# How two high school students solved a 2,000-year-old math puzzle

A high school math teacher at St. Mary's Academy in New Orleans, Michelle Blouin Williams, was looking for ingenuity when she and her colleagues set a school-wide math contest with a challenging bonus question. That bonus question asked students to create a new proof for the Pythagorean Theorem, a fundamental principle of geometry, using trigonometry. The teachers weren't necessarily expecting anyone to solve it, as proofs of the Pythagorean Theorem using trigonometry were believed to be impossible for nearly 2,000 years.

But then, in December 2022, Calcea Johnson and Ne'Kiya Jackson, seniors at St. Mary's Academy, stepped up to the challenge. The \$500 prize money was a motivating factor.

After months of work, they submitted their innovative proofs to their teachers. With the contest behind them, their teachers encouraged the students to present at a mathematics conference, and then to seek to publish their work. And even today, they're not done. Now in college, they've been working on further proofs of the Pythagorean Theorem and believe they have found five more proofs. Amazingly, despite their impressive achievements, they insist they're not math geniuses.

"I think that's a stretch," Calcea said.

## The St. Mary's math contest

When the pair started working on the math contest they were familiar with the Pythagorean Theorem's equation: A² + B² = C², which explains that by knowing the length of two sides of a right triangle, it's possible to figure out the length of the third side.

When Calcea and Ne'Kiya set out to create a new Pythagorean Theorem proof, they didn't know that for thousands of years, one using trigonometry was thought to be impossible.  In 2009, mathematician Jason Zimba submitted one, and now Calcea and Ne'Kiya are adding to the canon.

Calcea and Ne'Kiya had studied geometry and some trigonometry when they started working on their proofs, but said they didn't feel math was easy. As the contest went on, they spent almost all their free time developing their ideas.

"The garbage can was full of papers, which she would, you know, work out the problems and if that didn't work, she would ball it up, throw it in the trash," Cal Johnson, Calcea's dad, said.

Neliska Jackson, Ne'Kiya's mother, says lightheartedly, that most of the time, her daughter's work was beyond her.

To document Calcea and Ne'Kiya's work, math teachers at St. Mary's submitted their 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,'" Ne'Kiya said. "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."

## Why Calcea' and Ne'kiya's work "blew up"

The reaction was insane and unexpected, Calcea said. News of their accomplishment spread around the world. The pair got a write-up in South Korea and a shoutout from former first lady Michelle Obama. They got a commendation from the governor and keys to the city of New Orleans.

Calcea and Ne'Kiya said they think there's several reasons why people found their work so impressive.

"Probably because we're African American, one," Ne'Kiya said. "And we're also women. So I think-- oh, and our age. Of course our ages probably played a big part."

Ne'Kiya said she'd like their accomplishment to be celebrated for what it is: "a great mathematical achievement."

In spite of the community's celebration of the students' work, St. Mary's Academy president and interim principal Pamela Rogers said that with recognition came racist calls and comments.

"[People said] 'they could not have done it. African Americans don't have the brains to do it.' Of course, we sheltered our girls from that," Rogers said. "But we absolutely did not expect it to come in the volume that it came."

Rogers said too often society has a vision of who can be successful.

"To some people, it is not always an African American female," Rogers said. "And to us, it's always an African American female."

## Success at St. Marys

St. Mary's, a private Catholic elementary and high school, was started for young Black women just after the Civil War. Ne'Kiya and Calcea follow a long line of barrier-breaking graduates. Leah Chase, the late queen of Creole cuisine, was an alum. So was Michelle Woodfork, the first African American female New Orleans police chief, and Dana Douglas, a judge for the Fifth Circuit Court of Appeals.

Math teacher Michelle Blouin Williams, who initiated the math contest, said Calcea and Ne'Kiya are typical St. Mary's students. She said if they're "unicorns," then every student who's matriculated through the school is a "beautiful, Black unicorn."

Students hear that message from the moment they walk in the door, Rogers said.

"We believe all students can succeed, all students can learn," the principal said. "It does not matter the environment that you live in."

About half the students at St. Mary's get scholarships, subsidized by fundraising to defray the \$8,000 a year tuition. There's no test to get in, but expectations are high and rules are strict: cellphones are not allowed and modest skirts and hair in its natural color are required.

Students said they appreciate the rules and rigor.

"Especially the standards that they set for us," junior Rayah Siddiq said. "They're very high. And I don't think that's ever going to change."

## What's next for Ne'Kiya and Calcea

Last year when Ne'Kiya and Calcea graduated, all their classmates were accepted into college and received scholarship offers. The school has had a 100% graduation rate and a 100% college acceptance rate for 17 years, according to Rogers.

Ne'Kiya got a full ride in the pharmacy department at Xavier University in New Orleans. Calcea, the class valedictorian, is studying environmental engineering at Louisiana State University. Neither one is pursuing a career in math, though Calcea said she may minor in math.

"People might expect too much out of me if I become a mathematician," Ne'Kiya said wryly.

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