Bernard Lidický begins many explanations the same way: by drawing.
On a nearby whiteboard, a cluster of dots appears. Lines connect them. Shapes emerge. Soon, what looks like a simple sketch becomes a puzzle—one about rules, relationships, and balance. It’s how Lidický likes to work, and how he likes to explain.
“I like drawing pictures,” says Lidický, professor of mathematics at Iowa State University. “It makes it easier for me to see things. Some people like long formulas. I’m not famous for long formulas.”
Lidický works in discrete mathematics, a research field that focuses on countable structures—objects you can list, connect, and rearrange. His specialty, graph theory, studies networks made up of points and the connections between them. The ideas can feel abstract at first, but they show up everywhere once you know how to look for them.
Consider a state map. Divide it into counties, then color those counties so no two neighbors share the same color. Use as few colors as possible. The question sounds simple, almost playful—but it challenged mathematicians for more than a century. The famous four‑color theorem, finally proved in the 1970s with the help of computers, showed that four colors are always enough for flat maps. Back then it took a whole year of computer time.
“That problem took a hundred years to solve,” Lidický says. “Now it’s relatively easy for a computer.”
A similar structure appears in a Sudoku puzzle. Each square must hold a number from 1 to 9, different from the others in its row, column, and region. Replace numbers with hookup rules and squares with points, and Sudoku becomes another graph problem. What looks like a game is really mathematics quietly at work.
Lidický’s research isn’t about completing puzzles—it’s about understanding why solutions exist and what forces them. He studies what properties of networks guarantee that limited resources—colors, time slots, frequencies—can be shared without conflict, and what structures may make problems harder than they first appear.
Those types of questions place his work at the intersection of mathematics and computer science. Scheduling classes so students aren’t double‑booked? That’s graph theory. Assigning frequencies to cell phone towers so they don’t interfere with one another? Same math.
But Lidický isn’t writing software to solve these problems directly. His focus is theoretical.
“I’m interested in what properties guarantee that a graph needs only a small number of colors,” he says. “What forces complexity to appear.”
Computers play an important role in exploring those questions. Unlike some mathematicians who prefer to stay at the whiteboard, Lidický is comfortable moving between theory and computation—using computers to test ideas, search for patterns, and push against the limits of what’s known.
In one research project, his team worked with large optimization models that strained commercial software tools. Their mathematical formulations exposed weaknesses that helped developers improve the software itself.
“Sometimes the applications come much later,” he says. “It’s basic research. You don’t always know where it will lead.”
That patience with uncertainty seems to extend well beyond his research. After completing his doctoral work in the Czech Republic, Lidický pursued a postdoctoral position at the University of Illinois before joining Iowa State in 2014.
Outside the office, Lidický’s curiosity takes a different form: kayaking. He spends time on local waterways, particularly at Lake Ada Hayden, and has even competed in kayak slalom events at the Iowa Games—earning gold medals he describes with equal parts pride and humor.
“It’s relaxing,” he says. “And it’s fun to be on the water. But there aren’t many who compete in that event. If you signed up, you might get a gold medal, too.”
That blend of playfulness and challenge mirrors how he approaches mathematics itself. Problems may start small, even simple, but they deepen quickly. What looks obvious often isn’t. And the most interesting discoveries emerge not from rushing to an answer, but from paying close attention to structure.
“Those little puzzles get very complicated very quickly,” Lidický says.
By Susan McNicholl, Iowa State University Office of the Vice President for Research