Calcea Johnson and Ne’Kiya Jackson, who surprised the world of mathematics when they produced innovative solutions to a 2,000-year-old puzzle, they once again wowed the world of mathematics by presenting several new ways to prove the Pythagorean theorem via trigonometry.

The two men, now students, found five ways to solve the problem using trigonometry as well as a method that reveals five other proofs. One of their proofs had already been presented at a conference and their new solutions were published Monday in the American Mathematical Monthly journal.

They began studying the math problem as part of a high school math competition at St. Mary’s Academy in New Orleans. One of their proofs had already been presented at a conference and their new solutions were published Monday in the American Mathematical Monthly journal.

“I was quite surprised to be published,” Jackson said in a press release. “I didn’t think it would go this far.”

Della Dumbaugh, editor-in-chief of the American Mathematical Monthly, said Jackson and Johnson’s work draws attention to the promise that new perspectives can bring to the field.

“They also highlight the important role of teachers and schools in fostering the next generation of mathematicians,” Dumbaugh said.

Jackson is now a student in the pharmacy department at Xavier University in New Orleans, where she has completed a full tour. Johnson, who was valedictorian in high school, is studying environmental engineering at Louisiana State University. Neither is pursuing a career in mathematics, although Johnson has previously stated 60 minutes she may have a minor in mathematics.

“I’m 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 letting other young women know that they can do whatever they want, so it makes me very proud to be able to hold this position,” Johnson said.

St. Mary’s Math Competition

Students began their investigation in a school-wide maths competition with a challenging bonus question, which asked them to create a new proof of the Pythagorean theorem, a fundamental principle of geometry, by using trigonometry.

Over the years, many mathematicians have proven the theorem using algebra and geometry. For thousands of years, a proof by trigonometry was considered impossible. Mathematician Jason Zimba submitted one in 2009 and now Johnson and Jackson have added to the canon.

They were in their final year of high school during the math competition, motivated by the promise of a $500 prize. For several months, the students spent almost all their free time developing their ideas.

Mathematics teachers in Sainte-Marie then submitted Johnson and Jackson’s proofs to an American Mathematical Society conference in Atlanta in March 2023.

“Well, our professor approached us and said, ‘Hey, maybe you could present this,'” Jackson told 60 Minutes. “I was like, ‘Are you kidding me?’ But it wasn’t. So we went up there and it went well, and it blew up.

Despite their impressive results, the students insisted to 60 Minutes that they are not math geniuses.

“I think it’s overblown,” Johnson said.