According to US News and World Report, Louisiana is ranked 47th in education. Despite this, there are some schools providing students with a good education. One of those is St. Mary’s Academy of New Orleans.
To say trigonometry is hard would be an understatement. For those who are mathematically challenged like myself, it likely involves several hours each day studying, creating note cards, reading and rereading chapters, watching class videos and YouTube videos. By the time I was done, I was proud I could perform basic equations. There was no way on Earth I could create something new and unique out of it.
Two arguably brilliant alumnae of New Orleans East’s St. Mary’s Academy did just that. St. Mary’s, an all-girls, African American primary school, recently had two of its graduates solve the unsolvable. Calcea Johnson and Ne’Kiya Jackson, according to an interview they gave to 60 Minutes, were initially motivated by a cash prize of $500, as Jackson admitted in the interview.
“I was motivated because there was a monetary incentive.”
Johnson agreed. “’Cause I was like, $500 is a lot of money. So I– I would like to at least try.”
Both individuals managed to solve a math problem that supposedly was unsolvable. According to Elisha Scott Loomis, who is most famous for his book “The Pythagorean Proposition” a book that contains 344 proofs, it could not be done. He writes, “…that no trigonometric proof is possible.” He also writes: “There are no trigonometric proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem…”
In other words, according to an article in Scientific American, “Loomis believed that if you used these functions in a proof of the Pythagorean Theorem, you would have assumed the Theorem to begin with—a circular argument and thus an unforgivable mathematical error.”
For those who have not suffered through trigonometry, or have forgotten geometry altogether, the formula is simply a² + b² = c² which according to Brian Whittaker of 60 Minutes: “In plain English, when you know the length of two sides of a right triangle, you can figure out the length of the third.”
The bonus question was to create a Proof of the Pythagorean Theorem using trigonometry. According to the abstract Jackson and Johnson gave to the American Mathematical Society on March 18, 2023, they said:
“In the 2000 years since trigonometry was discovered it’s always been assumed that any alleged proof of Pythagoras’s Theorem based on trigonometry must be circular. In fact, in the book containing the largest known collection of proofs (The Pythagorean Proposition by Elisha Loomis) the author flatly states that “There are no trigonometric proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem.” But that isn’t quite true: in our lecture we present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry—the Law of Sines—and we show that the proof is independent of the Pythagorean trig identity \sin^2x + \cos^2x = 1.
Since both young women individually came up with the proof, Brian Whittaker of 60 Minutes was compelled to ask, “So are you math geniuses?” Jackson and Johnson were quite humble in response.
Johnson replied, “I think that’s a stretch.” And Jackson added, “Not at all.”
When asked why people might be especially impressed, besides only one other person creating a new proof in 2000 years, Jackson 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.”
While their accomplishment is impressive, St. Mary’s has many impressive things about it. In the last 17 years, the school boasts a 100 % graduation rate and a 100% college acceptance rate, and St. Mary’s is known for helping children reach a high potential.
Whittaker also interviewed the young pair’s former math teacher, Michelle Blouin Williams. “They’re not unicorns?” he asked.
Teacher Michelle Blouin Williams is clearly proud of her students and the school. “Oh, no no. If they are unicorns, then every single lady that has matriculated through this school is a beautiful Black unicorn.”
St. Mary’s Interim Principal and President, Pamela Rogers, agrees, “We believe all students can succeed, all students can learn. It does not matter the environment that you live in.”
Exactly how Jackson and Johnson’s Proof works is not yet publicly available online since their results have only recently been presented to the Math Institute and are not fully published yet. However, a couple of places on YouTube have some guesses based on the images WWL-TV posted in their video interview with them.
