The Jackson-Johnson Proof and 9 more!
- Gayatri Tendulkar
- Nov 15, 2024
- 2 min read
Two high school classmates from Louisiana have defied mathematical odds by publishing ten new proofs of the Pythagorean theorem using trigonometry. This accomplishment not only expands our understanding of this fundamental theorem but also challenges the notion that groundbreaking discoveries are limited to established academics.
Ne'Kiya Jackson and Calcea Johnson, now college students, completed this work while attending St. Mary's Academy in New Orleans. The Pythagorean theorem is a fundamental concept in geometry relating the lengths of sides in a right triangle. For over 2,000 years, mathematicians have proven it numerous times using algebra and geometry. However, trigonometry, a branch of mathematics dealing with angles and side lengths, was believed to be an unsuitable tool to prove it.
In 2022, presented with a bonus math question offering a $500 prize, Jackson and Johnson tackled this seemingly impossible question. Their initial solution, along with four additional proofs, shocked the math world. They later developed a method leading to five more potential proofs, bringing the total oto ten.
Their journey wasn't easy. "There were many times when both of us wanted to abandon this project," they write in their published paper, appearing in the prestigious American Mathematical Monthly. However, their hard work paid off, and their proof demonstrates that significant contributions can come from unexpected places.
"Some people have the impression that you have to be in academia for years and years before you can actually produce some new mathematics," says Álvaro Lozano-Robledo, a mathematician at the University of Connecticut. "But Jackson and Johnson's work demonstrates that you can make a splash even as a high school student."
This achievement dismantles the idea of limitations in mathematical exploration. "Mathematicians, I think, have learned not to make a bold claim that something is impossible," says Stuart Anderson, a retired professor at Texas A&M University-Commerce.
Jackson and Johnson's work not only expands our knowledge of the Pythagorean theorem but also serves as an inspiration to young mathematicians, particularly young women and minorities who are often underrepresented in the field. "I am very proud that we are both able to be such a positive influence in showing that young women and women of colour can do these things," says Johnson.
This discovery is a testament to the power of curiosity and perseverance. It encourages students to embrace challenges and explore the vast possibilities within mathematics.
A kind YouTuber reconstructs their (likely) argument in this video, so if you are interested, check it out!
