LEHI -- Before he learned how to drive a car, Lehi High School student Brock Brown designed a simple way to solve binomial expansions.
Assistant Professor Ben Moulton from UVU's Math Department is traveling with Brown on Nov. 1 to Anaheim, Calif., to present "Brock's Theorem: An Alternate to the Binomial Theorem" at a math conference.
The American Mathematical Association of Two Year Colleges sponsor the annual event.
In many ways, Brock Brown is a typical teenager. He has an after school job, doesn't like homework, and enjoys making music and spending time with friends.
Last spring, as a sophomore, he was sitting in his math class learning to use Pascal's triangle to solve binomial expansions, and devised a quicker formula that according to Moulton is elegant and simple.
"It's going to take a really long time on the homework if I do it this way," Brown said he told himself.
Unlike his high school peers, Brown pondered the pattern he saw in Pascal's triangle and found a short cut. Currently a junior at Lehi High School, he got his homework done faster, which was his intent, and also got the attention of university scholars.
Binomials are an algebraic expression showing the sum or difference of two terms. An expansion raises a binomial to a power. As long as the powers are low, binomial expansions can be solved simply. With higher powers, multiplying binomials can quickly become very complicated.
"Multiplying down 20 rows creates lots of room for error," said Sharon Gourley, Brown's LHS math teacher.
After class, Brown approached his teacher and said he could do the homework without using Pascal's triangle.
"While I was teaching, I could just see his brain going. When he told me after class, I knew right away that he probably had something really cool," Gourley said.
Brown said he hated doing homework but knows it's sometimes necessary. He thought creating his theorem was easier because he hadn't done the class assignment yet. "Homework locks you into doing things the expected way," he said.
At the same time Brown was wowing his math teacher, his mother, Sarah Brown, was attending a math class at UVU for her graphic design major.
While going over difficult course work, Brown's mother told her professor that her son really excels in math and could probably solve anything he could throw at him.
"I sort of took that as a personal challenge and began sending Sarah home with really tricky problems for Brock to solve, but I never stumped him," Moulton said.
"When his mother kept bringing back his work with the right answers I thought 'Who is this kid?' " he said.
Brock Brown showed his formula to Moulton.
"When we brought it to him he was blown away by it and volunteered to create a proof," Brock Brown said.
Moulton worked with his department chair to mathematically show this theorem works in every case. He said at UVU they're always looking to nurture curiosity and promote education in the community.
Sarah Brown credits Gourley with creating the environment in a high school class where her son could use his unique talent.
"In the university setting, they're constantly publishing and rewriting theorems. You just don't expect to see it from a high school student," Gourley said.
Moulton submitted Brock's Theorem to the AMATYC, and they were invited to participate in the upcoming conference.
"All we did was a little mathematical thing. Other people have created similar formulas but Brock's work is really elegant and simple," Moulton said.
Brock Brown said his LDS faith inspires every aspect of his life. His success in mathematics aside, he said he dreams of one day becoming a seminary teacher.
He said people should strive for more than just knowledge about various subjects.
"Knowledge is a step toward understanding, which is a step toward teaching," he said, adding that "The key is to not simply take things apart, detail by detail; not simply to compartmentalize and segregate; but also to unify and put the pieces back together."