High school seniors crack 2000-year-old mathematical problem once deemed impossible

Emma Johnson and Claire Jackson, students at St Mary’s Dominican High School in New Orleans, have presented an innovative proof of the Pythagorean theorem to the Mathematical Association of America. This 2,000-year-old theorem establishes that the sum of the squares of a right triangle’s shorter sides equals the area of the square on the hypotenuse. Traditionally, its connection to trigonometry has raised concerns about circular reasoning. However, the students’ proof is claimed to be independent of such reasoning, challenging established perspectives in the field.

Johnson and Jackson assert that their proof, rooted in the Law of Sines, establishes the possibility of demonstrating the Pythagorean theorem using trigonometry without falling into circular reasoning. Their presentation took place in a session that featured contributions not only from fellow students but also from researchers affiliated with institutions such as the universities of Alabama, Louisiana State, and Texas Tech.

In an interview with WWL-TV, Johnson expressed the profound sense of accomplishment derived from presenting their work alongside university researchers. She shared that their school’s motto, “No excellence without hard labor,” was a significant inspiration for their efforts. Jackson commended their teachers at St Mary’s for pushing them to achieve what was widely perceived as an impossible feat in the realm of mathematics.

The Pythagorean theorem stands as one of mathematics’ most renowned theorems, having been a staple of education worldwide for generations. Named after the ancient Greek philosopher Pythagoras, who is attributed with its discovery, the theorem holds immense significance. Its applications span diverse fields like architecture, engineering, and physics. Additionally, the theorem plays a pivotal role in trigonometry, the mathematical domain focused on triangular relationships involving angles and sides. Trigonometry’s practical uses range from surveying and navigation to computer graphics and engineering.

The presentation by Johnson and Jackson is a remarkable accomplishment, particularly considering their youthful age.

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Representative Image Source: Pexels/ Photo by: Karolina Grabowska

The efforts of these two teenagers hold implications not only for algebraic number theory and cryptography but also extend to other fields. Remarkably, they plan to channel their talents into different career paths, with one aiming for a future in environmental engineering and the other aspiring towards biochemistry.

ITV reported that Catherine Roberts, the executive director of the American Mathematical Society, stated, “Members of our community can examine their results to determine whether their proof is a correct contribution to the mathematics literature. We encourage them to continue their studies in mathematics.”

Roberts also added that members of the American Mathematical Society “celebrate these early career mathematicians for sharing their work with the wider mathematics community.” Notably, notable individuals who attended St Mary’s Academy include Judge Dana Douglas and restaurateur Leah Chase.

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