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🇺🇸 Calcea Johnson

고등학생 시절, 피타고라스 정리에 대한 새로운 삼각법 증명을 공동 발견 — 2024년 주요 수학 저널에 게재

뉴올리언스 · 2005년생 · 세인트 메리 아카데미 졸업생 대표(2023년) · 루이지애나 주립대학교 환경공학 전공

학교 수학 경시대회의 500달러짜리 보너스 문제는 1927년의 한 서적에서 불가능하다고 선언했던 과제, 즉 삼각법을 이용한 피타고라스 정리의 증명을 요구했습니다. 칼시아 존슨(Calcea Johnson)과 그녀의 급우 네키야 잭슨(Ne’Kiya Jackson)은 이를 하나 발견해냈고, 이어 더 많은 증명을 찾아냈습니다. 2024년 10월, 『미국 수학 월간지(The American Mathematical Monthly)』는 이들의 논문을 게재했습니다.

Calcea Johnson and Ne’Kiya Jackson at St. Mary’s Academy

WWL-TV’s March 2023 report that made the story go viral.

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A $500 bonus question

In late 2022, St. Mary’s Academy — a historically Black Catholic girls’ school in New Orleans, founded in 1867 by the Sisters of the Holy Family — was running a schoolwide math contest. The bonus question offered $500 for something a well-known 1927 book had called impossible: a new proof of the Pythagorean theorem using trigonometry. Two seniors took it on. “$500 is a lot of money,” Calcea Johnson later told 60 Minutes. “So I — I would like to at least try.”

Nobody expected an answer. “I wasn’t necessarily looking for a solve,” said Michelle Blouin Williams, the teacher CBS credits with setting the challenge. “I was just looking for some ingenuity.” (The students’ paper credits another teacher, a former volunteer it calls “Mr. Rich,” with running the contest.) Starting in December 2022, the two spent about two months that winter on the problem, each working independently. Calcea’s mother counted 20 or 30 pages of her daughter’s work, and her father remembers a garbage can full of discarded attempts. “I started something,” Calcea said. “I need to finish it.”

Why it was supposed to be impossible

The theorem — in a right triangle, the square on the hypotenuse equals the sum of the squares on the other two sides — is older than Pythagoras: Babylonian scribes were recording number triples that satisfy it nearly 4,000 years ago, and Euclid proved it in Book I of the Elements. In The Pythagorean Proposition — first published in 1927 and expanded to 370 proofs in its 1940 edition — the American teacher Elisha Loomis ruled out a whole category: “There are no trigonometric proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem.”

His reasoning was the trap of circular logic. The identity sin²θ + cos²θ = 1 is the Pythagorean theorem in disguise, so a proof that leans on it assumes what it sets out to prove. But “impossible” was already out of date: Jason Zimba published a trigonometric proof in 2009, and Nuno Luzia another in 2015. What the St. Mary’s students found was a new route.

The Babylonian clay tablet Plimpton 322
Plimpton 322, a Babylonian clay tablet of about 1800 BC listing number triples that satisfy the theorem — which is older than Pythagoras.Photo: Unknown photographer · Public domain · Wikimedia Commons

The “waffle cone”

Diagram of the Pythagorean theorem with squares on each side of a right triangle
The Pythagorean theorem: the areas of the squares on the two shorter sides add up to the area of the square on the hypotenuse.Photo: Wapcaplet · CC BY-SA 3.0 · Wikimedia Commons

Their first proof begins with a right triangle whose two shorter sides differ in length. Reflect it to form an isosceles triangle; place that inside a larger right triangle — the shape the students nicknamed the “waffle cone” — and fill the cone with an infinite chain of ever-smaller similar triangles. Add up the lengths with a geometric series, then finish with the law of sines. The circular identity never appears.

Their paper also does some mathematical housekeeping. It separates what the authors call “cyclotopic” trigonometry — sine and cosine defined on the unit circle, where the Pythagorean theorem is built in — from trigonometry defined directly on right triangles, where it is not. “None of the theorems we use in our proofs … have already assumed the Pythagorean theorem to be true,” they wrote. Álvaro Lozano-Robledo, a mathematician at the University of Connecticut, told Science News of the first proof: “It looks like nothing I’ve ever seen.”

