### Two Teenagers May Have Solved 2,000-Year-Old Math Problem

In a groundbreaking development for the field of mathematics, two New Orleans high school students have reportedly solved a 2,000-year-old mathematical theorem that had previously been thought impossible to prove.

The teenagers, Calcea Johnson and Ne’Kiya Jackson from St. Mary’s Academy, presented their findings at a recent meeting of the American Mathematics Society, where they explained that they had been able to prove Pythagoras’ Theorem using trigonometry instead of circular logic.

Pythagoras’ Theorem deals with triangles that are not perfectly symmetrical and states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides, expressed as a2+b2=c2. For 2,000 years, no mathematician had been able to demonstrate the truth of this theorem without using circular logic, which is not accepted as evidence of proof.

Johnson and Jackson reference Elisha Loomis’s The Pythagorean Proposition, a book that investigates this concept and “flatly states that ‘there are no trigonometric proofs because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem,’” the girls wrote. However, the young women managed to untangle this conundrum by presenting “a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry — the Law of Sines — and we show that the proof is independent of the Pythagorean trig identity.”

Catherine Roberts, executive director for the American Mathematical Society, encouraged the students to submit their work for peer review and to continue their studies of mathematics to further advance the field. The two young women expressed their excitement at presenting their findings to the society, describing it as an “unparalleled feeling” and emphasizing the importance of young people pursuing challenging academic pursuits.

“There’s nothing like it — being able to do something that people don’t think that young people can do,” Johnson said in an interview with WWL New Orleans. “You don’t see kids like us doing this — it’s usually, like, you have to be an adult to do this.” With their groundbreaking achievement, these two exceptional students have not only demonstrated the power of youthful determination and intellectual curiosity but also underscored the enduring importance of mathematics as a field of study.