Standing on my tiny sphere, I look out to the endless body of knowledge and wonder how I may step further to into the unknown. While I am fascinated by the intricacies all around me, more often I catch myself linking objects that seem obscure from one another like examining two pieces of a puzzle to see if they are connected. At times, I feel as though I have seen some parts of something larger and there is the urge in me that wants to join the fragments together to make sense of this unsettled feeling.
The first spark
Prior to my pursue in mathematical biology, my first two years of undergraduate was filled with much-needed explorations and uncertainty. Unlike many of my peers, while they were busy preparing for college, I was busy practicing to pass the English portions of the AIMS (Arizona's Instrument to Measure Standards) that was required for my high school graduation. As the first person in my extended family in the US to go to college, I have the Joaquin Bustoz Math Sciences Honors Program (Barrett, ASU) to thank for preparing me mentally. Mrs. Hannum (one of my math teachers at Alhambra High School) told me about the opportunity. For me, it was either that or another ESL summer school, so I sent in the application. And for the first time since coming to the US, I was on my own - in an actual college dorm - for a completely new experience. This experience truly transforms my perspective, but it was the second time around that I got to experience a hint of the research in mathematical biology.
I believe 2012 was the first time that the program implemented a research component into its summer curriculum. Aside from the "standard" coursework of Calculus II with Professor John McDonald, my group of four oblivious students decided to take on the task to use mathematics to study the potential impact of a biological warfare (What wonderfully imaginative kids we were!) Unfortunately, as I would be exploring physics and a myriad of other subjects, I would not return to the mathematical biology until my meeting with my current advisor three years later.
Research Statement
Sciences should only be carried out with respect to what can (potentially) be measured, so does mathematical modeling.
The first implication is that this statement explains why there has been an explosive growth in the mathematical community. Technology is rapidly getting more impressive each year, which allows scientists to measure what would have been impossible many decades ago. This opens up a gap between the amount of data and our ability to make use of them to better understand and predict biological processes. The abundance of data is significant. Mathematics was able to be a crucial part in the development of modern physics due to this feature. Without data to validate the mathematical descriptions of nature, mathematics is just a complex chess game with a fixed set of rules and logical moves.
The second point is the answer to the question "what can be measured?" In physics, a controlled experiment is as close as it can be to the definition of a controlled experiment. The same cannot be said about biology. While we have laws that are incredibly representative of the observable universe in physics, the complexity of biological systems makes a deterministic set of laws difficult to obtain. If we equate complexity and uncertainty, maybe we can get some probabilistic laws like quantum mechanics on a macroscopic scale for biological systems. Nevertheless, the point is that it is not a trivial matter to attribute certain biological measurements clearly to a biological factor.
This is what I keep in mind when I do research. However, while I genuinely think it is important to establish biological laws, it is not necessary for many applications. Researchers can be very creative to make something work even when we barely scratch the surface of understanding, but that was also how physics started.
Research Interest
Professor Eric J. Kostelich, one of my mentors at ASU, told me that research is like putting a brick on the wall of human knowledge. It took me years to start appreciating this viewpoint. For someone from my background, research was a way for me to further fulfill and go beyond expectations (think the A+ Asian stereotype). Thus, while I always enjoy doing research, it had caused much friction and unnecessary pressure when I first started. But eventually, I took a long walk on the hermit path and came to this realization.
Like almost all researchers that I have met in academia, interesting questions excite me, especially ones that either solve a practical problem or provide a fundamental insight. To be able to realize that a question is interesting, one needs to have sufficient knowledge in related areas for the assessment. This means as I learn, I become more capable of appreciating the questions. Unfortunately, I only have a finite amount of time, so I just work on the interesting problems in the order that they appear to me.
At least for the next six months, I will be focusing on several aspects of prostate cancer modeling.