Mathematical research: My new world of challenges, possibilities and elation
By Michael Ma, senior at Plano West Senior High School and Regeneron Science Talent Search 2018 finalist
I used to think that research math would be similar to competition math, which I have been doing since the second grade: you have a problem and use all the techniques you know and sometimes think of new ones to solve the problem or reduce it to an easier one and eventually solve it.
But mathematical research opened up a whole new world for me. I’ve learned how to overcome great challenges and persist in doing what I want to.
I first learned about the possibilities open to me thanks to my ability to do math and apply high-level problem-solving skills in eighth grade while participating in the Math Olympiad Summer Program. I spent three weeks with the country’s top math students being taught by incredibly intelligent and knowledgeable professors and former students. I learned that with math I could explore other sciences like physics or computer science, I could enter fields like finance or economics, or I could even go on to do research math.
I was first introduced to high-level research as a junior through the MIT Primes USA program. With the help of my mentor William Kuszmaul, I got my start in the field of permutation pattern replacement equivalence relations, an area totally new to me.
In a test, when I fail to solve a problem it’s over. There’s someone to tell me the answer and explain the intuition behind the solution to help me solve similar problems next time.
That doesn’t exist in mathematical research. There’s no magical solution to every problem, and when I fail to solve a problem after a couple hours, it’s still there — waiting — for me to solve. It’ll be there nagging at my brain, demanding to be solved.
Sometimes, I don’t even know if I have the knowledge to solve it. That can be both terrifying and demoralizing.
One of my largest research challenges was not being able to solve a problem or even make progress — for weeks or even months at a time. Not producing any meaningful progress is definitely one of the most frustrating feelings ever. It can make you want to scream out loud and cry in despair. Sometimes you can’t even see the light at the end of the tunnel.
My love of math and solving problems was a huge part of my motivation to keep working. Deep down, I really wanted to solve that math problem — I really wanted to gain a deep intuitive understanding of the problem. That desire can, in the end, overcome any temporary frustration or disappointment.
In contrast to not being able to solve a problem, solving a major problem is one of the greatest feelings of all time.
Taking a longtime barrier, a wall that you’ve been hacking at for what feels like forever and just getting past it feels like a wonderful release. Even more, the feeling of contributing to the math community and pushing the boundary of math research forward feels amazing. Knowing that I did something no one has done before — something that is truly my own — is an incredible feeling.
The elation once it’s done and the rush of gratification and excitement when solving a problem is one of the most intense things I have ever felt. It is motivation enough to allow me to persist in what I do and continues to drive me forward, even today.
