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Richards a believer in the beauty of mathematics

Barry McNamara
MONMOUTH, Ill. – Monmouth College professor Trevor Richards has an interesting analogy for solving higher-level mathematical problems, and it goes back to the math puzzles his father asked him to solve as a child.

“All through my childhood, I viewed mathematics as a knot to untie – a very complicated knot,” said Richards, who joined Monmouth’s faculty last fall after serving as a visiting assistant professor at Washington and Lee University in Lexington, Va. “You pull a little bit on it here, loosen it a bit and make progress, but maybe get stuck again. Then you pull on it somewhere else and go about loosening that.”

Seeing mathematics in that way is an important part of what he tries to do in the classroom.

“Beyond the base clarity of transmission of material, my No. 1 goal when I teach is to draw students into the development of mathematics,” said Richards. “I view mathematics as an organic structure that grows in a sensible way. I don’t want students to view math as opaque formulas they follow mechanistically. I try to combat that by drawing them into the development phase.”

Richards said his typical class sessions include about 15 minutes of lecture including “a robust back and forth” with the students to develop methods to solve the problem.Then the students come to the whiteboard to work the problem.

While Richards’s love of mathematics goes back as long as he can remember, he definitely recalls the year when he decided to teach it. He was a junior high student in Lansing, Mich.

“I had a really inspiring teacher in seventh grade,” he said. “He had a really engaging approach for bringing out the remarkable and wondrous aspects of mathematics. Since then, I knew I wanted to teach.”

Richards thought at first he’d become a high school teacher, but he found success in graduate school at the University of Florida, where he also completed his undergraduate degree. “Attracted by the research aspects,” he decided to become a college professor, instead.

Richards’s research interest is the “topological and measure-theoretic properties of level sets of functions.”

“My approach to research is really aesthetic,” he said, referencing a statement by systems theorist Buckminster Fuller: “When I am working on a problem, I never think about beauty, but when I have finished, if the solution is not beautiful, I know it is wrong.”

“My research problems have aesthetic elements,” said Richards, who said he used to joke in graduate school about solving the “cartoon version” of a problem, even using crayons. Although he rarely uses crayons today, he said he still enjoys “drawing pictures and finding intuitive answers, which leads me to more rigorous answers.”

At Monmouth, Richards teaches the calculus sequence, leading into real analysis and complex analysis. He called the real analysis class “a first step into my own current field of research – it was my favorite class when I took it as an undergraduate.”

When not teaching or solving his own research problems, Richards enjoys solving problems on a chess board. He has a board in his office and enjoys the challenge of battling department colleague Mike Sostarecz. He also grew to love frisbee golf and ultimate frisbee during his time at the University of Florida and has played a few rounds at the disc golf course at Monmouth Park.