Who Are Calcea Johnson and Ne’Kiya Jackson?

My VIPs for this week are Calcea Johnson and Ne'Kiya Jackson, two teenaged girls from New Orleans. According to an article by Asia Brown in the Deseret News, the two young women created a new proof for the Pythagorean theorem using trigonometry. When teacher Michelle Blouin Williams first started the math contest, she did not expect anyone to finish it. 

Johnson and Jackson proved her wrong when they figured out the answer in 2023. The two girls were then seniors at St. Mary’s Academy in New Orleans, a prestigious Catholic school for girls. The record for the school itself is beyond outstanding as the school has maintained “a 100% acceptance rate to colleges and 100% graduation rate for 17 years.”

The girls were first enticed with the $500 prize. However, it was their inner drive that took over once the work became difficult. The two girls worked for two months to answer the problem that took “over 20 or 30 pages” to work it, according to one mother.

Brown said that “teachers at St. Mary’s recognized the importance of [the girls’] work and submitted their proof to the American Mathematical Society for recognition at a conference in March 2023, where the students presented their work.”

In case you are wondering what the Pythagorean theorem is and what is a proof, Brown’s article gave the answer as follows.

In essence, the mathematical theorem states that knowing the lengths of two sides of a right triangle enables you to figure out the length of the third using this formula: a² + b² = c².

It’s associated with Greek mathematician Pythagoras, but evidence suggests it was known earlier, in Babylon and Iron Age India, per Britannica. Its practical uses include construction and architecture, two-dimensional navigation, and surveying.

A mathematical proof is exactly what it sounds like: reasoning that proves a mathematical theorem is true. American mathematician Daniel Kane explains proofs as being like essays, but using math.

According to the “60 Minutes” episode, “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.”

In 1927, mathematician Elisha Loomis said as much in his book, “The Pythagorean Proposition.” Loomis argued that there could be no trigonometric proof of the theorem because it would be circular.

Sturt Anderson, a professor emeritus of mathematics at Texas A&M University-Commerce, told Scientific American, “A lot of the basic trig ‘identities’ are nothing more than Pythagoras’ theorem.”

Loomis argued that using trigonometric functions to prove the Pythagorean theorem would be like going in circles, but the girls differed in their opinion. They said 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.”

Their accomplishment puts Johnson and Jackson into “an extremely small group” of people who have accomplished the same feat. Mathematician Jason Zimba created a new proof in 2009. After they submitted their proof for final peer review this spring, they continued to work on more proofs. Johnson and Jackson laugh at the idea that they are geniuses. They prefer to consider their accomplishment as “a great mathematical achievement.”