, which also meant that a young generation of mathematicians who are now working in Indian institutions lost the chance to be trained by other distinguished mathematicians in the country. Beginning from the 1990s, however, India began to lose mathematicians at an even younger age.
This list includes Sucharit Sarkar (now at Columbia University), L Mahadevan (at Harvard), and Kannan Soundararajan, who had left India for his undergraduate education in the US. The list would be longer if you include those who are applied mathematicians. “At that time there were no good institutions in India for undergraduate education in mathematics,” says Soundararajan.
However, this story could have a happy ending. Like in the 1950s, when India created TIFR, the past two decades have seen the creation of a number of quality institutions. It includes the Chennai Mathematical Institute (CMI) and the Institute of Mathematical Sciences (IMS), both in Chennai, and the Harish Chandra Research Institute in Allahabad.
All the three institutions have attracted talent and have started producing good mathematics. The IISc has strengthened its mathematics department during the past decade, with the return of many mathematicians from the US.
“There is instability if mathematics is confined to one institute,” says Seshadri, who had headed both the institutions in Chennai. “But new institutions have now started producing a strong middle class in mathematics.” We will wait for the middle class to start producing the stars.