Atlanta, March 18, 2023

The next step surprised the students most. “Our teacher approached us and was like, ‘Hey, you might be able to actually present this,’” Ne’Kiya Jackson recalled. “I was like, ‘Are you joking?’ But she wasn’t.” On the morning of March 18, 2023, at the American Mathematical Society’s spring southeastern meeting at Georgia Tech in Atlanta — a gathering where some 800 mathematicians were expected — the two 17-year-olds presented “An Impossible Proof of Pythagoras” in a session on undergraduate research.

“I saw a bunch of people writing down stuff and pulling up things on their computers,” Calcea said afterward. Ne’Kiya remembered: “Some people apparently started recording.” The Society’s executive director, Catherine Roberts, encouraged them to submit the work to a peer-reviewed journal. The internet ran its own review in the meantime: one economist-blogger noted that a slide visible in a news report held enough detail to reconstruct the proof, and explainer videos followed within weeks.

Viral, doubted, celebrated

A WWL-TV report in late March went viral. Within a week the students were on Good Morning America and ABC News. Michelle Obama praised them, Governor John Bel Edwards commended them, the Louisiana Senate passed a resolution in their honor, and in April Mayor LaToya Cantrell gave them keys to the city of New Orleans.

Not everyone applauded. Pamela Rogers, the school’s president, told 60 Minutes that callers said “they could not have done it. African Americans don’t have the brains to do it.” Asked why so many people found the achievement striking, Ne’Kiya was direct: “Probably because we’re African American, one. And we’re also women.” She also said what she wanted instead: “I’d like to actually be celebrated for what it is. Like, it’s a great mathematical achievement.”

On May 5, 2024, Bill Whitaker profiled the pair on 60 Minutes; Calcea, who received the network’s first email, at first could not believe it was real. After the broadcast Charles Barkley pledged $1 million to St. Mary’s Academy, paid in $100,000 installments.

Five or ten new proofs

The paper went to The American Mathematical Monthly, among the most widely read mathematics journals in the world. It was received in February 2024, accepted in May and published online in late October as “Five or Ten New Proofs of the Pythagorean Theorem” — the lead article of the November 2024 issue (volume 131, number 9, pages 739–752). Ne’Kiya Jackson and Calcea Johnson are its only authors.

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The title is exact. The paper writes out five proofs — four for right triangles whose shorter sides differ and a fifth that covers every right triangle — and describes a method that yields at least five more. Four of the published proofs are new since the Atlanta talk, Calcea told LSU. “I was pretty surprised to be published,” Ne’Kiya said. “I didn’t think it would go this far.” Calcea saw a wider point: “I am very proud that we are both able to be such a positive influence in showing that young women and women of color can do these things.” Della Dumbaugh, the journal’s editor, said the Monthly was “honored and delighted to publish the work of these two students.”

St. Mary’s Academy, New Orleans
St. Mary’s Academy in New Orleans East, founded in 1867 by the Sisters of the Holy Family. Both students graduated in 2023.Photo: Beautifully_Shared · CC BY-SA 4.0 · Wikimedia Commons

Born in the year of Katrina

Both were born in 2005, the year Hurricane Katrina flooded New Orleans. Ne’Kiya’s mother evacuated before the storm and gave birth to her in Georgia a week later, two months early. Calcea spent her first year in a FEMA trailer on the lawn of her family’s flooded home. Her parents, Cal and CeCe Johnson, appeared with her on 60 Minutes; so did Ne’Kiya’s mother, Neliska Jackson, who admitted she never checked the math — “most of the time I don’t understand what she’s doing.”

Calcea graduated as valedictorian of St. Mary’s class of 2023 and is a Girl Scout Gold Award recipient; the two left school with nearly $3 million in scholarship offers between them. In the paper’s author notes she lists video games, K-pop and musicals among her interests; Ne’Kiya lists cats and rabbits, billiards, anime and manga.

Where are Calcea Johnson and Ne’Kiya Jackson now?

Calcea studies environmental engineering in the Roger Hadfield Ogden Honors College at Louisiana State University, which she entered in 2023; LSU’s review of the 2024–25 year and CBS’s updated report of August 2025 both place her there. After 60 Minutes, environmental engineers wrote to her offering mentorship. “I want to be able to come back and help the New Orleans communities, since they helped raise me,” she has said. Math will stay close, but not as a career: “I may take up a minor in math. But I don’t want that to be my job job.”

Ne’Kiya is at Xavier University of Louisiana, on the College of Pharmacy’s track toward a doctorate in pharmacy — on a full scholarship, CBS reported. Neither has published a second paper as of September 2026. And both still wave off the word this site is built on. Asked on 60 Minutes whether she was a genius, Calcea said: “I think that’s a stretch.”

