By, Phoenix Robertson

Dedication

I’d like to dedicate this article to my middle-school math teacher, who taught me about math and life in the seventh and eighth grades. She has always been a wonderful mentor to me, even all these years later. You taught me that math can take me on adventures, but our adventures always seemed to track back to the pyramids. It was always a joy to build pyramids with you. Thank you for everything, and I’m sure you’ll be as equally excited as I was to learn about this topic. 

A² + b² = c² is a famous theorem that has haunted school children and mathematicians alike for thousands of years, although be it for drastically different reasons. Students hate it because it doesn’t have the visual appeal of 2 + 2= 4 and mathematicians hate it because in 2000 years there’d only been 1 proof done of the theorem using geometry. For those of you who aren’t particularly algebraic, to nod to the famous Adventure Time catchphrase, the proof is a way of telling if a mathematical concept is true or not. The general rule of thumb is that the more proofs something has associated with it, the more plausible it is. There are various methods of performing proofs including paragraph proofs and, my personal favorite, two-column proofs. I’ll spare you the gory details of how to do proofs on your own because chances are, you don’t care, but it is crucial to understand that proofs are how anything gets done in the math world, so when new proofs emerge for a centuries-old theorem, which was the case for  two high schoolers, you can imagine the shock that ensued.

The History of the Pythagorean Theorem

The Pythagorean Theorem was coined by, you guessed it, Pythagoras. Pythagoras was an ancient Greek mathematician and philosopher who was responsible for the creation of the Pythagorean Brotherhood– a secret society dedicated to the study of math. His most famous mathematical venture was the study of a theorem that can be used to find the side length of a right triangle, provided you have the length of two of its sides. He didn’t create this idea, as The relationship was shown on a 4000-year-old Babylonian tablet now known as Plimpton 322, yet Pythagoras is attributed to the popularization of the theorem. The theorem is still used today and is crucial in various fields, including construction, manufacturing, and navigation, enabling precise measurements and the creation of right angles for large structures. 

Theorems Emerge 

After a few thousand years on the block, mathematicians are still hard at work finding new ways to prove the Pythagorean Theorem, but recently two unsuspecting students were able to crack the code– twice. Calcea Johnson and Ne’Kiya Jackson attend St. Mary’s Academy in New Orleans and were able to find 2 new proofs for the Pythagorean Theorem using trigonometry. The two revealed their findings at a meeting for the American Mathematical Society and said “It’s an unparalleled feeling, honestly, because there’s just nothing like it, being able to do something that … people don’t think that young people can do.”

This all started when the pair were in their final year of high school and were given a math contest bonus question to work on over their winter break. In response to the question, they came up with two new proofs for the theorem in a way that was thought to be impossible. Johnson’s proof is called the “Wafflecone.” She described to 60 Minutes that if you create two congruent right triangles, followed by an infinite series of smaller right triangles going downwards, then the Pythagorean Theorem will be proved. Jackson’s proof stems from her idea that if you have a right triangle and place that triangle inside of a circle, that you can then divide the triangle using a perpendicular bisector. A perpendicular bisector is a line that bisects another line segment at a right angle, through the intersection point. The use of this bisector creates a smaller right triangle and proves the theorem yet again. Now as college students, they are receiving a great deal of fame in the math world for their discoveries. 

Many are rushing to acclaim the discovery as an amazing mathematical feat achieved by two African American high school girls and, technically, they aren’t wrong. Johnson and Jackson are African American and attended a school that is partly an all-girls school, but the pair of young mathematicians don’t want to just be recognized for their race and gender. In response to being asked why people are finding their proofs so fascinating, Johnson had this to say on 60 Minutes: “Probably because we’re African American, for one, and we’re also women and our age has played a big part. I’d like it to actually be celebrated for what it is; it’s a great mathematical achievement.” 

The findings of Johnson and Jackson are fascinating and will without a doubt change the face of the math world forever. Their findings will be revered for years to come as a new feat of mathematics and as a testament to the things that can be achieved by youth. If you’re ever faced with the question of “To do or not to do, should I do this bonus question?”, do it! You never know if you’ll manage to come up with a never-before-done proof of a mathematical concept. Thanks for reading, and stay algebraic!