The TCU Department of Mathematics does more than just solve equations and plug in numbers -- faculty members seek to solve real-world problems, beginning with research. Department Chair and Professor Greg Friedman focuses his research on the subject of topology, stating, topology is, “similar to geometry but a little less well known—both are about spatial type objects, but in topology the objects are allowed to bend and stretch.” Topology’s day-to-day application can be seen in knotting neck ties, as sequences of wrapping each end over one another occurs. Topology has grown Friedman’s interest in research, as the field is rich for people with curiosity. Research in math, similar to any other field, allows an analyst to go in depth with areas of interest and explore their studies in a new field.
Greg Friedman - Topology
“I study these things abstractly just for their inherent topological properties”, said Friedman, but he hopes to one day see a real-world application made. Friedman said, “math is a patience game,” and as a society, we never know when a theory can be applicable to solve a problem. According to Friedman, one example includes Number Theory, the study of integers and whole numbers, which began in the 17thcentury as a hobby for wealthy Europeans with free time, but is now the foundation for technology. Similar to mathematicians, 17th century Europeans weren’t looking to make foundational discoveries; however, breakthroughs occur as curiosity leads an individual into a particular study. Mathematician’s first concern with research isn’t real world application, but when applications result, it is all the more impactful.
Many of TCU’s mathematics faculty are active in research in a variety of fields. This motivation for research comes from the endless possibilities still waiting to be discovered in mathematics. Friedman says, “even without knowing the possible future applications, mathematicians remain passionate about confronting a challenging problem for the same reason George Mallory wanted to climb Mount Everest: ‘because it’s there.’” The Department of Mathematics looks to instill this way of thinking into its students as they pursue degrees in a variety of subjects, all with potential real-world impact.
Ze-Li Dou - Artificial Intelligence
Ze-Li Dou, associate professor, bridges mathematics and computer science to study the ancient East Asian board game, “Go.” His research is centered on artificial intelligence and the instillation of human intelligence in computers in order to discover how the program became so strong. In addition to studying the intelligence of technology, Dou is surfacing possible deficiencies within the program. Dou explains the game as, “a strategy game like chess, played between two people and there is no luck involved...you are playing strengths to determine who the winner is going to be.”
In the 1960s, mathematicians introduced the concept of computer programs playing board games against people, but they didn’t expect that a program would be created to beat “Go” for another hundred years. In 2016, the first artificial intelligence program was created to beat a world champion in “Go,” which immediately interested Dou. He works with Liran Ma, associate professor in the department of computer science, to investigate the abilities of artificial intelligence within “Go.”
In addition, Dou and Ma have been able to invite students into their research to discover more conceptual knowledge behind artificial intelligence. He states in regard to working with student helpers, “I firmly believe even if the experiment is an entire failure, experiences are very important.” Research is the beginning of discovery, and it is “based on curiosity,” said Dou. In regard to real-world application, Professor Dou states,“mathematicians are playing ‘a game of patience’ motivated by curiosity rather than immediate worldly applications and gains, and if real-world applications may come hundreds or even thousands of years later, but come they do nevertheless, then they are romantics indeed, every single one of them.”
Eric Hanson - Applied Geometry & Topology
Eric Hanson, instructor in the Department of Mathematics, spreads his research interests amongst applied geometry and topology, focusing on data analysis. Hanson’s motivation is a result of the desire to apply mathematical concepts in new ways to analyze data. Hanson says in regard to his pursuit of math, “I liked the idea of the firm foundations of something. You start with very reasonable assumptions and you build something from that. The assumptions made sense to me.”
Hanson’s recent research includes topological data analysis, taking data and asking questions about what shape it forms and what that information tells us. Through this research, Hanson and one of his students were able to, “take this idea that exists mathematically and put it into practice somewhere.” Hanson’s current project looks at interval metrics, measuring distance in the lanes on a freeway, analyzing the different lines, curves and distances of cars traveling, and arranging them into classes.
TCU’s Department of Mathematics utilizes their knowledge and curiosity to uncover new concepts through research. The opportunity within math research is endless, and these analysts will continue to chase after new discoveries with “a curiosity that never goes away.”
