For more than 2,000 years, it has been widely accepted that trigonometry cannot serve as a foundation to prove Pythagoras’ Theorem, since trigonometric functions rely on it as a starting point. This long-held belief was taught as fact, thought to be indisputable—until two high school students from Louisiana challenged this notion.
Calcea Johnson and Ne’Kiya Jackson, students at St. Mary’s Academy in New Orleans, gained international attention after unveiling several trigonometric proofs of the Pythagorean Theorem that, according to them, avoid the classic logical circularity. Their groundbreaking presentation took place at a respected American Mathematical Society (AMS) gathering in March 2023, standing out among an audience mainly composed of advanced academics rather than teenage students.
While many have proposed new formulations of the theorem, Johnson and Jackson’s work stands out for its mathematical rigor and gaining formal recognition. Experts have encouraged them to submit their discoveries for peer review, with reports indicating the American Mathematical Monthly is expediting consideration of one of their proofs.
The Substance of Their Proof
The Pythagorean theorem, expressed as a² + b² = c², describes the relationship between the sides of right triangles, a staple of textbook geometry. However, attempts to demonstrate it via trigonometry were historically dismissed because sine, cosine, and tangent functions are defined using the theorem itself. Critics likened this to attempting to prove water’s wetness by describing rainfall.
The innovative approach of Johnson and Jackson sidesteps this issue. They employ the Law of Sines, a fundamental trigonometric rule, while deliberately avoiding the standard identity sin²x + cos²x = 1, which itself depends on the Pythagorean theorem. This distinction is crucial, as it eliminates the possibility of circular logic, based on a summary of their research.
In an abstract submitted to the AMS, the students dispute the assertion made in Elisha Loomis’s influential 1927 book The Pythagorean Proposition, which claims that trigonometric proofs of the theorem cannot exist.
They assert: “That isn’t quite true.”
From Classroom Challenge to Worldwide Recognition
Their proof originated not in a university lab, but as a bonus problem in a school math contest, posed by teacher Michelle Blouin Williams at St. Mary’s Academy. The contest offered a $500 prize. What started as a side challenge quickly consumed the girls’ evenings. “Papers were tossed in the garbage when attempts failed,” said Calcea’s father.
After months of persistence, refining their logic and verifying their work, the results astonished their teachers. Invited to share their findings publicly, they presented alongside university researchers from LSU, Ohio State, and Texas Tech—making them the sole high school participants at the conference.
The media quickly picked up the story. Outlets like CBS News, The Guardian, and 60 Minutes featured the breakthrough. Honors followed: the girls received keys to New Orleans, recognition from the Louisiana governor, and a nod from Michelle Obama.
However, the journey included adversity. According to CBS, St. Mary’s principal Pamela Rogers shared that the school faced racist skepticism doubting the girls’ capabilities. “They claimed African Americans lack the intellect for this,” she said. The school worked to protect the students from such negativity.
Community and Academic Reception
The mathematics field responded with notable enthusiasm. Catherine Roberts, AMS executive director, told The Guardian their presentation was authentic and deserving of peer-reviewed evaluation. She emphasized, “We celebrate these emerging mathematicians.”
Tom Murdoch, an independent mathematician, called their work “a wake-up call,” highlighting that they devised several distinct proofs, opening potentially fresh perspectives in trigonometry.
Previously, physicist Jason Zimba attempted a trigonometric proof in 2009, but it achieved limited acceptance. The contributions of Johnson and Jackson enrich this niche set of proofs, possibly broadening the scope of established validations for this foundational mathematical concept.
Dr. Michael Dorff, former president of the Mathematical Association of America, told CBS News their findings warrant “serious scrutiny and peer review,” as is customary for new discoveries.
The Future for Johnson and Jackson
Despite their acclaim, neither plans to pursue a mathematics career. Johnson is studying environmental engineering at Louisiana State University, while Jackson has secured a full pharmacy scholarship at Xavier University of Louisiana.
Both hope their achievement inspires other students—especially girls and young people of color—to tackle ambitious academic challenges. They continue to explore further proofs during their free time.
St. Mary’s Academy remains dedicated to excellence. This all-girls Catholic institution, founded shortly after the Civil War, boasts a 100% graduation and college acceptance rate for the past 17 years. Its graduates include federal judge Dana Douglas, the first Black woman to serve on the Fifth Circuit Court of Appeals, and the late Leah Chase, an iconic Creole chef.
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