US teens say they have new proof for 2,000-year-old mathematical theorem

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Abstraction: High schoolers' trigonometric proof challenges 2,000-year circular reasoning prohibition

Key points:

Calcea Johnson and Ne'Kiya Jackson of St Mary's Academy, New Orleans, presented proof at American Mathematical Society southeastern chapter meeting in March 2023
Proof uses the Law of Sines and is explicitly independent of the identity sin²x+cos²x=1, avoiding the circular reasoning that mathematicians have long said makes any trig-based proof invalid
Elisha Loomis's "The Pythagorean Proposition" (the largest known collection of proofs) flatly states "there are no trigonometric proofs" — the students directly refuted this claim
They were the only high schoolers presenting at a meeting attended by university researchers from Alabama, Georgia, LSU, Ohio State, Oklahoma, and Texas Tech
AMS executive director Catherine Roberts encouraged them to submit to a peer-reviewed journal

Connections: American Mathematical Society · Mathematics · Trigonometry · Mathematical Proof