“제가 시작한 일이니, 끝을 봐야 했어요.”
칼시아 존슨, 『60분』 (2024년)
“저는 그냥 그 성과 자체로 축하받고 싶어요. 정말 훌륭한 수학적 성과니까요.”
네키야 잭슨, 『60분』 (2024년)
“내가 본 적 없는 것 같아요.”
알바로 로사노-로블레도, 코네티컷 대학교, 『사이언스 뉴스』에
Age 02005Age 172022Age 17Age 182023Age 18Age 18Age 18Age 18Age 192024Age 19Age 19Age 19Age 202025MILESTONES IN ORDERBORN 2005
Calcea Johnson — every milestone on this page, placed by age.
2005
출생두 학생 모두 허리케인 카트리나가 발생한 해에 태어났습니다.
Dec 2022
경시대회두 명의 졸업반 학생이 500달러짜리 보너스 문제에 도전합니다: 삼각법으로 피타고라스 정리 증명하기.
Winter 2022–23
두 달각자 독립적으로 증명을 찾아냅니다.
Mar 18, 2023
애틀랜타미국 수학회에서 '피타고라스의 불가능한 증명' 발표.
Late Mar 2023
바이럴WWL-TV 보도가 퍼지고 며칠 내로 전국 방송들이 뒤를 잇습니다.
Apr 2023
도시의 열쇠라토야 캔트렐 시장이 표창하고 루이지애나 주 상원이 치하합니다.
May 2023
졸업칼시아가 세인트 메리 아카데미 2023년 졸업생 대표가 됩니다.
Aug 2023
대학칼시아는 LSU, 네키야는 루이지애나 제이비어 대학교에 입학합니다.
Feb–May 2024
동료 평가2월에 접수, 5월에 채택.
May 5, 2024
60분(60 Minutes)빌 휘태커가 다룸; 찰스 바클리가 나중에 학교에 100만 달러 기부를 약속함.
Oct 2024
게재'피타고라스 정리에 대한 5~10개의 새로운 증명', 미국 수학 월간지.
Nov 2024
EBONY Power 100두 사람 모두 STEM 분야의 개척자로 선정됨.
Aug 2025
업데이트CBS가 칼시아는 LSU에서, 네키야는 약대에서 공부 중이라고 보도.

Visual story: Calcea Johnson on camera

ABC 뉴스, 2023년 3월: 인터뷰에 응한 두 졸업생

60분(60 Minutes), 2024년 5월: 빌 휘태커의 보도를 포함한 전체 에피소드

인물국가이정표나이 / 기록
Calcea Johnson미국피타고라스 정리에 대한 새로운 삼각법 증명 (네키야 잭슨과 공동)17
Blaise Pascal프랑스자신의 '신비한 육각형' 정리 발표16
Terence Tao호주국제수학올림피아드 금메달13
Ruth Lawrence영국옥스퍼드 입학; 13세에 수석 졸업12
Daniel Larsen미국카마이클 수에 관한 새로운 결과 증명17
Hannah Cairo바하마 / 미국미조하타-타케우치 추측 반증17

What is documented — and what is not

✓ Documented

  • They presented new trigonometric proofs at the American Mathematical Society meeting in Atlanta on March 18, 2023.
  • Their peer-reviewed paper appeared in The American Mathematical Monthly (November 2024), with the two students as its only authors.
  • What is new: geometric constructions with infinite chains of similar triangles, summed as a geometric series and closed with the law of sines.
  • Charles Barkley pledged $1 million to St. Mary’s Academy after 60 Minutes.
  • Calcea studies environmental engineering at LSU; Ne’Kiya is on Xavier’s pharmacy track.

? Unverified, disputed or wrong

  • “The first trigonometric proof ever” — false: Zimba (2009) and Luzia (2015) came first.
  • “Solved a 2,000-year-old problem” — misleading; the theorem had hundreds of proofs. What is new is the method.
  • “Ten new proofs” — five are written out; the rest are left to the reader.
  • “Youngest ever to present at the AMS” — not confirmed by the Society.
  • Who ran the contest: CBS names Michelle Blouin Williams; the paper credits “Mr. Rich.”

칼시아 존슨과 네키야 잭슨은 수학자들이 기록보다 더 가치 있게 여기는 일을 해냈습니다. 그들은 모두가 이미 믿고 있는 명제에 대해 진정으로 새로운 논증을 발견했고, 고등학생이 사용할 수 있는 도구로 그것을 해냈습니다. 그들의 증명은 검증과 동료 평가를 거쳐 그들의 이름만으로 게재되었습니다.

