LSU Freshman Discovers New Pythagorean Theorem Proof While in High School

March 22, 2024

An LSU freshman is on her way to having her name and work part of mathematics history. Meet Calcea Johnson. While in high school in New Orleans, Johnson discovered a new proof for the Pythagorean Theorem.

LSU student Calcea Johnson seen walking on campus

LSU student Calcea Johnson and a high school classmate discovered a new proof for the Pythagorean Theorem.

– Katherine Seghers, LSU

“It really started with a math contest by our high school. This was its second year, and it had a bonus question: to create a new proof of the Pythagorean Theorem,” Johnson said. “There was also a monetary incentive, $500, and that was really great for a senior in high school. But $500 is not that much when you start doing all this work. We were the only two in the whole school to come up with a solution to the bonus question."

The work done by Johnson and her classmate, Ne’Kiya Jackson, proved Pythagorean’s Theorem using trigonometry. The 2,000-year-old theorem states that in a right-angled triangle, the square of the hypotenuse side equals the sum of squares of the other two sides.

“It was a lot of trial and error,” Johnson said.

They presented their work at the American Mathematical Society semi-annual conference. Johnson said they are waiting for it to be published in a leading mathematical journal.

“If it is accepted into a journal, which we hope it is, then it would mean that our work has been accepted by the math community, which means it's solid and valid. We've had a lot of mathematicians look over our paper beforehand, and they've all said, ‘The math is good. It's valid. This is a good proof,’” Johnson said.

While the proof is on its way to becoming part of the annals of mathematics, her story has received national and international attention.

LSU Freshman Discovers New Pythagorean Theorem Proof While in High School

– Katherine Seghers, LSU

“I would have never expected that this would go so far, so quickly, because it just really took off,” Johnson said. “I feel really blessed to have this recognition and for people to see that young people, people of color, and women can do these things. So even though I am getting the attention, I feel like it's important to remember the other people who are also doing these things who I represent.

When she’s not being interviewed about her mathematics discovery, Johnson is an LSU Ogden Honors College student studying environmental engineering.

“LSU just felt so welcoming, and all of the professors seemed like they cared about the students,” Johnson said. “I really, really felt that love, and I felt that there were a lot of resources for students.”