US teens devise 5 innovative methods to prove Pythagoras’ theorem

In an remarkable academic achievement, two US college students, Calcea Johnson and Ne’Kiya Jackson, have expanded upon Pythagoras’ famous theorem by developing five new solutions using trigonometry. Their findings have been published in the journal American Mathematical Monthly, further enriching the field of mathematics and challenging long-held beliefs about proving this ancient theorem.
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Pythagoras’ theorem, summarised by the equation a2+b2=c2, describes the relationship between the sides of a right-angled triangle, where the square of the hypotenuse is equal to the sum of the squares of the other two sides. For centuries, mathematicians have sought various ways to prove this theorem using algebra and geometry. However, attempts to approach it through trigonometry were often deemed impossible.
That was until Johnson and Jackson, who first captured attention as high school students, tackled the problem head-on without relying on circular reasoning—something that had eluded professional mathematicians in the past. Their initial success in 2022 astonished the academic community and paved the way for their latest exploration.
Now, as college students, Johnson and Jackson have ventured further, presenting not only five distinct solutions but also unveiling a method that leads to an additional five proofs, culminating in a total of ten new insights into Pythagoras’ theorem. This impressive contribution dramatically increases the body of knowledge surrounding a theorem that had only one established proof before their work.
“I was pretty surprised to be published. I didn’t think it would go this far,” Jackson shared in a recent news release, expressing her amazement at the recognition their work has received.
The duo’s achievement holds particular significance in promoting interest in STEM (science, technology, engineering, and mathematics) fields. Jackson reflected on the changing perceptions of STEM, stating, “It’s very exciting for me because I know when I was growing up, STEM wasn’t really a cool thing. So the fact that all these people actually are interested in STEM and mathematics really warms my heart and makes me really excited for how far STEM has come.”
Della Dumbaugh, editor of American Mathematical Monthly, expressed her pride in the journal’s role in publishing such vital research, acknowledging the contributions of the Editorial Board, particularly Grant Cairns, who helped refine the presentation of their work.
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Despite their extraordinary talent in mathematics, neither Johnson nor Jackson plans to pursue a career in the field. Jackson is currently studying pharmacy at Xavier University in New Orleans, while Johnson is focused on environmental engineering at Louisiana State University, showcasing the breadth of talent and ambition among today’s young scholars.