Two Teenagers Solve a 2,000-Year-Old Math Problem

By: Beth Moreton | Published: May 12, 2024

Over the years, many math questions have puzzled many, including one that remained unsolved for 2000 years.

However, two teenagers managed to solve the problem after their teacher assigned it to their class, not thinking anyone would actually manage to do it.

The 2000-Year-Old Pythagorean Theorem

The Pythagorean Theorem is a 2000-year-old theory that has been taught to countless children in schools all over the world.

A drawing of the Pythagorean theorem. The drawing is of two triangles stuck together with different letters from A to H on each side.

Source: Castle Queens/Wikimedia Commons

The way they have been taught is that, when squared, the two shorter sides of a triangle equal the squared longer side of the triangle. 

Proof of Pythagorean Theorem Using Trigonometry

One question that has puzzled many mathematicians for years is how the Pythagorean theorem can be proved using trigonometry. 

A drawing showing trigonometry. The drawing shows a triangle with a Y and X axis.

Source: MikeRun/Wikimedia Commons

Many theories have been proposed about the problem over the years, but now, two teens from New Orleans have been able to refute these and solve the problem. 

The Teens Were Motivated by a $500 Cash Prize

Their teacher, Michelle Blouin Williams, offered her class a $500 cash prize if they could solve it and genuinely believed they wouldn’t be able to.

A pile of $100 notes secured with a black elastic band.

Source: bearfotos/Freepik

However, she was proved wrong when the two teenagers, Calcea Johnson and Ne’Kiya Jackson, were able to solve the problem, as they were motivated by the $500 cash prize. 

Johnson and Jackson Took Two Months to Solve the Problem

It took Johnson and Jackson a total of two months to be able to solve the problem.

Jackson and Johnson are standing before some blue, black and white balloons, smiling.

Source: @DarkBlue420/X

The pair also worked on the problem on over 30 pieces of paper until they eventually figured it out. 

Johnson and Jackson Found Five Proofs for Trigonometry and Pythagorean Theorem

Over the years, every mathematician has looked at this problem and decided that it was impossible to solve.

Jackson and Johnson during their “60 Minutes” interview. They are talking to Bill Whitaker and are sitting on wooden chairs. A screen on the wall shows their proof, which includes a triangle and letters against each side of the triangle.

Source: @60Minutes/X

However, over a year since they first solved the problem in 2023, Johnson and Jackson have been able to find five more proofs and have also discovered a general format that could produce a further five proofs.


Jackson and Johnson Presented Their Findings to the American Mathematical Society

Once they made their discovery, Jackson and Johnson presented their findings to the American Mathematical Society.

Jackson and Johnson at the American Mathematical Society meeting. They are standing in front of a sign that says “Welcome” in multiple languages.

Source: @siwonch/X

In doing so, they became the first high schoolers to present their findings to the society. 


Johnson and Jackson Credited Their Teachers With Their Findings

Johnson and Jackson attended St. Mary’s Academy in New Orleans, an all-girls Catholic school.

Jackson and Johnson are standing in front of a screen projector, showing their method for proving the link between the Pythagorean theorem and trigonometry.

Source: @true2thestory/X

They credited their teachers with helping them make the discovery, as they always pushed them to achieve what was previously thought to be impossible. 


Johnson and Jackson Have Contradicted Elisha Loomis

Since Johnson and Jackson have proved that there is trigonometric proof of the Pythagorean theorem, they have also contradicted Elisha Loomis’ theory.

A black and white image of Elisha Loomis. He has a thick mustache and is wearing a suit. His head is turned off to the side.

Source: Finkel, B. F./Wikimedia Commons

Elisha Loomis was a mathematician whose book, “The Pythagorean Proposition,” stated there was no trigonometric proof of the Pythagorean theorem and that if there was, it wouldn’t be correct. 


Mathematicians Thought Trigonometry Was Based on the Pythagorean Theorem

Part of Loomis’ theory was that trigonometry was based on the Pythagorean theorem.

A Pythagoras triangle with each side labeled a, b and c. Underneath is its links to trigonometry, which says sin x = a/c, cos x = b/c and tan x = a/b.

Source: Rusae/Wikimedia Commons

He said that using trigonometry to prove the Pythagorean theorem would result in going in circles, but it has since been proved wrong. 


Some Dismissed the News as Fake

Despite the proof Johnson and Jackson provided, a few people who have dismissed them solving the problem as fake.

Jackson and Johnson are going to high-five each other.

Source: @WordInBlack/X

The girls said these people had dismissed their achievements due to them being African-American women and teenagers, with the pair saying they just wanted their achievements to be celebrated as they are. 


Johnson and Jackson Were Given the Keys to the City

Despite some people not being overly convinced by their achievement, others have given Johnson and Jackson high praise.

Jackson and Johnson with Mayor LaToya Cantrell in the middle. The girls are holding their keys to the city.

Source: @BlkCathStories/X

So much so that they were given the keys to the city of New Orleans, a medieval tradition that means the honored persons can enter and leave a city of their own free will.