Devangshu Datta: Zero in on maths

India will do well to tackle red tape that hobbles its academia and encourage its mathematicians to build ties abroad

Despite Ramanujam, Varadhan and a host of other talented Indian mathematicians, the subject occupies little space in public consciousness. There is even a rancid joke to the effect that India invented the zero and after that, India’s contribution to maths is zero.

It was never true. But many talented Indian mathematicians work abroad, with a few exceptions such as Manindra Agrawal, Neeraj Kayal and Nitin Saxena, the trio that generated the AKS Primality Test at IIT, Kanpur.

There are few opportunities for locals to interact with practitioners based elsewhere. The recently-concluded International Congress of Mathematicians (ICM) in Hyderabad was a good first effort at breaking the ice.

ICM started in Zurich in 1897 at the behest of the International Mathematicians Union (IMU). India hosted the quadrennial event for the first time. Incidentally, IMU also elected its first-ever woman president, Ingrid Daubechies of Princeton.

Every seminal maths problem, including a vast array of applied problems, has been ventilated at the ICMs. But as Oswald Veblen once explained, the ICMs are “ not congresses of mathematics, that highly organised body of knowledge, but of mathematicians, those rather chaotic individuals who create and conserve mathematics”.

The “killer app” is that academics get ample opportunity to meet informally. They discuss not only papers they’ve published but also discarded drafts and blind alleys. The value of that interaction cannot be quantified. An unstructured conversation may lead to a big collaborative effort or insightful breakthroughs.

Massively collaborative efforts like Tim Gower’s Polymath Project and Stanford-Berkeley’s MathsOverflow Project are now common. The Polymath Project solved the Density Hales-Jewett theorem (which had defeated everyone for years) in 37 days in an online effort, involving 800 people, who collectively signed off as “DHJ Polymath”. The use of social networking techniques completes a circle because those applications are built on mathematics.

Events like ICM create preconditions for future collaboration. Of course, the agenda is structured around the valedictory with the handing out of awards and prizes. The biggest award is the Fields Medal. The Fields carries only $15,000 in monetary terms. But it’s the Nobel-equivalent for mathematicians. It is only awarded to somebody under 40. No Indian has ever won.

There was some excitement when 39-year-old Vinay Deolalikar claimed a solution to the “N Vs NP problem” in early August, just days before the ICM. N Vs NP is one of seven “Millennium Problems”, in which the Clay Mathematical Institute offers a $1 million award. Unfortunately Deolalikar’s proof was flawed.

The Fields winners were Cedric Villani (France), Ngo Bao Chau (Vietnam), Elon Lindenstrauss (Israel) and Stanislav Smirnov (Switzerland). Other awards included the Rolf Nevanlinna Prize for work in computer science to Danny Speelman (US), and the Gauss Prize for applied maths to Yves Mayer (France), as well as the new Chern Prize for lifetime achievement, to Louis Nirenberg (US).

Another new award was the Leelavati Prize (named after Bhaskara’s Sanskrit textbook) for “outstanding public outreach” to Simon Singh, (“Fermat’s Last theorem”, “Codebook”). The Kenneth May prize for work on the History of Mathematics went to Radha Charan Gupta for his history of “desi” trigonometry in “Mathematics in India”.

A couple of events piggybacking ICM generated publicity, some negative. One was the brilliant theatrical adaption of Ramanujam’s life story in “A Disappearing Number”, which was performed by Complicite in several locales.

Another was the needless controversy over the citizenship of world chess champion Viswanathan Anand. Anand, who gave a simultaneous display against 40 mathematicians, was due to be awarded an honorary PHD before the HRD Ministry tied itself in bureaucratic knots.

This was a sad reversion to the sort of red tape that hobbles Indian academia. The Government of India (GoI) is generally tardy in processing applications from foreign academics. It did a good job for ICM but it has to get better at bread-and-butter work-permit clearances.

Despite India’s mammoth technical pool, it has few pure research institutes like TIFR, IISC and ISI. There is little pressure to publish, given time-bound promotions. This creates a vicious circle with a small local pool isolated from the mainstream.

If India’s policy makers wish to change this situation, they must create conditions in which the best want to come and work here. They must also help India academics to interact more easily and build ties abroad. Visas are only part of the problem, of course.

The myth of the borderline lunatic, mathematical loner persists and it’s perpetrated by geniuses like Grigori Perelman and John Nash. Everyone knows about Nash and his beautiful mind. Perelman who has refused to accept either the Millennium (for solving the Poincare Conjecture) or the Field Medal, is famously reclusive.

They’re exceptions. It is no accident that most of awardees at ICM 2010 have worked in several countries. It is normal for papers to be co-authored, to be published online and thus, open to multiple peer-review.

ICM demonstrated that the Indian mathematical community enjoys meeting up with their global counterparts. The fruit of such associations will only be apparent over time. One hopes that the GoI’s strong support in hosting ICM was not an aberration but a signal of a new policy that encourages more intimate contact.