Chapter 1: A Historic Breakthrough

In a remarkable turn of events in the realm of mathematics, two high school students from New Orleans have allegedly cracked a theorem that has stumped mathematicians for two millennia. Calcea Johnson and Ne’Kiya Jackson, who attend St. Mary’s Academy, shared their revolutionary findings at a recent American Mathematics Society conference. They articulated their proof of Pythagoras’ Theorem, utilizing trigonometry rather than the circular reasoning that has long been the norm.

Pythagoras’ Theorem pertains to non-symmetrical triangles, asserting that the area of the square on the hypotenuse (the side opposite the right angle) is equivalent to the sum of the areas of the squares on the other two sides, mathematically expressed as a² + b² = c². For 2,000 years, no mathematician has successfully validated this theorem without resorting to circular logic, which is generally not considered valid proof.

Johnson and Jackson referred to Elisha Loomis’s work, The Pythagorean Proposition, which claims that "there are no trigonometric proofs because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem." However, the duo disentangled this complexity by proposing "a new proof of Pythagoras’s Theorem, grounded in the Law of Sines, demonstrating that the proof is independent of the Pythagorean trigonometric identity."

Catherine Roberts, the executive director of the American Mathematical Society, encouraged the students to submit their findings for peer evaluation and to continue their mathematical studies to propel the field forward. The excitement expressed by the young scholars upon presenting their findings was palpable, with one of them describing the experience as an "unmatched feeling," highlighting the significance of youth engaging in rigorous academic challenges.

“There’s nothing quite like it — achieving something that many believe young people cannot,” Johnson remarked in an interview with WWL New Orleans. “Typically, you don't see kids like us venturing into this territory — it’s usually reserved for adults.” Through their extraordinary accomplishment, these two gifted students have not only showcased the potential of youthful perseverance and intellectual curiosity but also reinforced the vital role of mathematics in education.

The first video titled "New Orleans teens make mathematical discovery unproven for 2,000 years" delves into the details of their groundbreaking proof and the implications it holds for mathematics.

Chapter 2: A New Perspective on an Old Problem

As the discourse around their findings continues, questions arise about what might have been overlooked in this age-old problem.

The second video, "What did we all miss in this 2000 year old problem?" explores the insights and revelations that led to this historic achievement, prompting viewers to reconsider what they thought they knew about Pythagoras’ theorem and its proofs.