High school students prove the Pythagorean Theorem with trigonometry and get published

Two young mathematicians, Calcea Johnson and Ne'Kiya Jackson, made headlines with a groundbreaking discovery in mathematics. In 2022, as high school students, they found a new approach to proving Pythagoras' theorem using trigonometry, a method long thought impossible.

Their journey began with a local school competition in New Orleans, where they quickly caught the attention of educators and mathematicians. Soon, the city honored their achievement by awarding them the keys to New Orleans, and former First Lady Michelle Obama even commended their efforts.

Now, their work has achieved a new milestone with the publication of their paper in the American Mathematical Monthly, a peer-reviewed journal. This publication places Johnson and Jackson among a small group of mathematicians who have managed to prove the theorem without relying on circular reasoning.

Over 2,000 years old, Pythagoras’ theorem is a cornerstone of mathematics. Known as a2+b2=c2a^2 + b^2 = c^2a2+b2=c2, it relates the sides of a right-angled triangle. Traditionally, mathematicians have proved it through algebra and geometry, but trigonometric proof remained elusive because trigonometry itself relies on Pythagorean principles.

Johnson and Jackson, however, tackled this challenge from a fresh angle. Independently, they devised proofs free from the assumptions that previously prevented trigonometric solutions.

The duo's paper details five unique proofs, one of which they had shared at an American Mathematical Society meeting in 2023. Additionally, they identified five more potential proofs, bringing the total to ten, of which nine are entirely new.

Jackson described her reaction to being published as one of surprise. “I didn’t think it would go this far,” she admitted. Johnson echoed her enthusiasm, noting, “To have a paper published at such a young age — it's really mind-blowing.” She spoke about how much the STEM (science, technology, engineering, and mathematics) field has evolved, saying, “The fact that all these people actually are interested in STEM and mathematics really warms my heart.”

One key insight in their paper challenges conventional trigonometric teaching. The students argue that the discipline contains two distinct versions that cause confusion among learners. Defined with the same terms, these versions overlap in ways that obscure understanding.

Jackson and Johnson propose a separation of these versions, focusing on one to unlock a wider range of Pythagorean proofs. They liken the existing approach to interpreting a picture with two different images superimposed — complex and unclear. Their approach offers clarity by isolating trigonometric elements, revealing new methods to prove mathematical relationships.

Currently, Jackson and Johnson are pursuing advanced studies in fields unrelated to pure mathematics. Jackson is enrolled in a doctoral program in pharmacy at Xavier University of Louisiana, while Johnson studies environmental engineering at Louisiana State University’s Roger Hadfield Ogden Honors College.

The two students have also become role models, particularly for young women and women of color in STEM fields. Johnson expressed her pride in this role, saying, “We are both able to be such a positive influence in showing that young women and women of color can do these things.”

Their accomplishment is drawing praise from leaders in the mathematics community. Della Dumbaugh, editor-in-chief of the American Mathematical Monthly, described the publication as an honor for the journal. “The Monthly is honored and delighted to publish the work of these two students,” Dumbaugh stated.

She emphasized the fresh perspective that students bring to mathematics and credited the influence of dedicated teachers. “Their results highlight the important role of teachers and schools in advancing the next generation of mathematicians,” Dumbaugh added, aligning Johnson and Jackson’s contribution with the journal’s founding mission.

As Johnson and Jackson’s findings gain recognition, their story illustrates the potential of young minds to contribute meaningfully to established fields. Their success underlines the role of support networks, such as teachers and family, in guiding young talent toward groundbreaking achievements.

Now, as they continue their studies, these young innovators leave a lasting impact on both the mathematical community and on future generations eager to explore the limitless possibilities of STEM.

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