High Schoolers Find ‘Impossible’ Proof For 2,000-Year-Old Math Rule

They have proved the Pythagorean theorem using trigonometry, a feat mathematicians long thought could not be done.

Ne'Kiya Jackson (left) and Calcea Johnson | Credit: Calcea Johnson / MMA

In December 2022, a high school in Louisiana challenged its students with a bonus math question that came with a $500 cash prize: Using trigonometry, they had to create a new proof of the Pythagorean theorem, the 2,000-year-old rule that explains the relationship between the lengths of sides on a right triangle. No one told the teenagers that mathematicians had long considered this task “impossible.”

So, when Ne’Kiya Jackson and Calcea Johnson came up with a solution, it sent shockwaves through the math world. They presented their proof a few months later at the American Mathematical Society in 2023, but it still needed further review. This week, the pair of students, who are now in college, have published their findings in a new study - along with additional proofs of the theorem.

The research published in The American Mathematical Monthly outlines “five or ten” new ways to prove the Pythagorean theorem using trigonometry. That is to say, each of their proofs demonstrates that the square of a right triangle’s longest side equals the sum of the squares of the two shorter sides.

Jackson and Johnson spent months coming up with their original proof, even working on weekends and holidays. In the new paper, they describe that achievement and, equally as extraordinary, four new proofs that they worked out afterward. They also outline a new method that could result in five additional proofs.

Although the Pythagorean theorem has been proved with algebra and geometry, mathematicians previously thought that it couldn’t be proved using trigonometry. Until these two remarkable high schoolers came along!

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