LSU’s Calcea Johnson Publishes Groundbreaking Research in The American Mathematical Monthly

Calcea Johnson, an LSU environmental engineering sophomore, has achieved a milestone few undergraduates reach: publication in The American Mathematical Monthly, one of the field’s most respected journals.

Johnson and her former high school classmate Ne’Kiya Jackson discovered a new way to prove Pythagorean’s Theorem using trigonometry as part of a high school math contest. 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.

They presented their findings at the American Mathematical Society's Spring Southeastern Sectional Meeting in March of 2023 and then submitted their work for publication while Johnson was a freshman at LSU.

“I am honored to be published in The American Mathematical Monthly and proud of myself for staying with this project until the end,” Johnson said. “The process of writing the paper was challenging and felt tedious at times, but the reward of it being published was worth it.”

That proof is now the lead article for the November issue of The American Mathematical Monthly, called “Five or Ten New Proofs of the Pythagorean Theorem.” Their work outlines five new ways of proving the theorem and a method that reveals five more proofs, totaling 10 proofs altogether. Only one of those proofs was previously presented at the conference, meaning nine are totally new.

“Four of the proofs in the paper are new in relation to the American Mathematical Society conference. Only one of the proofs from the conference is featured in the paper, and we created new proofs while composing the paper,” Johnson said.

The American Mathematical Monthly is published by the Mathematical Association of America or MAA. The group focuses on expository articles that bring significant mathematical advances to a broad audience. Known for its rigorous standards, the journal has played a key role in shaping modern mathematical thought and fostering scholarly communication.

“The Monthly is honored and delighted to publish the work of these two students on its pages,” said Della Dumbaugh, editor of The American Mathematical Monthly. “Their results call attention to the promise of the fresh perspective of students on the field. They also highlight the important role of teachers and schools in advancing the next generation of mathematicians. Even more, this work echoes the spirit of Benjamin Finkel when he founded the Monthly in 1894 to feature mathematics within reach of teachers and students of mathematics.”

Johnson and Jackson, both from New Orleans, have received national attention for their findings, including a feature on “60 Minutes.”

“After the “60 Minutes” story, I heard from many environmental engineers offering mentorship and advice from their experiences. I am very glad that this experience has connected me with people in my field,” Johnson said.

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