Two American Teenage Girls Challenge 2,000 Years of Mathematics with a Groundbreaking Proof of Pythagoras’ Theorem – The Daily Galaxy –Great Discoveries Channel
Two students from Louisiana have shaken the foundations of mathematics with a fresh take on an age-old theorem. Their work challenges a long-standing assumption about trigonometry and Pythagoras’ theorem. What seemed impossible for centuries has now been reexamined in a surprising way. The implications of their discovery could reach far beyond the classroom.In an astonishing breakthrough, two young students from Louisiana have done what many thought was impossible: proving Pythagoras’ theorem using only trigonometry. Their discovery has rocked the world of mathematics and sparked new discussions on fundamental geometric principles.For over 2,000 years, Pythagoras’ theorem has stood as one of the cornerstones of mathematics. It states that in a right-angled triangle, the sum of the squares of the two shorter sides equals the square of the hypotenuse. Despite thousands of proofs—ranging from Euclid to modern algebraic approaches—it was widely believed that a purely trigonometric proof was impossible.Why? Because trigonometry itself is built upon the very theorem it seeks to prove. Any attempt at using sine, cosine, or tangent to verify Pythagoras’ equation seemed destined to rely on the theorem itself, leading to a circular argument. But two high school students refused to accept this limitation.In 2022, Ne’Kiya Jackson and Calcea Johnson, then students in Louisiana, set out on a daring mission: to prove Pythagoras’ theorem in a way never seen before. After four years of research and refinement, they unveiled their groundbreaking proof in March 2023 at the Mathematical Association of America‘s annual conference in Atlanta.Their approach? A trigonometric proof that bypasses the traditional foundations of sine and cosine, removing any dependency on Pythagoras’ theorem itself. Instead, they relied on fundamental angle properties and proportional reasoning, breaking free from the supposed paradox.The reaction from the mathematical community was nothing short of stunning. Experts who had long dismissed the possibility of such a proof were forced to take a second look. Their work was not only praised at the conference but also fast-tracked for publication in the prestigious American Mathematical Monthly.Their proof didn’t just solve the problem—it opened the floodgates. The students introduced multiple approaches, including one that generates five additional proofs, proving their method’s versatility.Mathematician Tom Murdoch described their work as a game-changer, stating that it could inspire new perspectives in geometry, trigonometry, and beyond.Une publication partagée par Mayor LaToya Cantrell (@mayorcantrell)While their work has made them stars in the world of mathematics, Ne’Kiya Jackson and Calcea Johnson remain focused on their future careers.Their message is clear: the next generation of scientific breakthroughs can come from anyone, regardless of age.Beyond its impact on educational inspiration, their proof could lead to practical applications. Trigonometric techniques are widely used in engineering, physics, and computer science, and a deeper understanding of these principles could improve optimization algorithms, structural designs, and mathematical modeling.As their discovery continues to make waves, one thing is certain: mathematics is far from being a solved field. The work of two high school students has reminded the world that even the oldest theorems can still hold surprises—and that the next big discovery might come from the least expected places.Got a reaction? Share your thoughts in the commentsEnjoyed this article? Subscribe to our free newsletter for engaging stories, exclusive content, and the latest news.This make it a black history of America. This should be in the black history museum. Today is a great improvement of black history and great history of women of color.This story is very misleading. They did not solve an unsolved problem like the media is incorrectly repeating. There was a mathematician in the late 1800s who was named Elias Loomis who was Ph.D at Yale. He said it was impossible to make a proof of the Pythagorean theorem using Trigonometry because any proof of the Pythagorean theorem that used Trigonometry would be circular reasoning. The reason he said this is because he used the “Unit Circle” definition of Trigonometry, which is a the universally accepted definition of trigonometry. If you use the Unit Circle definition of trigonometry then any proof of the Pythagorean that uses Trigonometry uses circular reasoning and is invalid. That is true for Jason Zimba’s proof and it is true for this girl’s proof. This girl then tries to use an alternative definition of Trigonometry based on Symmetry to claim her proof is valid. Not all mathematicians accept the Symmetry definition as a valid definition of Trigonometry, but if you do you can claim their proof is valid. However, under the Symmetry definition MANY trigonometric proofs of the Pythagorean theorem are valid and she can’t claim to solve an unsolved problem or a problem that has only been solved once. So they didn’t solve the impossible problem and the problem they did solve has been solved many times before.Xhat are the consequences of this discovery on the El-Kashi theorem which expanded the Pythagorean theorem to the the field of non rectangular triangle ?I sense some serious bullshit, and questionable timing (black ‘history’ month).It is sad that these keen girls are encouraged to believe such embarrassing nonsense.
There is as much merit in this as there is in the ridiculous claim that Nigerian Enoch Opeyemi cracked the Riemann Conjecture – viz., none.
Shame on those who have corrupted mathematics with DEI wokery and mediocrity.Is that you, Charlie Kirk? I would say if their work was published in the American Mathematical Monthly is has merit.Please keep them far from MAGAs, and Trump.Interesting! Kirk comments above need to be investigated and proved to clear the confussion and purported mislead.I would hope these young ladies are receiving scholarships…truly brilliant minds that would be an asset to any college. Well done young ladies!First to ‘Kirk’, “this girl” (as your comment states) is actually two girls and their names are Ne’Kiya Jackson and Calcea Johnson. After reading your comment I’m not even confident you’re real. Also, while I’m not versed enough to be able to break it all down myself the fact that this news got instant coverage years ago and then renewed coverage upon peer-reviewed publication indicates it’s a much bigger deal than you would like others to believe.Now to Daily Galaxy: Where have you been?? Were you waiting on peer review as well?? If 60 Minutes has covered these bright intellects over a year ago, it’s really not news anymore. I know a lot happens every day in the galaxy but you should try to catch up. At the same time, kudos for giving this story even belated bandwidth in this time of insecurity for both minorities and scientific facts.It’s so embarrassing whenever merely “language” graduates or whatever try to speak on STEM issue. Learn fist, the writhe your article.Comment Save my name, email, and website in this browser for the next time I comment.
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