Kedar Karhadkar is not just a typical student at Harriton High School, but has been acclaimed by many of his peers as, “Harriton’s Math God.” Winning a gold medal in Academic Decathlon States, being the highest scorer in both the Pennsylvania Math League Competition and American Mathematics Competition, and getting qualified for the American Invitational Mathematics Competition, there is no wondering why Karhadkar was the most popular student recommended for Ram of the Week for his mathematical talents. We were able to sit down with Karhadkar for an interview.

Harriton Banner: Since when did you become so interested in math?
KK: I’ve been interested in math for as long as I can remember. I’ve always been interested in patterns, numbers, and logic, so it was my favorite subject in school since kindergarten. But I think that my interest in it grew by a lot in eleventh grade when I started teaching myself real analysis. That was when I started to get a true understanding of what math was, and do it much more for fun.

HB: How did you become so good at math?
KK: I improved in math in the same way that anyone gets good at anything; I just worked on it for a long enough time. I always try to challenge myself with problems that I have never seen before and are just slightly harder than what I am used to. When working on math, there’s certain types of reasoning that one develops that makes solving problems much easier. As you build this sort of reasoning enough, the tools that you have at your disposal are much better.

HB: What math classes at Harriton have you benefited from the most?
KK: Well, I moved to Harriton in tenth grade, so I certainly haven’t experienced as many math classes in this school as some other people have. But I think that Senior Seminar was by far the most beneficial class that I took, because it was much different from the average high school class. I feel that a lot of math classes in high school encourage a bunch of arcane techniques without caring why they are true or why they are significant. Seminar comes much closer to the exploration and challenges that are present when working on math. The class focuses much more on challenging problems and developing mathematical intuition, which I believe are extremely useful skills to have.

HB: There’s definitely a difference between being good at something and enjoying something. Do you truly love math as much as you are talented in it?
KK: Definitely. The only way that one can become good at anything is by dedicating a lot of time to it, which usually requires that you enjoy what you are doing. The ability to do math is not a talent that someone is born with or picks up overnight; the only reason I can do it is because I spend so much of my spare time on it. I also think that my interest in math increased greatly as I learned more of it. Being able to see the nuances of a subject allows you to appreciate it much more.

HB: What has been your most challenging moment in mathematics?
KK: It’s hard to pin down one particular moment, but there was one that really stood out to me. In ninth grade, there was a guest speaker at my school who presented us with the following equation: 2^x = 15 (mod 101). (Here, the modulo just means that when you take the remainder when you divide 2^x by 101, you get 15. So, for instance, 5 = 2 (mod 3)). He asked us if we could verify if solutions existed, and whether there was a way to find them. I did the naïve thing at first and just tried as many values for x as I possibly could, until I got an answer. But the difficult part of this question eluded me; how can you know when an equation like this even has solutions? For instance, if you are taking powers of 3 modulo 9, you get 3, 0, 0, 0, … and never hit anything else. I thought about this for quite a bit of time, which allowed me to find some cool patterns. The process of thinking about problems like this one is really the challenge and the heart of math.

HB: What is your favorite number?
KK: -1, because some of the coolest and most beautiful parts of math are found in inverses. If you think about the real numbers under multiplication geometrically, it’s the nicest one, since it’s a reflection and keeps looping back to itself. It’s also a very powerful number in the sense that if you know something about all positive numbers and something else about -1, you can often combine that information to make statements about negative numbers.

HB: Who is your favorite teacher at Harriton?
KK: My favorite teacher is Mr. O, because he genuinely cares about what he does. He teaches in a way that actually makes people want to learn, rather than to pass some test. Also, he’s just a really nice person to talk to.

HB: Who is your role model?
KK: Probably my parents.

HB: What is a motto that you live by?
KK: Never do anything today that you can put off until tomorrow.

HB: Do you have any advice for younger students at Harriton who may want to pursue a carrer in math?
KK: Yes; the most important thing to remember when doing anything math related is to ask yourself why the idea that you are looking at works. Then, if you are able to come up with a reason, ask why that reason works as well. If you can do this enough, there’s nothing that is out of your understanding.