Recreational mathematics

Posted by
On April 5, 2023

Nicholas Fleece looking into a series of connected mirrors. Photo by Michael Pierce, Missouri S&T.

Ph.D. student Nicholas Fleece studies magic at Missouri S&T.

At least, that is what he will tell you.

“My research focus in mathematics is on magic squares,” says Fleece. “You can kinda think of them like sudoku or other math puzzle games.”

Magic squares are a theoretic subject that consist of a square of numbers where the sums of the numbers in each row, column and both diagonals are the same. The smallest examples are a square of three numbers down and three across, totaling nine numbers.

Ph.D. student Nicholas Fleece. Photo by Michael Pierce, Missouri S&T.

Where is the magic?

Fleece is studying these squares to determine more about their implications for the mathematics and statistics field, which he says could lead to innovations in areas like actuarial work and equity trading, including calculating financial costs of risk for businesses.

“Some types of magic squares have never been created, but we cannot prove that it cannot be done,” says Fleece. “My research team aims to attack this problem using nonstandard methods, something we haven’t seen much in the literature. Answering this question would solve a decades old problem – a mathematician’s dream.”

Magic squares are classified as “recreational mathematics” and not traditionally researched in formal education. But that has not stopped Fleece from pursuing his research at the highest level.

“I think everything I study and learn about is recreational mathematics because it is all fun to me,” Fleece says. “I fell in love with math while earning my master’s degree at another university. My thesis was on the Hamiltonicity of subgroup lattices, a topic in group theory and graph theory, and given how much I enjoyed this experience, there was no doubt in my mind that I had to pursue a doctorate degree.”

Research to research

Fleece says that his experience with mathematics research is something that he wouldn’t want to change and encourages other students to pursue their research interests.

“I would advise anyone who may be interested in research to start right now,” says Fleece. “Do this by looking up fruitful areas of research and then begin building your knowledge base in those areas.

“It is a classic saying that ‘the more you know, the more you know that you don’t know’ and, in this instance, I would modify it to say ‘…the more you know that we don’t know,’” says Fleece. “The ‘we’ is representing the collective knowledge of academia and the more you learn, the more areas you can find that humans know little about. These are the areas you want to dive into — these are the areas that will lead to innovation.”

About Missouri University of Science and Technology

Missouri University of Science and Technology (Missouri S&T) is a STEM-focused research university of over 7,000 students. Part of the four-campus University of Missouri System and located in Rolla, Missouri, Missouri S&T offers 101 degrees in 40 areas of study and is among the nation’s top 10 universities for return on investment, according to Business Insider. For more information about Missouri S&T, visit

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