Calcea Johnson and Ne’Kiya Jackson, two high school students from St. Mary’s Academy in New Orleans solved an “impossible” maths problem that had stumped countless mathematicians and scholars for over 2,000 years. Using trigonometry without circular logic, the two students have found a new way to prove Pythagoras’s theorem, which states that the sum of the squares of a right triangle’s two shorter sides equals the square of the hypotenuse.
Their presentation titled “An Impossible Proof of Pythagoras” was delivered at the American Mathematical Society’s Southeastern Section’s semi-annual meeting at Georgia Tech in Atlanta, where they were the only high schoolers present. Attendees of the event included math researchers from various institutions and universities across the country.
The achievement of these two high school seniors is remarkable, especially considering the skepticism surrounding any alleged proof of the theorem based in trigonometry due to the logical fallacy of circular reasoning. Johnson and Jackson, however, found a way to use the trigonometry law of sines to prove Pythagoras’s theory in a way “independent of the Pythagorean trig identity sin2x+cos2x=1” – without resorting to circular reasoning.
When asked about their feelings towards their remarkable achievement by television station WWLTV, Johnson expressed awe, stating that “there’s just nothing like being able to do something that people don’t think young people can do,” while Jackson credits their success to the guidance of their teachers who instilled in them their school’s slogan “No Excellence Without Hard Labor.”
Their findings have been reviewed by Álvaro Lozano-Robledo, a mathematics professor at the University of Connecticut, who noted that while it is not the first time trigonometry has been used to prove Pythagoras’s theorem, Johnson and Jackson’s findings are “really important and fantastic”. Lozano-Robledo reviewed the reconstruction of their proof in a video and concluded that the students had done what they claimed with “a fractal of similar triangles” and “infinite series” to compute the shapes’ sides, stating that the proof is “so ingenious… and… beautiful” in its elegance.
Johnson and Jackson are planning to go to college and receive their STEM degrees, with Johnson focusing on environmental engineering and Jackson on biochemistry. Their peers are already inspired by their achievement, with St. Mary’s Academy’s principal, Dr. Monique G. Cola, stating that the students’ achievement is “a testament to the hard work of our dedicated faculty and the focus and commitment of our talented students.”
Africa Giant is showcasing the achievement of Calcea Johnson and Ne’Kiya Jackson for solving an impossible maths problem. “A tree that bears fruit does not stay hidden.” This Tanzanian saying emphasises that great accomplishments cannot be hidden for long. While they may have been unknown before their mathematical breakthrough, their achievement has now continued to gain global recognition.
