Vidya and Associates

Two Teenagers have once again proved an Ancient Math Rule

Two years ago, two high school classmates created an innovative trigonometric proof of the Pythagorean theorem. Today, they’ve unveiled ten additional proofs, advancing knowledge that has challenged mathematicians for over 2,000 years.

Ne’Kiya Jackson and Calcea Johnson, now students at Xavier University of Louisiana and Louisiana State University respectively, published their groundbreaking work in the American Mathematical Monthly on October 28. Their achievements remind us that anyone, including high school students, can contribute profoundly to mathematics.

Reflecting on their journey, mathematician Álvaro Lozano-Robledo from the University of Connecticut shared, “Jackson and Johnson show that remarkable discoveries are not bound by years of academic experience. You can make a splash even as a high school student.”

Through persistence and dedication, Jackson and Johnson created proofs once thought impossible, challenging an assumption by mathematician Elisha Loomis from 1927, who argued that proving the Pythagorean theorem using trigonometry would require circular logic.

After showcasing their early work in 2023, the two scholars committed to publishing their research, tackling complex tasks like LaTeX coding and peer-review standards, all while transitioning to college. Johnson explains, “Publishing our proofs was essential to affirming the validity and respectability of our work.”

Their trigonometric proofs offer insights using unique methods, like their impressive “infinite triangle” approach which utilizes calculus—a feat that Lozano-Robledo noted as a true novelty in the field.

Jackson and Johnson have also provided guidance for aspiring mathematicians, sharing a detailed lemma to support the discovery of additional proofs. Their contributions now lay a foundation for future explorations, potentially inspiring others to apply, expand, and further generalize these groundbreaking ideas.

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