Indian mathematicians concerned about few takers for subject

"The number of takers for the subject in the country has over the past few decades reduced and this is leading to some kind of a crisis. This may affect the future of mathematical activity in the country," eminent mathematician from the Tata Institute of Fundamental Research Prof M S Raghunathan observed.

Many Indian mathematicians attending the ongoing nine-day International Congress of Mathematicians too have echoed similar concerns on the issue.
The increasing number of students preferring disciplines like engineering, information technology and management is leaving little number of wards for mathematical research, particularly in basic maths, they said.

It is a matter of concern that the number of bright students getting admitted to higher studies in mathematics is gradually coming down in India. Actually, in the past two-three decades the inflow of talented students opting for pure math studies has reduced and this is leading to some kind of crisis, Raghunathan said.

Bright students after their school education are seeking careers in engineering and medical courses for big salaries, he pointed out, adding, "hence we are not finding good quality (competitive) people to teach math at the higher levels."

According to the Clay Mathematics Institute the "P versus NP problem" is "determining whether questions exist whose answer can be quickly checked, but which requires an impossibly long time to solve by any direct procedure."

Here P stands for "polynomial time" and refers to a set of problems where one can find the solution in a reasonably quick time, while NP stands for "non-deterministic polynomial time" and refers to problems where one can easily verify it if a solution is given, says Sarkar.

Sanjit Chatterjee, a post-doctoral fellow at the Centre for Applied Cryptographic Research at the University of Waterloo, Canada, says the significance of the 'P versus NP' problem transcends the conventional border of computer science as many other branches of natural science have come up with related problems.
He says, "These include problems from various domains such as operations research, scheduling, logic, network design, computational molecular biology and optimisation problems."

Among the possible solutions for the "P versus NP problem" are either "P is equal to NP" or "P does not equal to NP".
"A proof that P is not equal to NP might not have a dramatic effect, but at a philosophical level it tells something about the limitation of the computing capacity," points out Chatterjee.

Indian mathematician, Vinay Deolalikar, Principal Research Scientist at Hewlett Packard Labs in California, had earlier this month brought out a research paper that claimed to have proved that P is not equal to NP.

However, his paper is currently under review and researchers in this area are suspecting that the proof may not be correct. Thus, the problem still remains open.
On the other hand, a proof that P equals NP might have more dramatic impact, though most mathematicians believe it was least likely, says Chatterjee.

He cites cryptography, the science of keeping a data secret.
"Security of many cryptographic techniques is based on the complexity of certain mathematical problems. P = NP will imply that there might be very efficient methods to solve such problems and hence those crypto systems become potentially insecure," he says.

The "P vs NP problem," formulated by Stephen Cook and Leonid Levin in 1971, is one of the seven Millennium Prize Problems of the CMI, which had instituted the one million dollar prize in 2000 for solving any of the seven problems.
Only one of the seven problems was solved by Grigori Perelman, a Russian mathematician, but he refused to accept the prize earlier this year.

Another delegate and author of several books on mathematics, T K V Iyengar, said,"The best students of maths at school and Intermediate level opt for engineering courses and hence the number of talented people opting for maths studies has gone down tremendously. This has affected the quality of student research in the subject."
Srinivasa Varadhan, a former mathematician at the Indian Statistical Institute and 2007 winner of the Abel Prize, said,"We need more people into basic research. Our best students are going into engineering or other careers, no doubt motivated by financial security. If more people were present and the number of basic research institutes was increased, the next 10-15 years would see more high-class work."

To promote youngsters who are interested in research in math, the ICM has sponsored the participation of 400 research scholars from across the country interested in attending the event, organisers said.