In recent years, young women in various scientific fields have proven that creativity and knowledge know no bounds, especially in mathematics. In 2022, two students from Louisiana, Nikia Jackson and Kalsia Johnson, managed to present a proof that seemed “impossible” for the Pythagorean theorem, which amazed the mathematical community. But their story did not stop there; they recently managed to present nine completely new solutions to this multi-faceted theorem, reflecting their genius and unique vision in facing mathematical challenges. In this article, we explore the exciting details about their scientific achievements and how their approaches to proving the Pythagorean theorem changed the conventional understanding of this ancient theorem.
The Experience of Nikia Jackson and Kalsia Johnson
In 2022, two high school students from Louisiana, Nikia Jackson and Kalsia Johnson, impressed the mathematical community after presenting a proof regarding the Pythagorean theorem, one of the oldest theorems in mathematics. These girls were in their senior year when they managed to develop two proofs based on trigonometry. Although many mathematicians believed that proving the theorem using this science would be difficult, Jackson and Johnson proved otherwise by presenting an innovative solution.
The story began when the girls were participating in a school math competition. They received an unexpected additional question, prompting them to provide an answer that reflected their creativity. This work was presented at the American Mathematical Society meeting in 2023, and the new research paper published on October 28, 2023, confirmed that the solution successfully passed peer review, with the girls adding nine additional solutions to the Pythagorean theorem using triangles. This achievement is not only a milestone for them but also serves as encouragement for young women, particularly those of color, to enter the fields of science, technology, engineering, and mathematics (STEM).
The “Impossible” Proof and the Impact Circle
One of the most notable achievements made by Nikia and Kalsia is their invention of a proof that can be considered “impossible”. They succeeded in using the sine theorem without reverting to the basic information that assumes the Pythagorean theorem is correct, thus bypassing what is known as the logical circle. This accomplishment challenged previously accepted concepts in trigonometry. This type of scientific creativity not only showcases the girls’ talent but also reflects young people’s ability to think critically and outside the box, which is the essence of modern science.
Additionally, the formation of the new proofs reflects their dedication and efforts to clarify the ideas related to trigonometry further, enhancing the collective understanding of this theorem and helping to build confidence in young women’s abilities in mathematics. As Kalsia said: “Having a published research paper at this age is incredibly amazing.” This success not only opens doors to new opportunities in the world of graduate studies and scientific research but also represents an inspiration for young women to enter these scientific fields that have traditionally been male-dominated, contributing to changing social and cultural orientations.
New Technical Directions in Trigonometry
In their extraordinary research paper, Nikia and Kalsia addressed the different ways to define sine and cosine functions, showing how these definitions can be presented in various forms, which could lead to confusion in understanding. The distinction between these two methods and clearly explaining each can enhance understanding and lead to discovering a large new set of proofs for the Pythagorean theorem. This type of clarification reflects the spirit of scientific research and curiosity, which is one of the foundations driving progress in mathematics.
The girls also acknowledged that using different approaches to trigonometry could lead to finding new solutions to current problems. This focus on exploring different methods heralds a promising future for mathematics research and confirms that traditional approaches are not the only ones that can lead to remarkable results. This research serves as a launchpad for those interested in the world of geometric numbers and mathematical theory, opening the door to refreshing old ideas and presenting them in new and innovative ways.
The Challenges
And the Future
Young women like Nikiya and Kalsia face a range of challenges in the sciences, including social stereotypes and cultural biases. Their success is an achievement not just for themselves, but for all young women in STEM fields. Jackson stated: “I never thought this experience would go this far.” Publishing a research paper at this age reflects their efforts and determination to overcome difficulties.
Success stories like these girls encourage a greater interest in the sciences among young people, especially girls. Support from the academic community and attention from the media can significantly contribute to fostering a spirit of innovation and perseverance. Ultimately, providing sustainable role models of success benefits everyone in society and raises awareness of the importance of mathematics and science.
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