Teens' Math Finding Was Once Thought to Be Impossible

They've discovered multiple trigonometric proofs of Pythagorean theorem
By Rob Quinn,  Newser Staff
Posted Oct 30, 2024 2:30 PM CDT

Two young women from New Orleans who amazed mathematicians two years ago by coming up with a new trigonometric proof of the 2,000-year-old Pythagorean theorem have repeated the feat multiple times. A peer-reviewed paper from Ne'Kiya Jackson and Calcea Johnson published in the American Mathematical Monthly Journal outlines their original proof, four more, and a method that they say leads to at least five more.

  • Their proofs demonstrate that "the square of a right triangle's longest side equals the sum of the squares of the two shorter sides," per Smithsonian. The theorem has been proven many times over thousands of years with algebra and geometry, but experts say using trigonometry is "particularly challenging because trigonometry as a field is essentially based on Pythagoras' theorem; thus using trigonometry to prove the theorem typically requires what mathematicians call 'circular reasoning," CNN reports. Jackson and Johnson wrote that none of the theorems they used, however, "have already assumed the Pythagorean theorem to be true."

  • Jackson and Johnson came up with their original proof two years ago in response to a bonus question in a math contest at their high school, St. Mary's Academy. Before that, only two trigonometric proofs of the theorem existed, one from 2009 and one from 2015, Science News reports. The achievement had long been thought impossible.
  • In the paper, Jackson and Johnson wrote that they were surprised when their "high school work was taken seriously, and we were approved to present at the American Mathematical Society's Southeastern Sectional conference in March of 2023," where they were the youngest presenters in the conference's history. They wrote that they were encouraged to submit their findings to an academic journal, which "proved to be the most daunting task of all" because of their lack of experience.

  • Mathematician Álvaro Lozano-Robledo of the University of Connecticut in Storrs tells Science News that contrary to perceptions that you have to be an academic for many years before you can produce new mathematics, Jackson and Johnson have shown that "you can make a splash even as a high school student." One of their proofs, which involves filling a larger triangle with an infinite sequence of smaller ones, "looks like nothing I've ever seen," Lozano-Robledo says.
  • Jackson and Johnson are now college freshmen. Jackson is studying pharmacology at Xavier University of Louisiana and Johnson is studying environmental engineering at Louisiana State University, the New Orleans Times-Picayune reports.
  • In a news release, they described having a paper published at such a young age as "mind-blowing." "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," Johnson said.
(After hearing about the achievement, Charles Barkley pledged to donate $1 million to their high school.)

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