Kaneenika Sinha studies the properties and patterns of special numbers as an assistant professor of mathematics at the Indian Institute of Science Education and Research (IISER) in Pune. An enthusiastic science communicator, she unpacks tricky mathematical concepts for non-math folks in articles frequently published in leading newspapers and popular media.

**What drew you to mathematics and when did you know that you wanted to make a career of it?**

I enjoyed mathematics in school. It was my favorite subject, but I didn’t think about making a career of it at that point. My ideas of career choices then were more influenced by my parents’ suggestions and what people around me did. When I was in college, however, I started attending workshops outside of the college curriculum conducted by people who were researchers in the field of mathematics. That’s really when I realized that you can actually “do” mathematics for a living, and decided to pursue it.

To me, this also really shows how important outreach is. Had these people just chosen to sit in their offices and work, many young people like me would have never been exposed to this world of mathematics.

**Can you give us a flavor for the problems you think about and work on?**

I am a number theorist, and in particular I am an analytic number theorist. In general terms, I study prime numbers—numbers that don’t have any proper divisors.

One of the oldest questions that fascinated mathematicians was whether there was a pattern to prime numbers. Another interesting question was simply how many primes are there? This basic question was answered by Euclid, who showed that there are infinite prime numbers.

Following this, the questions became more refined. So, for example, suppose I give you a big number, let’s say a million, and asked how many prime numbers are there up to a million. Is there a formula for that? And as you go up to 10 million or a billion, do the prime numbers become sparse? This question really is the birth of analytic number theory.

In understanding these patterns, and proving conjectures made about these numbers, many new mathematical techniques have been discovered over centuries. And the techniques developed led to the branch of analytic number theory. Now you don’t have to restrict yourself just to prime numbers. There are many other interesting sequences and one can ask similar questions about their distribution patterns. While investigating such questions, one discovers surprising connections with other innate properties of the sequences.

**What do we learn by studying these special numbers and their patterns? Do we encounter them in our daily lives?**

Oh yes we do! Our modern-day usage of credit cards or any online transactions has to be done in a secure way, which happens to use prime numbers. So, you need a method where the user can feed the information easily, and the bank or online vendor has a way of receiving this information, knowing it has come from a genuine source. Meanwhile, nobody should be able to intercept the information in the middle. The techniques used for online interactions to achieve this go back to what is called the RSA method, an algorithm that depends upon are prime numbers.

I recently wrote an article that, among other things, explains an important application of prime numbers to safe internet transactions.

**You write a blog. When you began, it was a first-hand account of a young researcher who had just returned to India and started her academic tenure. Tell us a little about why you started it.**

When I came back to India, I was happy with my choice of job and the Institute was very welcoming, but I was still a little nervous because I had lived in Canada for almost a decade. I was a bit apprehensive about the kind of social pressures I would face and the effect on my career. However, my fears were mostly unfounded. What I noticed instead was that a faculty position brings newfound confidence. You feel very empowered. It becomes very exciting. My blog was basically an expression of that excitement.

**Apart from writing the blog you also make an effort to communicate mathematics to a broad audience. Is this challenging?**

I think it takes a willingness to spend some time to think about what is the best way to communicate ideas. Giving talks is a good starting point. Occasionally somebody who is not a mathematician may attend and ask questions that get you thinking about how you would communicate with them. Conversely, when you attend others’ talks, you really learn how to express ideas to people and what clicks—what engages people rather than turns them off. Also, one has to spend some extra time, but it is really worth it. Often, people who believe in science communication are people who have benefited from it themselves.