Mathematician’s mathematician

Nikhil Shrivastava on why he thinks of math as magic

The Microsoft building in the posh Bangalore neighbourhood of Lavelle Road is swish. Some furtive peeps from the waiting area reveal glimpses of corporate rigidity mixed with money-no-bar interiors. In the middle of this, Nikhil Srivastava appears, not in pricey button-down shirts or designer jeans like the other employees, but in a T-shirt and comfortable shorts, clutching a cycling helmet in one hand.

New Delhi-born Srivastava, 30, and two others (mentor Daniel Spielman and Adam Marcus) cracked a proof that has been brain-worming math minds for half a century. Proving the Kadison-Singer conjecture has propelled these men into a rarefied crowd that finally culminated in them winning the George Pólya prize for 2014, given by the Society for Industrial and Applied Mathematics. An award for the mathematician’s mathematician, “it’s a prize that’s given for specific areas of mathematics that George Pólya himself was interested in. The Pólya prize makes you visible and makes your career options bigger. Companies such as Microsoft Research probably know about it, but it isn’t like the Fields Medal, which is known outside [the world of] mathematics”, says Srivastava in his halting, considered manner.

The trio had worked on the problem for almost five years, breaking it down into three parts, in which the first two parts involved proving that some polynomials (multiple-term algebraic equations) have real roots. The third part was to find the bounds of the real roots of the specific polynomial. There were periods of struggle, frustration, dead ends and false starts, but all through, there “was a lot of cool stuff happening”. The turning point came when they realised they needed to narrow down their many approaches to one, applying them to solve a simpler proof than the Kadison-Singer. Even here success took a few months. Once they realised how beautifully it worked, their new knowledge, buoyed by waves of confidence, helped them crack the actual proof. The impact of that has many future implications that remain to unfold. “There are no practical applications yet, but it comes down to improving some very basic facts about matrices. You can then include all kinds of things that use matrices such as graphs or signal processing and free transformation,” says Srivastava.

If you don’t understand this, like most people, there is no need to fear, says Srivastava, just as there’s no need to fear math itself. “There’s something about the way math is taught over here [in India]. What I see happening is that when people don’t understand something, they feel dumb. The state of not understanding is how it is most of the time, even for us. And, there is some cultural bias to just being able to quickly grasp stuff. So, it has to be taught in a way that it isn’t a problem to not understand something right away.”

Even Srivastava had his time of math-related despair as a teen. As a child his family moved a lot, following his diplomat father to all corners of the globe, for three-year postings, including Syria right after he was born. Later, following a couple of years of acing academia in the US, he returned to the pressure cooker that is the CBSE in India. He entered the ninth grade and scored a demoralising 77 per cent in his first math paper. “I was bothered by it. Because my self-image was that I was supposed to be good at it,” he says, In fact, there’s a bit of the reluctant mathematician in him. He’d wanted to be an astronaut and a physicist before a dynamic math advisor in his undergraduate course at Union College, New York, inspired him to change paths. “I remember one summer I was working on some research with Professor Alan Taylor and it was the first time I proved something new and I remember it felt awesome. I was so excited I couldn’t sleep. It became clear to me that it felt awesome to prove something. I don’t even have a PhD in mathematics, it’s in computer science actually,” he continues.

With his five-day stubble, dry humour, droopy eyes and cyclist garb, Srivastava’s constant self-deprecation and easy humility belie a sharp, curious mind. “The main reason I like to do math is because it’s beautiful. So, the kind of problems I tend to be attracted to is mostly for aesthetic reasons. I actually think of mathematics as magic — a hidden layer of reality,” he says.