In a remarkable achievement, high school students Calcea Johnson and Ne’Kiya Jackson from Louisiana have done what was thought to be impossible for 2,000 years: they proved the Pythagorean theorem using trigonometry.
Johnson and Jackson’s journey began in 2022 at a math contest at St. Mary’s Academy in New Orleans, where their teacher introduced a seemingly unachievable bonus question: to prove the Pythagorean theorem, which states that the square of a right triangle’s hypotenuse is equal to the sum of the squares of the other two sides, using trigonometry. Intrigued by the challenge, the two students embarked on a journey of trial and error, balling up countless sheets of paper as they worked through their ideas. Despite the known difficulty and limitations of using trigonometry for such a proof, they persevered.
In 2023, they presented their findings at the American Mathematical Society annual conference, earning significant praise for their original proof. The math community took note, and even former First Lady Michelle Obama celebrated their achievement, recognizing its broader significance for young mathematicians, particularly African-American women in STEM.
After extensive analysis, Johnson and Jackson’s work was published in American Mathematical Monthly. Live Science reported that the two high schoolers were able to separate core trigonometric functions—sine and cosine—teasing apart methods to develop a proof that avoided the typical circular reasoning associated with proving the Pythagorean theorem through trigonometry. In an impressive turn, they further expanded their work to produce nine additional proofs, proving that once a mathematical insight is unlocked, possibilities abound.
Reflecting on the journey, Johnson said, “I would have never expected that this would go so far, so quickly, because it just really took off.” She added that she feels “blessed” for the recognition, especially as young women of color in a field where representation matters.