The Daily Populous Wednesday May 8th, 2024 night edition
Authored by theguardian.com and submitted by JLaws23

Two college freshmen who, during their final year of high school, found a new way to prove Pythagoras’s theorem by using trigonometry – which mathematicians for generations thought was impossible – have since uncovered multiple more such proofs, they revealed in a national interview on Sunday.

“We found five, and then we found a general format that could potentially produce at least five additional proofs,” Calcea Johnson said on CBS’s 60 Minutes, a little more than a year after she and Ne’Kiya Jackson collaborated on an accomplishment that earned them international recognition.

Nonetheless, in comments that stunned their interviewer, Bill Whitaker, the two graduates of St Mary’s Academy in New Orleans denied seeing themselves as math geniuses and dismissed any interest in pursuing careers in mathematics.

“People might expect too much out of me if I become a mathematician,” Jackson said, shaking her head. Johnson, for her part, added: “I may take up a minor in math, but I don’t want that to be my job job.”

Sunday’s conversation on CBS’s popular Sunday evening news magazine were perhaps their most extensive, widely broadcast remarks to date on the new ground that they broke with respect to the Pythagorean theorem.

The 2,000-year-old theorem established that the sum of the squares of a right triangle’s two shorter sides equals the square of the hypotenuse – the third, longest side opposite the shape’s right angle. Countless schoolchildren taking geometry have memorized the notation summarizing the theorem: a2 + b2 = c2.

For 2,000 years, mathematicians maintained that any alleged proof of the Pythagorean theorem that was based in trigonometry would constitute a logical fallacy known as circular reason – in essence, trying to validate an idea with the idea itself.

But the bonus question on a math contest that Johnson and Jackson took home to complete during the Christmas break of their final year at St Mary’s served as the impetus for them to plot out a new way to demonstrate that one could indeed use trigonometry to prove Pythagoras’s theorem.

Their work was so compelling that the pair went to a regional meeting of the American Mathematical Society in Atlanta in March 2023 to outline their findings. At the organization’s recommendation, Jackson and Johnson have submitted their discoveries for final peer review and publication – as well as working on additional proofs while that process is pending, as 60 Minutes noted.

The 60 Minutes interview gave Johnson and Jackson occasion to reflect on the intense reaction caused by initial media reports on their innovative work at St Mary’s, a Catholic high school that has been dedicated to educating Black girls since its founding shortly after the US civil war.

Some of it was negative. Some in the math community smarted at claims in a press release issued by St Mary’s that asserted Jackson and Johnson’s research was “unprecedented”. And they flocked to social media demanding that a 2009 trigonometry-based proof for Pythagoras’s theorem get its due.

Yet a lot of the reaction to Johnson and Jackson was positive, especially as mathematicians who picked apart their work confirmed that – by all indications – they had arrived at a valid new proof, a celebration-worthy accomplishment.

Michelle Obama wrote a post on social media that linked to a story about Johnson and Jackson, adding the text: “I just love this story. … Way to go, Ne’Kiya and Calcea! I’m rooting for you and can’t wait to see what you all do next.”

They also received a commendation from Louisiana’s then governor as well as symbolic keys to the city of New Orleans.

Asked on 60 Minutes why they thought people were so impressed with what they had done, Jackson said she thought the public was surprised young Black women could author such a feat.

“I’d like to be celebrated for what it is,” Jackson said. “Like – it’s a great mathematical achievement.”

Jackson is now attending New Orleans’ Xavier University and enrolled in its pharmacy department. Meanwhile, Johnson – who graduated from St Mary’s as its valedictorian – is now an environmental engineering student at Louisiana State University in Baton Rouge.

NyriasNeo on May 7th, 2024 at 13:41 UTC »

I read the proof. It is actually quite clever. The simple standard algebraic proof uses the "square in a square" set up, but have to reply on (a+b)^2 = a^2 + 2ab + b^2 to complete the proof.

This one only uses ratios. But the core concept is not too different. You are constructing a set up where you can calculate the area of a target shape by TWO different method (typically one by straight simple calculation ... like the right triangle on part 10/13 and the other by adding up areas of multiple pieces), set them to equal, and let the final answer comes out. The square in square proof also do this.

So the trick is finding the right pieces to add up, using only ratios. That is the real contribution here. I wonder how they find the set up ... they must have pretty good intuition.

flux_capacitor3 on May 7th, 2024 at 12:15 UTC »

I consider myself pretty decent at math. But, when I took a Proofs class during my engineering program, dang, that class made me feel dumb. Great work from these two!

randomsnowflake on May 7th, 2024 at 11:01 UTC »

Article is mostly filler and doesn’t explain the five additional ways to prove the theorem. This is a wonderful achievement for both Ms. Jackson and Ms. Johnson. Just wish the article went into the work a bit more.

Edit: Well, heck. This post blew up. Let’s add some sauce:

Polymathematic’s video breakdown I kept up through the trig but he lost me at the calculus 😵‍💫 it only explains one of the ways they proved the theorem.

60 Minutes segment from this post Sunday, which goes into more detail but keeps it high level and focuses on their achievements through interviews with their parents and teachers.

There’s also a bunch of links to check out in the replies below.