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In a remarkable academic achievement, two We College students, Kelsea Johnson and Nekia Jackson, have extended Pythagoras’ famous theorem by developing five new solutions using trigonometry. Their findings, published in the journal American Mathematical Monthly, have enriched the field of mathematics and challenged long-held beliefs about how this ancient theorem can be proven.
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A New Perspective on the Pythagorean Theorem
Pythagoras’s theorem, summarized by the equation a2+b2=c2, describes the relationship between the sides of a right triangle, where the square of the hypotenuse is equal to the sum of the squares of the other two sides. Over the centuries, mathematicians have found various ways to prove this theorem using algebra and geometry. However, attempts to reach this through trigonometry were often considered impossible.
That was until Johnson and Jackson, who first attracted attention as high school students, approached the problem without relying on circular reasoning—something that had eluded professional mathematicians in the past. Their initial success in 2022 surprised the academic community and paved the way for their latest exploration.
Ten proofs and a new frontier
Now, as college students, Johnson and Jackson have not only come up with five different solutions, but also unveiled a method that leads to an additional five proofs, bringing the Pythagorean theorem to a total of ten. Resulting in new insights. This influential contribution dramatically increases the body of knowledge surrounding a theorem that had only one established proof prior to his work.
“I was very surprised to be published. I didn’t think it would go this far,” Jackson shared in a recent news release, expressing his surprise at the recognition of his work.
Inspiring the new generation
The achievement of both holds special significance in promoting interest in STEM (science, technology, engineering and mathematics) fields. Jackson reflected on the changing perceptions of STEM, saying, “It’s very exciting to me because I know when I was growing up, STEM wasn’t really a cool thing. So the fact that all these people are really interested in STEM and math really touches my heart and makes me really excited about how far STEM has come.
Della Dumbaugh, editor of American Mathematical Monthly, expressed pride in the journal’s role in publishing such important research, acknowledging the contributions of the editorial board, especially Grant Cairns, who helped refine the presentation of their work.
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Diverse educational paths forward
Despite their extraordinary talent in mathematics, neither Johnson nor Jackson planned to pursue careers in the field. Jackson is currently studying pharmacy at Xavier University in New Orleans, while Johnson is focusing on environmental engineering at Louisiana State University, reflecting the breadth of talent and ambition among today’s young scholars.
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