Arezki Amiri Published on April 20, 2025
In an extraordinary achievement that has stunned the global mathematics community, two high school students from Louisiana have developed a novel way to prove the Pythagorean theorem—and their approach is unlike anything seen before.
Ne’Kiya Jackson and Calcea Johnson, now college students, have published a peer-reviewed paper demonstrating that the theorem can be proven using only trigonometry, a feat long thought to be mathematically impossible due to what scholars have described as unavoidable “circular reasoning.”
A Theorem Rooted in History, Reimagined by Teenagers
The Pythagorean theorem has been a cornerstone of mathematics for over two millennia. It is used to calculate the length of a side in a right-angled triangle and is typically written as a² + b² = c², where c represents the hypotenuse. Despite thousands of existing proofs, all known methods using trigonometry were considered logically flawed.
This is because trigonometric functions such as sine and cosine are built on relationships derived from right-angled triangles. Using these functions to prove a theorem that justifies their own existence was seen as an inherent contradiction.
As CNN notes, “trigonometric functions are based on sine and cosine, which are expressed as ratios of certain lengths of a right-angled triangle. It’s quite easy to get into a circular argument.”
But Jackson and Johnson managed to do what many believed was out of reach. They crafted a set of proofs that rely on fundamental angle properties and proportional reasoning, without invoking any results that assume the Pythagorean theorem itself.
From High School Math Contest to Scientific Journal
Their journey began in 2022 during a high school math contest at St. Mary’s Academy in New Orleans. A bonus question on the Pythagorean theorem sparked their curiosity.
With the encouragement of a volunteer at their school, the students pursued the idea and presented their first trigonometric proof in March 2023 at the Mathematical Association of America’s Southeastern Sectional Conference in Atlanta.
Their appearance at the conference drew widespread attention. It led to a feature on “60 Minutes,” accolades from the city of New Orleans—including symbolic keys to the city—and even a public recognition from Michelle Obama.
Now, both students have taken their findings further. They’ve authored a paper published in the American Mathematical Monthly, one of the most prestigious journals in the field. As noted by CNN, the published paper includes ten total proofs—the original, plus nine more developed afterward.
Breaking Old Assumptions with Fresh Eyes
The originality of their work lies in the logic structure of their proofs. While trigonometry is normally intertwined with the theorem itself, Jackson and Johnson bypassed these dependencies. As their study explicitly states, “None of the theorems we use in our proofs … have already assumed the Pythagorean theorem to be true.”
The implications of their method are significant. According to Tom Murdoch, honorary professor at the University of Bristol’s School of Mathematics, “what’s so appealing about this is they found a line of argument using sine and cosine that doesn’t assume Pythagoras is true.”
Murdoch described the achievement as “impressive” and praised the pair for their unconventional perspective. “I think sometimes having very little knowledge of the problem means that you are not bound by what’s gone before,” he told CNN.
Academic Trailblazers with a Message
While their mathematical contribution is being recognized across the world, Jackson and Johnson have also emerged as role models, particularly for young women of color in STEM. In a statement quoted by CNN, Johnson said, “I am very proud that we are both able to be such a positive influence in showing that young women and women of color can do these things.”
Now in college, both are continuing their academic journeys. Johnson is pursuing a degree in environmental engineering at Louisiana State University, and Jackson is working toward a doctoral degree in pharmacy at Xavier University of Louisiana.
Despite their youth and the daunting task of writing a scientific paper while starting college, they managed to navigate the peer-review process and deliver a study that is now part of the formal mathematical literature. As Johnson admitted in a video shared by the journal, “I’m so surprised that we’re getting published in a paper at such a young age.”
This is an improved version of an article originally published on February 2, 2025.
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