Calcea Johnson and Ne'Kiya Jackson have made history by proving a 2,000-year-old math theory using trigonometry without circular logic.
Editor's note: This article was originally published on March 28, 2023. It has since been updated.
Two high school students from St Mary's Dominican High School in New Orleans, Calcea Johnson and Ne'Kiya Jackson, have presented proof of the Pythagorean theorem, which they claim is independent of circular reasoning, to the Mathematical Association of America. According to The Guardian, the theorem, which dates back 2,000 years, states that the sum of the squares of a right triangle's two shorter sides equals the area of a square on the hypotenuse. Its importance to the study of trigonometry, which relies on the theorem, has previously led mathematicians to argue that any alleged proof which uses trigonometry is guilty of circular reasoning.
New Orleans students Calcea Johnson and Ne'Kiya Jackson say they've proved Pythagoras' Theorem -- something academics have thought was impossible for 2,000 years.— POCIT (@pocintech) March 27, 2023
Now, @amermathsoc is encouraging them to submit their work to a peer-reviewed journal.
Johnson and Jackson claim their proof, which is based on the Law of Sines, shows that it is possible to prove the theorem using trigonometry without resorting to circular reasoning. The teenagers' presentation was part of a session that also included presentations from researchers from institutions such as the universities of Alabama, Louisiana State and Texas Tech.
In an interview with WWL-TV, Johnson described it an "unparalleled feeling" to be presenting her work alongside university researchers, and explained that she and Jackson were inspired by the slogan of their school, "No excellence without hard labor." Jackson credited their teachers at St Mary's for pushing them to achieve something which many mathematicians considered impossible.
The Pythagorean theorem is one of the most famous theorems in mathematics and has been taught in schools around the world for generations. It is named after the Greek philosopher Pythagoras, who is said to have discovered it. The theorem has a wide range of applications in fields as diverse as architecture, engineering and physics. The theorem is also important in the study of trigonometry, which is the branch of mathematics concerned with the relationships between the sides and angles of triangles. Trigonometry has a wide range of practical applications, from surveying and navigation to computer graphics and engineering.
The presentation by Johnson and Jackson is an impressive achievement, especially given their young age.
The work of the two teenagers has implications for algebraic number theory and cryptography, among other fields. The students intend to pursue careers in environmental engineering and biochemistry respectively.
According to ITV, Catherine Roberts, executive director for the American Mathematical Society, said: "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 added that American Mathematical Society members "celebrate these early career mathematicians for sharing their work with the wider mathematics community." St Mary’s Academy's alumni include Judge Dana Douglas and restaurateur Leah Chase.