As a four-year-old, Lillian Pierce remembers watching her mother balance her checkbook and realizing that the numbers juxtaposed on the page were, in a sense, communicating with each other.

“My mother explained that the numbers told her what to write down next. It was remarkable to me that those symbols could talk to each other -- that they had specific relationships, and that it was possible to learn what those relationships were in order to play this game called long division.”

Today, Pierce, a 34-year-old mathematician at Duke University, works at the intersection of number theory -- a branch of mathematics that studies the properties of ordinary whole numbers like 1, 2, 3 -- and harmonic analysis, which studies properties of functions.

For Pierce, trying to solve a problem in her field is like piecing together an exquisite machine, one carefully placed gear, cog or spring at a time.

“What I like about math is that you can carve out a problem that exists on its own in a perfect crystalline framework where it’s extremely clear what the rules are,” she says. “For me it’s like opening a door and walking into another world.”

Pierce didn’t set out to become a mathematician. Originally from Southern California, she was mainly home-schooled until the age of 16. As a child she studied ballet, painted with watercolors and published illustrations in a children’s magazine called Stone Soup. Pierce started playing the violin at four years old and was playing professionally by the time she was 11.

“I always enjoyed math, but for a long time I was a violinist first and foremost, and I did math on the side. I didn’t know that being a mathematician was even a career choice until later,” she says.

She credits a university professor who would eventually become her Ph.D. advisor, Princeton mathematician Elias Stein, with getting her hooked on math as an undergraduate. Notorious for long hours of study on little sleep, she spent as many as 30 hours a week on a single math course.

“You’re not going to learn if you don’t do the work,” she says.

Pierce says she still applies many of the same mental skills she learned as a musician to math. “The focus and absorption and mental imagery it takes to memorize a piece of music and visualize how it works -- I inhabit the same mental space when I do math, too.”

When she graduated from Princeton in 2002 she was the valedictorian of her class. After college, she spent two years studying math in Oxford as a Rhodes Scholar before returning to Princeton to pursue a Ph.D. During her time at Oxford, in preparation for meeting Queen Elizabeth II in Buckingham Palace she received this piece of advice: “Whatever you do, don’t contradict the Queen.”

But Pierce couldn’t hold herself back when, after introducing herself to the queen as a pure mathematician, her majesty replied, “Not many girls have the head for pure maths.”

“In that moment I forgot everything I’d been told about decorum," Pierce says. "A friend who was standing next to me told me later what I said. It was something like, ‘Well actually, girls and women are told that they can’t do math, but they can.’”

Her latest contribution to number theory is joint work with Oxford mathematician Roger Heath-Brown that represents the first progress on a problem related to class numbers that researchers have pondered since the early 1800s.

While Pierce’s current research lies in pure mathematics, she is intensely interested in the intersection of math and other fields.

In college she worked as an intern for the National Security Agency, applying her math skills to classified research in cryptology -- the science of writing and cracking codes. She aims to develop a Duke course on cryptology and ethical questions related to rights and privacy in the digital age.

She is also in the process of developing a new course on math, music and the brain that she hopes to co-teach in the fall of 2015 with her husband Tobias Overath, a neuroscientist in the Duke Institute for Brain Sciences who studies how the brain processes sound.

Pierce and Overath are among 13 faculty members participating in the Faculty-in-Residence program. They live on East Campus in Blackwell residence hall with their two children.