March 12, 2026
Contact: Janese Heavin, heavinj@missouri.edu
Every March 14, University of Missouri Professor Stephen Montgomery-Smith’s wife buys him a pie — a lighthearted nod to his career and to π, the never-ending, never-repeating number that begins with 3.141592 and goes on forever.
More precisely, pi is a circle’s circumference divided by its diameter, a simple calculation quietly embedded throughout the world around us.
“Pi is like the oil or butter in the pie crust,” Montgomery-Smith said. “It’s essential but just there. Most people don’t think about it.”
Montgomery-Smith, however, is not most people.
By the age of 11, he was reading about the science of optics and lenses. At 13, he began teaching himself calculus. And over the course of his career at Mizzou’s College of Arts and Science, he has built a reputation for bridging deeply abstract mathematical concepts and real-world applications. It’s a balance that now underpins work he’s doing for NASA, where he helps develop simulation systems for lunar terrain vehicles, using π to calculate rotations, curvature and motion.
“For me, every day is Pi Day,” he said.
Mastering mathematics at Mizzou
Montgomery-Smith came to Mizzou in 1988 as a visiting professor specializing in Banach spaces, an area of mathematics that deals with infinite-dimensional collections of vectors.
“It was pure mathematics for the sake of mathematics,” he said. “It was so abstract at times I wondered, ‘Why am I doing this?’”
Mizzou’s collaborative environment soon gave him an answer. As he connected with others in his field and researchers in the College of Engineering, he found new ways to apply his theoretical background to practical problems. He began working on studies involving fluid dynamics — the movement of fluids and gases — where pi is used to describe rotation, curvature and oscillation. The same mathematical principles he explored in the abstract now had real-world consequences.
That blend of theory and application also shaped his teaching. Montgomery-Smith has long emphasized the reasoning behind the formulas, showing students that mathematics is not just a set of procedures but a creative way of understanding the world.
“Some people don’t appreciate how beautiful it is,” he said. “I think there are people who have the potential to really enjoy mathematics but might not be enticed if it’s taught as a process rather than as a creative endeavor.”
That philosophy has helped countless Mizzou students experience mathematics as a living, dynamic field.
Bringing pi to motion — and the moon
Montgomery-Smith’s focus on precision and creativity now fuels his work with NASA, where he’s helping create simulators that allow drivers to test lunar rovers before the vehicles explore the moon’s surface.
His role is to ensure the simulators don’t just show the rocks and craters; they let drivers feel them by recreating the sensory experience of motion.
“The vestibular system in the inner ear gives us our sense of balance and what’s known as six degrees of acceleration,” he said. “For instance, you might feel linear motion when you’re on a roller coaster going up and down, and you’d feel rotational movement if you spin very fast. That’s what we’re trying to replicate.”
He’s also working on docking systems, using six-legged robots to simulate motion in space. Stability is a central challenge and, once again, pi is part of the solution.
“Robots can sometimes go unstable and stability involves stopping oscillations, which are rotary motions,” he said. “So pi comes up a lot there when you’re analyzing stability. Pi is just all around a very useful number.”
And for Montgomery-Smith, it isn’t a number reserved for chalkboards or holidays. Pi is a constant that has followed him from childhood curiosity to abstract theory and, ultimately, to work that helps humans navigate the universe.
Pi is more than a number; it’s the mathematical language of curves, rotation and cycles — patterns that appear everywhere from wheels and flowing water to sound waves and planetary orbits. Because pi connects simple geometry to real-world motion, it plays a central role in math, science and engineering.
What makes pi so special?
In honor of National Pi Day, University of Missouri Professor Stephen Montgomery-Smith shares three facts about pi.
1. It was discovered, not invented.
Pi describes the relationship between a circle’s circumference and its diameter, a ratio that remains the same no matter the size of the circle.
Ancient civilizations across the world independently arrived at similar calculations for pi, with Greek mathematician Archimedes ultimately narrowing its value to between 3.14 and 3.142. In the 18th century, Leonhard Euler popularized the symbol π, and Johann Heinrich Lambert proved that pi is an irrational number, meaning its decimal expansion never ends or repeats.
“Pi is a reminder that the universe has structure,” Montgomery-Smith said. “It’s not random. We didn’t invent pi; we uncovered it. That’s the thrill of mathematics.”
2. It shows up far beyond circles.
Because pi is used to describe curves and waves, it plays a critical role in engineering, especially when designing structures that must withstand motion.
Engineers have learned this through experience, sometimes the hard way. Montgomery-Smith pointed to the famous Tacoma Narrows Bridge, a suspension bridge in Washington, which opened in 1940 and collapsed just months later under wind pressure.
“Bridges have natural frequencies,” Montgomery-Smith said. “If external forces match those frequencies, vibrations can amplify, potentially leading to collapse. That’s why engineers need pi and other mathematical models to predict oscillations and identify dangerous frequencies.”
3. You don’t need to memorize it.
Most everyday calculations only require a few digits of pi. Engineers typically use five to 10 decimal places. The world record for memorizing pi is more than 70,000 digits — impressive, but still only a tiny fraction of a number that goes on forever.
With today’s technology, though, memorizing it is no longer essential.
“Scientific calculators have a pi button, so you don’t really need to memorize it,” Montgomery-Smith said. “You just need to understand why it matters.”
