This summer I worked with the math department doing research about rainbow numbers! Doing math research is like solving a puzzle that you do not know the answer to and do not know if there is an answer. Some highlights of the internship include attending a baseball game, going on hikes to clear our minds, and, most notably, proving our initial conjecture.
Day to day activities included reading math literature, discussing the proofs, and then adapting or extending the ideas to fit our equation. For example, one paper discussed rainbow numbers for the equation x-y=z2. We were able to extend this paper for the equation x-y=zk. This exciting new discovery ultimately led to the proof of our initial conjecture.
Along with these exciting days, however, there were very frustrating days. On these days, progress on the research almost felt like it was at a standstill. These were the days where going on a walk was much needed. Sometimes, all I needed was to step away from the puzzlefor a couple hours and let the ideas churn in the back of my head. Only then was I able to meet the problem on full force!
I had two takeaways from this summer. The first one that I got from this summer was how to tackle a big problem. Going into the internship there was a huge problem that we were unsure of how to solve, but taking the problem day by day our research group was able to solve the problem. The second takeaway was practice on how to present research. Every week, the math, physics, and CS departments got together and practiced giving a research presentation. I know this will help me in the future when I need to be able to communicate my findings to others in a professional setting.
To conclude, I had a great summer internship experience. I would like to thank Wabash College and the Wabash College Mathematics and Computer Science department for making this internship possible. Also, a huge thank you to Dr. Ansaldi for giving me the opportunity to do the internship and helping guide us to proving our conjecture.