Ne’Kiya Jackson and Calcea Johnson, former high school students, have recently published 10 new trigonometry-based proofs of the Pythagorean theorem, a mathematical marvel that was previously believed to be impossible for over 2,000 years. Their work has been published in the American Mathematical Monthly and has garnered attention for their achievement as high school students. This goes to show that groundbreaking mathematics can be produced by individuals of any age and experience level.
Despite the belief held by mathematician Elisha Loomis in 1927 that trigonometry could not be used to prove the Pythagorean theorem without resorting to circular logic, Jackson and Johnson were able to succeed where others had failed. Their proofs were conceived while they were seniors at St. Mary’s Academy in New Orleans, and they were able to develop additional proofs by focusing on a particular method of defining trigonometric terms. This innovative approach led to the creation of five proofs for right triangles with sides of different lengths and one for right triangles with two equal sides.
After presenting their work at an American Mathematical Society meeting and facing the daunting task of publishing their findings in a peer-reviewed journal, Jackson and Johnson were ultimately successful in solidifying their work as correct and respectable. Despite the challenges of entering college and learning new skills such as coding in LaTeX, the duo remained motivated to see their work through to completion. Their paper not only showcases their proofs but also provides a lemma that can act as a guide for other mathematicians interested in discovering additional proofs based on their work.
One of their proofs, which involves filling a larger triangle with an infinite sequence of smaller triangles and using calculus to find the lengths of the larger triangle’s sides, has particularly caught the attention of mathematician Álvaro Lozano-Robledo. This unique approach demonstrates the creativity and ingenuity of Jackson and Johnson’s work. By leaving five proofs for interested readers to discover, the duo hopes to inspire further exploration and conversation within the mathematical community. Their publication opens up new possibilities for generalizing their proofs and ideas, contributing to the ongoing dialogue in mathematics.
Jackson and Johnson’s work stands as a testament to the importance of perseverance and dedication in overcoming obstacles. They hope that other students will be inspired by their journey and realize that challenges are a natural part of the learning process. By sticking with their work and pushing through difficulties, they were able to achieve more than they had initially thought possible. Their contribution to the field of mathematics serves as an example of the impact that determination and creativity can have in furthering our understanding of complex mathematical concepts.
