March 27, 2023

Have Two Black Teens Solved A 2,000-Year-Old Math Mystery?

Two Black high school students say they have solved a mathematical mystery that some claim has eluded mathematicians for over 2,000 years.

Calcea Johnson and Ne’Kiya Jackson, both students at St. Mary’s Academy, presented their new proof for the Pythagorean theorem at the American Mathematical Society’s Annual Southeastern Conference in Georgia on March 18.

The Pythagorean theorem is a fundamental theorem in trigonometry that describes the relationship between the three sides of a right-angled triangle. It is expressed with the formula a² + b² = c².

The theorem holds true in every plausible example and has been around since the days of the Ancient Greeks.

American mathematician Elisha Loomis argued that no mathematician has been able to establish its truth without using circular logic i.e. without using Pythagorean Theorem. The two students presented a new proof of Pythagoras’ theorem using the Law of Sines, which they claim did not rely on circular trigonometry.

a^2 + b^2 = c^2

The first to do it?

Several mathematicians have argued Pythagorean theorem can be proved without circular logic using the notion of similar triangles. Still, they applaud Calcea and Ne’Kiya for their innovative work.

“It appears these 2 students at least managed to 1) recognise Loomis’ statement was too sloppy/general to be true, and 2) produce a PT proof for which either the method or its described relation to trig (media coverage has been short on details) is not replicated in Loomis’ book,” said Cambridge mathematician Sarah Rasmussen wrote in a tweet.

“Both of these are excellent accomplishments, and the students should be very proud of the work they did.”

Putting the proof to the test

Calcea and Ne’Kiya were the only high school students at the conference, and their achievement was celebrated by the American Mathematical Society executive director Catherine Roberts.

She encouraged the teenagers to submit their findings to a journal to go through the rigorous academic peer-review process and be confirmed by other experts in the field, as per the Guardian.

Johnson and Jackson’s achievement is significant, not just for their school but also for young Black girls worldwide.

In an interview with New Orleans television news station WWL, Johnson expressed how it felt to present her and Jackson’s work alongside university researchers: “There’s nothing like it – being able to do something that people don’t think that young people can do. You don’t see kids like us doing this – it’s usually, like, you have to be an adult to do this.”

The girls credited their success to the hard work and dedication of their teachers at St. Mary’s Academy. Ne’Kiya said, “We have really great teachers.”


This article was corrected on March 28, 2023. The article previously stated that the Pythagorean theorem had yet to be proven without using circular logic. The article has been amended to acknowledge that this argument was posited by American mathematician Elisha Loomis and is not accepted by all mathematicians.

This article was amended on March 30, 2023 to include a quote by Sarah Rasmussen.

Samara Linton

Community Manager at POCIT | Co-editor of The Colour of Madness: Mental Health and Race in Technicolour (2022), and co-author of Diane Abbott: The Authorised Biography (2020)