What if we could reduce the complexities of mathematics to the simple act of counting shapes?  

According to Dr. Steven Senger, associate professor of mathematics, we can. 

About his focus 

Senger’s main interest is discrete geometric combinatorics.  

“Those are big words, but discrete basically means stuff you can’t chop up. Geometry means I’m using pictures, and combinatorics is just counting,” he said. “I count shapes, and that’s not an oversimplification.”

To say Senger’s area is simple is not to say the work is easy. 

“My research has very challenging, open problems that nobody knows how to solve. But the nice thing about that is I don’t need to be in front of a computer or waiting in a lab for test results to make progress,” he said. “I can just sit and think.”

Where should that thinking process start? Where does it end?  

The simple answer is that it will always fall somewhere in the middle. The fuel math runs on is ongoing conversation, Senger explains.  

“It’s like all mathematicians are in one big, dark mine. When somebody finds a gold nugget in one location, others go there to look for other valuable things,” Senger said. “I think of myself as one of the small movers. It takes a lot of us working together for the big names and famous people to really shine.” 

About his research 

Senger’s small moves have led to big results. His joint work on geometric measure theory has appeared in multiple publications.  

“Essentially, we adapted what somebody else had found to make a round shape that hits a lot of points evenly,” he said.  

Senger and his colleagues’ work served as a translation process. Their efforts inspired further research on other shapes and objects.  

Research on geometric measure theory is only one point of Senger’s work. The larger dimensions involve more studies related to data science.  

“I look for patterns that can provide people with information about large sets of data,” Senger said. 

Data science comes with its own overwhelmingly large dimensions. But identifying patterns in information makes understanding data possible.  

One application: It also allows businesses to beat out their competition.  

“It’s like when you go to the supermarket and swipe your frequent shopper card, which gives the store a whole bunch of data about your purchases,” Senger said. “The supermarket that can break down the data by finding patterns in purchases will eventually win out in the long run.” 

About the importance 

While the abstract concepts of math can often deter new learners, they can also bring those experienced within the field together.  

Senger stresses that finding answers in math ultimately stems from drawing connections. In that sense, the work of one can lead to further theories and results of many. 

It can also open the door to collaborating with others outside of the field.  

“When branching into different areas, we learn more about the world,” Senger said. “And when we work together, we do better than any one of us could alone.” 

Senger notes that the fundamental questions of math often don’t have direct answers. But the lack of a clear path to results expands the realm of learning to explore. 

“If you’re really interested in something that is challenging and interesting, then it probably has value to somebody,” he said. 

Senger believes there will always be more to contribute to the conversation of the math field. 

“In mathematics, there’s rarely a period at the end of the sentence,” he said. “There’s almost always an ’and then.”