Calcea Johnson and Ne’Kiya Jackson first made headlines in 2022 while still in high school when they came up with inventive solutions to a 2,000-year-old math problem. The two found a new way to prove Pythagoras’s theorem by using trigonometry – which mathematicians for decades thought was impossible.
The 2,000-year-old theorem states that “the sum of the squares of a right triangle’s two shorter sides are equal to the square of the triangle’s longest side (the hypotenuse),” Live Science wrote. Several mathematicians over the years have proved the theorem using algebra and geometry, and they had long believed that using trigonometry to prove the theorem was impractical, given that “the fundamental formulas for trigonometry are based on the assumption that the theorem is true,” Live Science noted.
In March 2023, the students presented their proof to a meeting of the American Mathematical Society. Johnson and Jackson have now come up with five ways of solving the problem using trigonometry as well as a method that reveals five other proofs. Their 10 proofs were published Monday in the journal American Mathematical Monthly.
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Jackson said in a news release, “I was pretty surprised to be published. I didn’t think it would go this far.”
The two, who are now college students, began studying the arithmetic issue as part of a high school math competition in New Orleans‘ St. Mary’s Academy.
Neither of them is interested in a career in mathematics. Jackson received a full scholarship and is currently enrolled in Xavier University’s pharmacy program in New Orleans. Johnson, the valedictorian of her high school class, is now studying environmental engineering at Louisiana State University.
Johnson, however, previously stated that she could minor in math on CBS’s 60 Minutes.
She remarked in a statement, “I am very proud that we are both able to be such a positive influence in showing that young women and women of color can do these things, and to let other young women know that they are able to do whatever they want to do. So that makes me very proud to be able to be in that position.”
According to Live Science, Jackson and Johnson are only the third and fourth people to have proved the Pythagorean theorem using trigonometry and without resorting to circular reasoning. The two other people were professional mathematicians.
