# New Orleans teens solve 2,000-year-old math problem

By Bo Beard | May 11, 2024

### Some ingenuity

Teacher Michelle Blouin Williams initiated a math competition with a bonus question tasking students to develop a new proof for the Pythagorean theorem using trigonometry, without anticipating that anyone would successfully tackle the challenge.

She said, “I was just looking for some ingenuity.”

### Williams' expectations

Calcea Johnson and Ne’Kiya Jackson exceeded Williams' expectations by successfully solving the challenge in 2023.

### St. Mary's Academy

These two teenagers, who were seniors at St. Mary's Academy in New Orleans, a renowned Catholic school for girls with impressive college acceptance and graduation rates, were featured on CBS News' "60 Minutes" to discuss their accomplishment.

### $500 reward

Initially enticed by the math competition's $500 reward, their determination to complete the task intensified as they delved into the complex bonus question.

### Two months

Over a period of two months, these high school seniors dedicated themselves to completing their proof.

### Pages and pages

During an interview with "60 Minutes," CeCe Johnson, the mother of Calcea, said “It was pages and pages and pages of, like, over 20 or 30 pages for this one problem.”

### The garbage can

Her father, Cal Johnson, added, “Yeah, 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.”

### Upon completion

Upon completion, the teachers at St. Mary's Academy acknowledged the significance of Calcea and Ne'Kiya's achievement and submitted their proof to the American Mathematical Society for recognition at a conference in March 2023, where the students presented their findings.

### The Pythagorean theorem

The Pythagorean theorem, at its core, states that knowing the lengths of two sides of a right triangle allows you to determine the length of the third side using the formula a² + b² = c².

### Pythagoras

While commonly attributed to the Greek mathematician Pythagoras, historical evidence suggests its existence in Babylon and Iron Age India. This theorem finds practical applications in construction, architecture, navigation, and surveying.

### A mathematical proof

A mathematical proof is a logical argument that demonstrates the truth of a mathematical theorem. American mathematician Daniel Kane likens proofs to essays, but rooted in mathematical concepts.

### Using trigonometry

As per the "60 Minutes" segment, “there had been more than 300 documented proofs of the Pythagorean Theorem using algebra and geometry, but for 2,000 years a proof using trigonometry was thought to be impossible.”

### Mathematician Elisha Loomis

Back in 1927, mathematician Elisha Loomis made a statement in his book "The Pythagorean Proposition." Loomis contended that a trigonometric proof of the theorem was impossible as it would create a circular argument.

### Stuart Anderson

Stuart Anderson, a retired mathematics professor from Texas A&M University-Commerce, mentioned to Scientific American, “A lot of the basic trig ‘identities’ are nothing more than Pythagoras’ theorem.”

### Trigonometric functions

Loomis contended that attempting to use trigonometric functions to prove the Pythagorean theorem would result in a circular reasoning loop, as the functions themselves are built upon the theorem. This, according to Loomis, would constitute a fundamental mathematical mistake.

### The law of sines

As reported by Scientific American, the teenagers challenged this notion during their presentation in 2023 and stated that “a trigonometric identity called the law of sines didn’t depend on the Pythagorean theorem and that they could use it to prove the theorem.”

### Final peer review

Calcea and Ne'Kiya are now part of a select few who have achieved a similar milestone, such as mathematician Jason Zimba, who developed a new proof in 2009. They submitted their proof for the final peer review earlier this year and are actively working on crafting additional proofs.

### In recognition

In recognition of their accomplishment, the teenagers were honored with the keys to the city of New Orleans and received commendations from the governor of Louisiana, along with other public acknowledgments.

### Widespread recognition

Despite the widespread recognition of their accomplishment which “blew up,” as Ne'Kiya expressed it, the two students maintain their humility and even chuckled at being labeled as geniuses.

### Surprised and skeptical

Upon the revelation of their achievement, there were individuals who appeared surprised and skeptical, dismissing the news as untrue, as mentioned by St. Mary's president Pamela Rogers during the interview.

### African Americans

“They were saying, ‘Oh, they could not have done it. African Americans don’t have the brains to do it.’ ... People — have a vision of who can be successful. And — to some people, it is not always an African American female. And to us, it’s always an African American female.”

### The significant reaction

When questioned by interviewer Bill Whitaker about their thoughts on the significant reaction, Ne’Kiya said, “Probably because we’re African American, one. And we’re also women. So I think — oh, and our age. Of course our ages probably played a big part.”

### Great mathematical achievement

“I’d like to actually be celebrated for what it is. Like, it’s a great mathematical achievement,” she continued.