Calcea Johnson and Ne’Kiya Jackson, who surprised the math world when they produced innovative solutions to a 2,000-year-old puzzle, wowed the math world again when they presented several new ways of proving the Pythagorean Theorem via trigonometry.

The two, now college students, have come up with five ways of solving the problem using trigonometry along with a method that reveals five other proofs. One of their proofs was previously presented at a conference and their new solutions were published Monday in the journal American Mathematical Monthly.

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

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

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

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

Jackson is now a student in the pharmacy department at Xavier University in New Orleans, where she got a full ride. Johnson, who was high school class valedictorian, is studying environmental engineering at Louisiana State University. Neither one is pursuing a career in math, though Johnson previously told 60 Minutes she may minor in math.

“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,” Johnson said.

The St. Mary’s math contest 

The students started researching as part of a school-wide math contest with a challenging bonus question, which asked students to create a new proof for the Pythagorean Theorem, a fundamental principle of geometry, using trigonometry.

Many mathematicians over the years have proved the theorem using algebra and geometry. For thousands of years, a proof using trigonometry was thought to be impossible. Mathematician Jason Zimba submitted one in 2009 and now Johnson and Jackson have added to the canon.

They were seniors in high school during the math contest, motivated by the promise of $500 in prize money. Over several months, the students spent almost all their free time developing their ideas.

Math teachers at St. Mary’s later submitted Johnson and Jackson’s proofs to an American Mathematical Society conference in Atlanta in March 2023.

“Well, our teacher approached us and was like, ‘Hey, you might be able to actually present this,'” Jackson told 60 Minutes. “I was like, ‘Are you joking?’ But she wasn’t. So we went. I got up there. We presented and it went well, and it blew up.”

Despite their impressive achievements, the students insisted to 60 Minutes that they’re not math geniuses.

“I think that’s a stretch,” Johnson said.