이 이야기는 성취가 얼마나 쉽게 왜곡될 수 있는지도 보여줍니다. 일부 헤드라인은 이를 '2,000년 된 난제 해결'로 부풀렸고, 일부는 그것이 그들의 성과일 리 없다고 부정했습니다. 낡은 교과서가 불가능하다고 했던 문제에 도전해 답을 찾아낸 두 고등학생이라는 정확한 버전이야말로 훨씬 더 인상적인 것입니다.

Questions people ask about Calcea Johnson

What did Calcea Johnson prove?

With Ne’Kiya Jackson she found new proofs of the Pythagorean theorem that use trigonometry — the law of sines and geometric series — without the circular reasoning that led a 1927 book to call such proofs impossible.

How old is Calcea Johnson?

Born in 2005, she was 17 when she presented at the American Mathematical Society in March 2023; she is 20 or 21 in 2026.

Where is Calcea Johnson now?

Studying environmental engineering in the Ogden Honors College at Louisiana State University, which she entered in 2023; CBS reported her still there in August 2025.

What college does Ne’Kiya Jackson attend?

Xavier University of Louisiana, in its College of Pharmacy program toward a doctorate in pharmacy.

How many proofs did they find?

The paper writes out five and describes a method that yields at least five more — hence the title, “Five or Ten New Proofs of the Pythagorean Theorem.”

Were they the first to prove Pythagoras with trigonometry?

No. Jason Zimba (2009) and Nuno Luzia (2015) published earlier trigonometric proofs. Johnson and Jackson’s proofs are new and take a different, geometric route.

Where was their proof published?

In The American Mathematical Monthly, volume 131, number 9 (November 2024), pages 739–752, as the lead article of the issue.

Who was their math teacher?

CBS’s 60 Minutes credits Michelle Blouin Williams with setting the challenge; the paper thanks “Mr. Rich,” a former volunteer, for running the school’s math contest.

Quick quiz: how well do you know Calcea’s story?

What prize did the school offer for the bonus question?

Which rule closes their “waffle cone” proof?

Where was their paper published?

Now test yourself: the free 8-minute IQ test →

Sources

  1. Teens come up with trigonometry proof for Pythagorean theorem (transcript) — CBS News / 60 Minutes, May 5, 2024; updated August 31, 2025
  2. High school students’ Pythagorean theorem proof — CBS News / 60 Minutes, May 5, 2024
  3. The inspiration for New Orleans’ St. Mary’s Academy — CBS News, updated August 31, 2025
  4. Teens’ Pythagorean theorem study published — CNN, October 29, 2024
  5. Teenagers found new proofs of the Pythagorean theorem — Science News, October 28, 2024
  6. Two high schoolers found an “impossible” proof — then nine more — Smithsonian Magazine, October 30, 2024
  7. 2 high school students prove the Pythagorean theorem. Here’s what that means — Scientific American, April 10, 2023
  8. Groundbreaking Pythagorean research featured in the Monthly — Mathematical Association of America, October 25, 2024
  9. Five or Ten New Proofs of the Pythagorean Theorem (DOI record) — Crossref, 2024
  10. Spring Southeastern Sectional Meeting program — American Mathematical Society, March 2023
  11. Calcea Johnson publishes in the American Mathematical Monthly — Louisiana State University, October 31, 2024
  12. Ne’Kiya Jackson will attend Xavier University of Louisiana — Xavier University of Louisiana, August 15, 2023
  13. High school students make math discovery 2,000 years in the making — WVUE (via WSAZ), March 28, 2023
  14. Georgia Tech to host the AMS Spring Southeastern Sectional Meeting — Georgia Tech School of Mathematics, 2023
  15. The Jackson–Johnson proof — Rajiv Sethi (Substack), May 3, 2023
  16. Senate Resolution No. 139 (2023 Regular Session) — Louisiana Legislature, 2023
  17. Ne’Kiya Jackson heads to Xavier — Black Catholic Messenger, September 11, 2023
  18. LSU freshman on her Pythagorean proof and 60 Minutes — Louisiana State University, 2024
  19. NBA legend Charles Barkley donates $1M to New Orleans school — theGrio, September 6, 2024
  20. LSU students named to the EBONY Power 100 — Louisiana State University, November 25, 2024
  21. The 2024–25 academic year at LSU — Louisiana State University, June 2025

Checked by the Geniuses.club editorial team. Ages are given as of September 2026.

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