by Rebekah Tilley

photos by Lee Thomas

“Welcome to Mathland” reads the white board in the seventh floor hallway of Patterson Office Tower, home to the UK Department of Mathematics. Above it is the mathematical equivalent of a joke; the punch line accessible only to those who know the difference between a function and a formula.

Katharine Ott came to this particular “Mathland” by way of a National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship. The fellowship is highly competitive, both for its prestige, and because the applicants are able to choose at which university they want to conduct research.

“Given the kind of research I do, the University of Kentucky was far and away the first choice of where I wanted to come,” Ott said. “Russell Brown, department chair Zhongwei Shen and John Lewis are just a few of the exceptionally strong researchers here at UK in the particular type of math I do. When I found out that I was being offered the fellowship, I accepted it immediately. It’s the kind of thing you do not pass up; it’s a three year opportunity to make the most of yourself.” 

Ott’s area of study is at the intersection of harmonic analysis and partial differential equations. She studies equations that model physical phenomena such as heat flow or the transfer of light. More specifically, Ott looks at boundary value problems. 

Here is basically how it works: If you’re sitting in a room right now, imagine that you know the precise temperature at each point along the walls, floor and ceiling of the room. These are the so-called boundary values. The temperature at the boundary may be influenced by outside factors – such as a space heater. Now suppose that you want to know the temperature in the room at the exact spot where your hands are touching your computer keyboard. “The question becomes, can I find a function telling me the temperature inside the room at any point knowing just the boundary values and certain special properties related to the air in the room and how heat travels,” Ott explains. 

For those not fascinated by knowing exactly how inadequate their heat is, another application of boundary value problems is computing information about the interiors of solid objects without breaking them open. “For instance,” Ott said, “an iceberg has certain conditions on its boundary depending on whether it is above the water or below the water. You might want to know what’s happening internally. It is going to split apart? Is it going to melt?”

As part of the fellowship, Ott teaches one undergraduate class each semester. She describes her teaching as a key component of her work, motivating and grounding her as a researcher. “One of the things I really like about math is that it is fundamental to all of the other sciences,” Ott explains. “It’s really a language and a tool that is used by many other disciplines, and that’s why I think teaching math is so important. As a teacher I’m not lecturing on the research I did yesterday, I’m teaching my students fundamentals that will hopefully be tools for them as they go out and do important things themselves.”  

While a graduate student at the University of Virginia, Ott took part in a number of workshops and outreach activities geared toward sparking an interest in mathematics in middle and high school students. She credits her high school teacher and college professors for encouraging her to study mathematics and wants to pass this along. “Anything to get more people aware of mathematics or interested in math, especially working with students, things like that I think are just as worthwhile as making a new research discovery.” 

Ott also spent a summer as an intern at the Milwaukee Journal Sentinel reporting on science. Sponsored by the American Association for the Advancement of Science, the internship is intended to increase, encourage and improve communication between the scientific community and the general public. She illuminated specific examples of how mathematics can be applied to real-world problems such as HIV infection, gene sequencing, and medical imaging.

Among the many things Ott learned as a science journalist, perhaps the most significant lesson was “realizing the importance for scientists to be able to convey what they do and why it is relevant," she stated. “Mathematicians in particular seem to be prone to keeping their work to themselves or refusing to put their research into laymen's terms. But if we cannot share our work with the general public, then the mathematical community risks being cut out of funding, being left out of interdisciplinary research, and being able to recruit fewer and fewer future researchers.”

The applications of the type of mathematics done by Ott and the rest of the UK Department of Mathematics to day-to-day life aren’t always as obvious as with other areas of science. Their research may not see a “real world” impact for generations to come or perhaps ever. Yet when asked what motivates her work, it’s hard not to hear faint echoes of British climber Mallory saying he was attempting Mt. Everest “because it’s there.” 

“People always ask: Why do you do math? Isn’t everything about math already known?” Ott said. “And the answer is absolutely not. You might walk around this whole floor and ask everyone what they do, and most of it will seem really abstract or confusing. But math can’t stop, science can’t stop. At least for me, the idea is that science is always progressing.”