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The Thrill of Discovery

Photo by Rob Johnson, graph by Stephen Humphries

While some may view math as a tedious, required class, mathematics professor Stephen Humphries believes that it is much more than that: Math is discovery.

“It’s the thrill of discovery that is part of what makes [math] exciting, fun, and interesting,” Humphries said.

Humphries has taught mathematics at BYU since 1987, and he shares the joy that comes from unearthing mathematical mysteries with his the students.

“I was meeting with one student a couple of weeks ago. We discovered something, and he shouted for joy,” Humphries said. “He thought it was so neat what we discovered. To experience that is wonderful.”

Humphries says that he always encounters surprising turns during his mathematics research.

“There’s always the unexpected,” said Humphries. “You’ll be studying a particular thing, then all of the sudden you’ll think to do something [different]. You check a few examples and you notice a pattern, and that pattern becomes a theorem.”

One of Humphries’ areas of focus is group theory, which consists of looking at the symmetries of various objects and shapes. These shapes may seem just like intertwined circles and shapes to most people, but Humphries knows their ins and outs.

“I tend to think of them as very beautiful objects,” Humphries said. “I have lots of fun studying them.”

Group theory is applicable to not just mathematics, but also to physics and other sciences. Humphries mentors a number of students to teach them how to perform research in mathematics.

“I like working with students and seeing how they do mathematics,” Humphries said. “I think of what I do as being an enabler of students to have a research experience.”

Although it may be difficult, Humphries says that providing proofs of results is integral to his job as a mathematician.

“The whole idea of mathematics is to produce proofs of significant and interesting mathematical ideas,” Humphries said. “That’s what a mathematician does.”

The task of being a mathematician also includes uncovering what the logic is in the problem.

“It’s not obvious what to do next,” Humphries said. “It’s only logical once you’ve seen how the argument works.”

Humphries thoroughly enjoys sharing the thrill of discovery with other students. He has seen a student come from Russia with no degree, to getting a second PhD. He also saw a former student of his return to BYU after 20 years to receive her master’s degree.

“I’ve enjoyed working with students. I’ve mentored a fairly large number of students in the time I’ve been here,” Humphries said. “That’s always been a rewarding and fruitful thing to do.”