Why Do Research?When first starting my undergraduate career, I was planning to pursue the videogame industry. I was drawn to their development by the blend of mathematics and computer science needed to make them, the creativity behind experimenting with unique play mechanics and designing the story/characters/places/etc., and the smiles that they brought to so many faces when people played. Believe it or not, research also has the blend of computer science with mathematics as well as many other areas of study, creativity to bring our dreams and imaginations into reality, and the power to make many people smile. Additionally, research provides an opportunity to explore the unknown and try to develop an understanding for that which we do not yet completely understand.Due to the research opportunities I was fortunate to have as an undergraduate student, I strongly believe in undergraduate involvement in research. Considering the lifechanging impact it had on me, I want to make sure that other undergraduate students have a chance to try it in case it would really interest them. There seem to be very few chances for undergraduate students to do research outside of REU Programs and institutions with small graduate student bodies. So for undecided undergraduates as well as young scientists and researchers, here is: The Official Origin Story of Rick Freedman (Abridged) If superheros and supervillains can have origin stories about how they obtained their superpowers and became a crimefighting vigilante or evildoer of antijustice, then why can't we ordinary people have tales about how we became the people that we are? I am quite certain that most of us have very exciting tales about how we found our passions in life. So here is mine about how I became a research scientist. It is also a small reminder that the naïvette of a young student can be useful in research. Far too often people think you must know everything about the field ahead of time in order to know what to look for, but that can also force the experienced mind to miss hidden details. As a disclaimer, some background is useful to have a few techniques available, avoid reinventing the wheel, and not repeat errors. In the third week of my freshman year in college at Wake Forest University, Dr. Stephen Robinson decided to start our multivariable calculus class with a math puzzle. As he says, "what better way to take a break from math than with more math?" So he told everyone to choose a positive integer, and then to either divide it by two if the number was even or multiply it by three and add one if the number was odd. Then he told us to do it again and again and again. After a few minutes of this, he asked how many of us had 4, 2, or 1, and most of the students in the class raised their hands in surprise. He explained that this is an unsolved problem in mathematics since no one has been able to prove that starting with any number will eventually yield these numbers. Clearly 3*1+1 = 4, 4/2 = 2, and 2/2 = 1 for an infinite loop. As an example, he used the number 7 that later became 11, the number I chose. It intrigued me that these sequences converged when they contained the same number, but I did not think anything else of it at the time. We then began class for the day. Later that night when I was going to start my multivariable calculus homework, I saw the sequences scribbled on the page from class. Looking at them, I thought that the problem was too simple to remain unsolved. I tried a few more sequences and still got 4, 2, and 1. Then I decided to plot it backwards from 1 to get 2, then 4, then 8 or 1, then 16, then 32 or 5, etc.. It quickly became apparent that the even numbers were unimportant in the sequences since they were repeatedly divided by 2 until the number became odd again. So I started to play with the transitions between odd integers in the sequences and found more patterns. It was difficult to interpret these patterns as numbers; thus I plotted the before/after transitions using a vector field (it was the visual representation method that we just learned in the class). I got really excited about the plot and spent most that weekend sketching the vector field over four sheets of graph paper. The following week, I taped the four sheets together and brought them to Dr. Robinson's office hours. I showed him the visual patterns and asked if he knew anything about them. His reply was simply, "I don't know. I only heard about the problem, but I never studied it. It is called the Hailstone Sequence. See what you can find about it on the internet, and keep playing with this. I am interested to see what you find." Dr. Robinson also sent me Lagarias's anthology of research done on the problem. As a freshman in college, most of the work did not make sense to me. However, it was amazing to see the volumes of work done on the problem and read that the great mathematician Paul Erdõs said that mathematics was not ready to handle the problem yet. This inspired me to further work on understanding the relationships in my plot since they may have contained the information necessary to make the problem solvable (ignorance is bliss). After spending most my spare time working on it for about two semesters (and learning new techniques in other math classes), I finally found a way to prove the relationship. Dr. Robinson was just as excited as I was to see this. After our discussion, he informed me that everything I had done is research. Having only worked in a chemistry lab and a biostatistics lab for two summers as a high school student, I didn't even think of this exploration and playing with ideas as research. I always thought research was just performing experiments and lab calculations according to a specifications manual. I was never on the creative side developing the questions and methods, and I absolutely loved it. It was during this meeting that I realized I wanted to do research as my lifelong pursuit.
