“Grant, you're doing it wrong,” my mentor, Dr. K, would always say in my Junior Spring semester. We began with real analysis and logic, going through proof after rigorous proof; all of them ending with that perfect little square that signaled the absoluteness of the proof. Everyday was filled with pages upon pages of readings, detailing proof after proof of various concepts, such as L’Hopital’s Rule, and the features of different mathematical constructions and spaces.
Early on, it was an incredibly frustrating task that took constant attention everyday. Before you gain a plethora of experience with proofs, you don’t necessarily have many tricks to do your own proofs; when in this stage, either you become inventive or you waste hours on the proof. But as time went by, I became more capable. With vast amount of experience and all the tricks and tools under my belt, I wasn’t struggling quite as much.
Mentorships aren’t quite as easy as they might seem to be. You could spend time in a lab, going through trial after trial and being faced with an inconclusive set of data every time. Stacks upon stacks of thick packets and books littered upon your desk could be staring back at you, all needing to be read in order to have the background knowledge for your mentorship project. Although not all mentorships are busy, you can be sure that many are.
Staying motivated can be a great difficulty that you face throughout the entire project. For me, all I had to look forward to was the books and packets mentioned before. Self studying mathematics isn’t the most difficult thing, but when you have a lot of it to get through in short periods of time it can become time consuming.
Often times I had to schedule on my calendar certain readings and problem sets to complete by certain dates to keep myself on track, and revise past work to help solidify my knowledge and motivate myself with the knowledge of how far I had come. Dr. K would correct me less and less, and gradually we could begin discussing mathematics on a more equal level of understanding.
“You're doing it wrong,” Dr. K still says during our problem set sessions this semester, and we’ve started from square one with multivariate calculus and vector spaces. Page after page, and proof after proof I’ve begun a similar journey in a different land, new territory with the same old sensation of being overwhelmed. But with a little smile I carry on, because I’ve begun doing what I want to do for the rest of my life.