Mathematics Logo

PRIMES: Ajay Saini's Story



For as long as I can remember, I have had an innate passion for problem solving. Early in life, my fascination with problem solving quickly propelled me towards an interest in math and later fostered my interest in computer science. I always enjoyed spending time thinking about and figuring out the solutions to mathematical and programming problems on my own. Fueled by a passion for problem solving combined with a deep interest in math and computer science, I immersed myself in competitions as a way to further my problem solving ability. However, even with all the interesting problems I worked on in both math and programming competitions, I always felt that there was something more I could do to enhance my problem solving experience. For me, performing research as a part of PRIMES gave me the experience I wanted.

Being part of PRIMES has definitely been one of the most rigorous, yet at the same time most fulfilling endeavors I have ever undertaken. Under the guidance of my mentor Dr. Natasha Markuzon, I worked on the project Modeling the Opinion Dynamics of a Social Network, which involved using data from real life scenarios to model the changes in a social network. Upon first beginning my research, I experienced firsthand how different the process was from my earlier problem solving experiences.

The greatest aspect of research is that you never know where your work may take you. Looking back on my experiences, I realize that problem solving can very well be described as walking along a road. In competitions, the road is often straight. You are given a problem with a known solution, and your goal is to find that solution. However, when performing research the road is often branched with many twists and turns along the way. Every new result opens up new paths for your research to follow, with each path having its unique intricacies and potential for new results. For me, the most exciting part of getting to conduct research was that the problem was not fixed but instead constantly evolved over time based off new findings. When I originally started working on my project, I thought I knew what direction the project would take throughout the process and had an end goal in sight. However, my research took an unexpected turn almost every step of the way. During our weekly meetings, my mentor and I always discussed alternative approaches to the project based off of current findings. New observations suggesting unexpected ideas would often come up, causing me to rethink my approach and make the necessary adjustments to what I was investigating. Consequently, I soon found myself immersed in an idea that had been scarcely touched upon in my research field. Knowing that I was researching a topic of interest that others had not significantly worked on made the prospect of discovering something new all the more exciting. When the time came to prepare to speak at the PRIMES conference, the presentation I had was significantly different from what I had originally thought. However, it was the fact that my final product was so different from what I had anticipated that pleased me the most. It showed that I had delved into unknown territory and discovered unique results.

PRIMES opened me up to a world of problem solving that I had previously thought was inaccessible to high school students. Performing research allowed me to experience what it is truly like to develop solutions to problems over long periods of time. Through PRIMES, I was able to experience my childhood passion for problem solving in a new, more practical setting. After working on my project, I feel as if I now thoroughly understand one of the most important lessons of problem solving: the most interesting and rewarding problems are those for which a solution does not already exist.

Being part of PRIMES is by far the most rewarding experience a high school student with an innate passion for problem solving and a willingness to work hard can go through. PRIMES provides high school students with a unique experience in that it allows them to experience problem solving in a way that is otherwise inaccessible. If you're a high school student who enjoys thinking about and solving problems, I wholeheartedly recommend PRIMES. It will be the greatest experience of your high school career.


Ajay Saini worked on the project Modeling the opinion dynamics of a social network under the mentorship of Dr. Natasha Markuzon.

Email us: