Teens come up with answer to problem that stumped math world for centuries

This is an updated mentation of a communicative archetypal published connected May 5, 2024.

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For galore precocious schoolhouse students returning to class, it whitethorn look similar geometry and trigonometry were created by the Greeks arsenic a signifier of torture. 

So ideate our amazement erstwhile we heard 2 precocious schoolhouse seniors had proved a mathematical puzzle that was thought to beryllium intolerable for 2 1000 years. 

We met Calcea Johnson and Ne'Kiya Jackson astatine their all-girls Catholic precocious schoolhouse successful New Orleans. And, arsenic we archetypal reported past year, we expected to find 2 mathematical prodigies.  

Instead, we recovered astatine St. Mary's Academy, each students are told their possibilities are boundless.

Come Mardi Gras season, New Orleans is live with colorful parades, replete with floats, and beads, and precocious schoolhouse marching bands.

In a metropolis wherever uniqueness is celebrated, St. Mary's stands retired – with young African American women playing trombones and tubas, twirling batons and dancing - doing it all, which defines St. Mary's, students told us.

Junior Christina Blazio says the schoolhouse instills successful them they person the quality to execute anything. 

Christina Blazio: That is kinda a modular here. So we purpose precise precocious - like, our purpose is excellence for each students. 

The backstage Catholic simple and precocious schoolhouse sits down the Sisters of the Holy Family Convent successful New Orleans East. The academy was started by an African American nun for young Black women conscionable aft the Civil War. The convent inactive supports the schoolhouse with the assistance of alumni.

In December 2022, seniors Ne'Kiya Jackson and Calcea Johnson were moving connected a school-wide mathematics contention that came with a currency prize.

Ne'Kiya Jackson and Calcea Johnson 60 Minutes

Ne'Kiya Jackson: I was motivated due to the fact that determination was a monetary incentive.

Calcea Johnson: 'Cause I was like, "$500 is simply a batch of money. So I-- I would similar to astatine slightest try."

Both were staring down the thorny bonus question.

Bill Whitaker: So archer me, what was this bonus question?

Calcea Johnson: It was to make a caller impervious of the Pythagorean Theorem. And it benignant of gave you a fewer guidelines connected however would you commencement a proof.

The seniors were acquainted with the Pythagorean Theorem, a cardinal rule of geometry. You whitethorn retrieve it from precocious school: a² + b² = c². In plain English, erstwhile you cognize the magnitude of 2 sides of a close triangle, you tin fig retired the magnitude of the third.

Both had studied geometry and immoderate trigonometry, and some told america mathematics was not easy. What nary 1 told them was determination had been much than 300 documented proofs of the Pythagorean Theorem utilizing algebra and geometry, but for 2,000 years a impervious utilizing trigonometry was thought to beryllium impossible, … and that was the bonus question facing them.

Bill Whitaker: When you looked astatine the question did you think, "Boy, this is hard"?

Ne'Kiya Jackson: Yeah. 

Bill Whitaker: What motivated you to say, "Well, I'm going to effort this"?

Calcea Johnson: I deliberation I was like, "I started something. I request to decorativeness it." 

Bill Whitaker: So you conscionable kept connected going.

Calcea Johnson: Yeah.

For 2 months that winter, they spent astir each their escaped clip moving connected the proof.

CeCe Johnson: She was like, "Mom, this is simply a small spot excessively much."

CeCe and Cal Johnson are Calcea's parents.

CeCe Johnson: So past I started looking astatine what she truly was doing. And it was pages and pages and pages of, like, implicit 20 oregon 30 pages for this 1 problem.

Cal Johnson: Yeah, the garbage tin was afloat of papers, which she would, you know, enactment retired the problems and-- if that didn't enactment she would shot it up, propulsion it successful the trash. 

Bill Whitaker: Did you look astatine the problem? 

Neliska Jackson is Ne'Kiya's mother.

Neliska Jackson: Personally I did not. 'Cause astir of the clip I don't recognize what she's doing (laughter).

Michelle Blouin Williams: What if we did this, what if I constitute this? Does this help? ax² positive ….

Their mathematics teacher, Michelle Blouin Williams, initiated the mathematics contest.

Michelle Blouin Williams 60 Minutes

Bill Whitaker: And did you deliberation anyone would lick it?

Michelle Blouin Williams: Well, I wasn't needfully looking for a solve. So, no, I didn't—

Bill Whitaker: What were you looking for?

Michelle Blouin Williams: I was conscionable looking for immoderate ingenuity, you know—

Calcea and Ne'Kiya delivered connected that! They tried to explicate their groundbreaking enactment to 60 Minutes. Calcea's impervious is appropriately titled the Waffle Cone.

Calcea Johnson: So to commencement the proof, we commencement with conscionable a regular close triangle wherever the space successful the country is 90°. And the 2 angles are alpha and beta.

Bill Whitaker: Uh-huh

Calcea Johnson: So past what we bash adjacent is we gully a 2nd congruent, which means they're adjacent successful size. But past we commencement creating akin but smaller close triangles going successful a signifier similar this. And past it continues for infinity. And yet it creates this larger waffle cone shape.

Calcea Johnson: Am I going a small too—

Bill Whitaker: You've been beyond maine since the beginning. (laughter) 

Bill Whitaker: So however did you fig retired the proof?

Ne'Kiya Jackson: Okay. So you person a close triangle, 90° angle, alpha and beta.

Bill Whitaker: Then what did you do?

Bill Whitaker with Calcea Johnson and Ne'Kiya Jackson 60 Minutes

Ne'Kiya Jackson: Okay, I person a close triangle wrong of the circle. And I person a perpendicular bisector astatine OP to disagreement the triangle to marque that tiny close triangle. And that's fundamentally what I utilized for the proof. That's the proof.

Bill Whitaker: That's what I telephone amazing.

Ne'Kiya Jackson: Well, convey you.

There had been 1 different documented impervious of the theorem utilizing trigonometry by mathematician Jason Zimba successful 2009 – 1 successful 2,000 years. Now it seems Ne'Kiya and Calcea person joined possibly the astir exclusive nine successful mathematics. 

Bill Whitaker: So you some independently came up with impervious that lone utilized trigonometry.

Ne'Kiya Jackson: Yes.

Bill Whitaker: So are you mathematics geniuses?

Calcea Johnson: I deliberation that's a stretch. 

Bill Whitaker: If not genius, you're truly astute astatine math.

Ne'Kiya Jackson: Not astatine all. (laugh) 

To papers Calcea and Ne'Kiya's work, mathematics teachers astatine St. Mary's submitted their proofs to an American Mathematical Society league successful Atlanta successful March 2023.

Ne'Kiya Jackson: Well, our teacher approached america and was like, "Hey, you mightiness beryllium capable to really contiguous this," I was like, "Are you joking?" But she wasn't. So we went. I got up there. We presented and it went well, and it blew up.

Bill Whitaker: It blew up.

Calcea Johnson: Yeah. 

Ne'Kiya Jackson: It blew up.

Bill Whitaker: Yeah. What was the blowup like?

Calcea Johnson: Insane, unexpected, crazy, honestly.

It took millenia to prove, but conscionable a infinitesimal for connection of their accomplishment to spell astir the world. They got a write-up successful South Korea and a shout-out from erstwhile archetypal woman Michelle Obama, a commendation from the politician and keys to the metropolis of New Orleans. 

Bill Whitaker: Why bash you deliberation truthful galore radical recovered what you did to beryllium truthful impressive?

Ne'Kiya Jackson: Probably due to the fact that we're African American, one. And we're besides women. So I think-- oh, and our age. Of people our ages astir apt played a large part.

Bill Whitaker: So you deliberation radical were amazed that young African American women, could bash specified a thing?

Calcea Johnson: Yeah, definitely.

Ne'Kiya Jackson: I'd similar to really beryllium celebrated for what it is. Like, it's a large mathematical achievement.

Achievement, that's a connection you perceive often astir St. Mary's academy. Calcea and Ne'Kiya travel a agelong enactment of barrier-breaking graduates. 

The precocious queen of Creole cooking, Leah Chase, was an alum. truthful was the archetypal African-American pistillate New Orleans constabulary chief, Michelle Woodfork …

And justice for the Fifth Circuit Court of Appeals, Dana Douglas. Math teacher Michelle Blouin Williams told america Calcea and Ne'Kiya are emblematic St. Mary's students.  

Bill Whitaker: They're not unicorns.

Michelle Blouin Williams: Oh, nary no. If they are unicorns, past each azygous woman that has matriculated done this schoolhouse is simply a beautiful, Black unicorn.

Pamela Rogers: You're good?

Pamela Rogers, St. Mary's president and interim principal, told america the students perceive that connection from the infinitesimal they locomotion successful the door.

St. Mary's Academy president and interim main Pamela Rogers 60 Minutes

Pamela Rogers: We judge each students tin succeed, each students tin learn. It does not substance the situation that you unrecorded in. 

Bill Whitaker: So erstwhile connection went retired that 2 of your students had solved this astir intolerable mathematics problem, were they universally applauded?

Pamela Rogers: In this community, they were greatly applauded. Across the country, determination were galore naysayers.

Bill Whitaker: What were they saying?

Pamela Rogers: They were saying, "Oh, they could not person done it. African Americans don't person the brains to bash it." Of course, we sheltered our girls from that. But we perfectly did not expect it to travel successful the measurement that it came.  

Bill Whitaker: And aft specified a fantastic achievement.

Pamela Rogers: People-- person a imaginativeness of who tin beryllium successful. And-- to immoderate people, it is not ever an African American female. And to us, it's ever an African American female.

Gloria Ladson-Billings: What we cognize is erstwhile teachers laic retired immoderate expectations that say, "You tin bash this," kids volition enactment arsenic hard arsenic they tin to bash it.

Gloria Ladson-Billings, prof emeritus astatine the University of Wisconsin, has studied however champion to thatch African American students. She told america an encouraging teacher tin alteration a life.

Bill Whitaker: And what's the difference, say, betwixt having a teacher similar that and a full schoolhouse dedicated to the excellence of these students?

Gloria Ladson-Billings: So a full schoolhouse is astir similar being successful Heaven. 

Bill Whitaker: What bash you mean by that?

Bill Whitaker and Gloria Ladson-Billings 60 Minutes

Gloria Ladson-Billings: Many of our young radical person their ceilings lowered, that determination astir 4th oregon 5th grade, their thoughts are, "I'm not going to beryllium thing special." What I deliberation is astir apt happening astatine St. Mary's is young women travel successful as, perhaps, ninth graders and are told, "Here's what we expect to happen. And here's however we're going to assistance you get there."

At St. Mary's, fractional the students get scholarships, subsidized by fundraising to defray the $9,000 a twelvemonth tuition. Here, there's nary trial to get in, but expectations are precocious and rules are strict: nary cellphones, humble skirts, hairsbreadth indispensable beryllium its earthy color.

Students Rayah Siddiq, Summer Forde, Carissa Washington, Tatum Williams and Christina Blazio told america they admit the rules and rigor.

Rayah Siddiq: Especially the standards that they acceptable for us. They're precise high. And I don't deliberation that's ever going to change.

Bill Whitaker: So is determination a heart, a philosophy, an essence to St. Mary's?

Summer Forde: The sisterhood—

Carissa Washington: Sisterhood.

Tatum Williams: Sisterhood.

Bill Whitaker: The sisterhood?

Voices: Yes.

Bill Whitaker: And you don't mean the nuns. You mean-- (laughter)

Christina Blazio: I mean, yeah. The community—

Bill Whitaker: So erstwhile you're here, there's conscionable nary question that you're going to spell connected to college.

Rayah Siddiq: College is each they speech about. (laughter) 

Pamela Rogers: … and Arizona State University (Cheering)

Principal Rogers announces to her 615 students the colleges wherever each elder has been accepted.

Bill Whitaker: So for 17 years, you've had a 100% graduation rate—

Pamela Rogers: Yes.

Bill Whitaker: --and a 100% assemblage acceptance rate?

Pamela Rogers: That's correct.

When Ne'Kiya and Calcea graduated, each their classmates went to assemblage and got scholarships. Ne'Kiya got a afloat thrust to the pharmacy schoolhouse astatine Xavier University successful New Orleans. Calcea, the people valedictorian, is studying biology engineering astatine Louisiana State University.

Bill Whitaker: So hold a minute. Neither 1 of you is going to prosecute a vocation successful math?

Both: No. (laugh)

Calcea Johnson: I whitethorn instrumentality up a insignificant successful math. But I don't privation that to beryllium my occupation job.

Ne'Kiya Jackson: Yeah. People mightiness expect excessively overmuch retired of maine if (laugh) I go a mathematician. (laugh)

But mathematics is not wholly successful their rear-view mirrors. Last autumn their precocious schoolhouse proofs were published aft last adjacent review. They've present submitted further proofs of the Pythagorean Theorem. Since their archetypal 2 ...

Calcea Johnson: We recovered five. And past we recovered a wide format that could perchance nutrient astatine slightest 5 further proofs.

Bill Whitaker: And you're not mathematics geniuses?

Both: No.

Bill Whitaker: I'm not buying it. (laughs)

Produced by Sara Kuzmarov. Associate producer, Mariah B. Campbell. Edited by Daniel J. Glucksman.