'Women of color can do these things': Teenage girls discover proof for Pythagoras' theorem, unfound by mathematicians for 2,000 years

In 2023, two ambitious teenagers from Louisiana, Ne'Kiya Jackson and Calcea Johnson, embraced a challenge presented in a bonus question during a high school math contest: to develop a new proof for the Pythagorean Theorem. Fast forward nearly two years, and the duo has published a groundbreaking paper that outlines their original proof.

How they proved Pythagoras right

Anyone who has studied math through high school is likely familiar with the Pythagorean Theorem, represented by the equation A? + B? = C?.

This theorem states that if you know the lengths of two sides of a right triangle, you can determine the length of the third side.

The story of Ne'Kiya Jackson and Calcea Johnson began in 2022 when Michelle Blouin Williams, a high school math teacher at St. Mary's Academy in New Orleans, decided to challenge her students with a school-wide math contest featuring a bonus question.

This question invited students to develop a new proof for the Pythagorean Theorem, a key concept in geometry, using trigonometry.

Pythagoras, an ancient Greek mathematician who lived over 2,500 years ago, is known for this theorem.

Credit: The Marginalian/ Art by J. Augustus Knapp, circa 1926

While many mathematicians have explained the theorem through algebra and geometry, Jackson and Johnson took a unique approach by using trigonometry, a branch of mathematics focused on triangles.

For nearly 2,000 years, proving the theorem with trigonometry was thought to be impossible, so teachers weren't expecting any solutions.

However, in December 2022, seniors Calcea Johnson and Ne'Kiya Jackson embraced the challenge, motivated in part by a $500 prize. After months of hard work, they submitted their innovative proofs to their teachers.

Following the contest, their educators encouraged them to present their findings at a professional conference, leading to their historic appearance as the youngest presenters at the American Mathematical Society's Southeastern Sectional Conference in Atlanta in March 2023.

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Now, as college students, Jackson and Johnson have reached another milestone by authoring an academic paper detailing their original proof and nine additional proofs. Their work was published in the American Mathematical Monthly.

'Young women and women of color can do these things'

"I'm so surprised that we're getting published in a paper at such a young age," said Johnson, a sophomore in environmental engineering at Louisiana State University, in a video shared by the journal publishers.

Jackson, who is pursuing a doctorate in pharmacy at Xavier University of Louisiana, added, "I didn't think it would go this far."

Tom Murdoch, an honorary professor at the University of Bristol's School of Mathematics, praised their achievement, noting, as CNN quotes, "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, and what's so appealing about this is they found a line of argument using sine and cosine that doesn't assume Pythagoras is true."

"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, and to let other young women know that they are able to do whatever they want to do. So that makes me very proud to be able to be in that position," Taylor & Francis quotes Johnson as saying.

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