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🇺🇸 Calcea Johnson

高校生がピタゴラスの定理の新しい三角法による証明を共同発見 — 2024年に有力な数学誌に掲載

ニューオーリンズ · 2005年生まれ · セント・メアリーズ・アカデミーの卒業生総代 (2023年) · ルイジアナ州立大学 (LSU) で環境工学を専攻

学校の数学コンテストで出された500ドルのボーナス問題。それは1927年の書籍で不可能だと宣告されていた「三角法を用いたピタゴラスの定理の証明」を求めるものだった。カルセア・ジョンソンとクラスメートのニキヤ・ジャクソンはその答えを見つけ、さらに多くの発見を成し遂げた。2024年10月、アメリカ数学月報 (The American Mathematical Monthly) が彼女たちの論文を掲載した。

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.”

“始めたからには、終わらせなければなりませんでした。”
カルセア・ジョンソン、『60 Minutes』(2024年)
“単に数学的な成果として評価してほしい。これは素晴らしい数学の成果なのですから。”
ニキヤ・ジャクソン、『60 Minutes』(2024年)
“これまで見たことがないようなものだ。”
アルバロ・ロサノ=ロブレド(コネチカット大学)、『サイエンス・ニュース』誌にて
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
誕生2人ともハリケーン・カトリーナの年に生まれた。
Dec 2022
コンテスト2人の高校生が500ドルのボーナス問題、三角法によるピタゴラスの証明に挑む。
Winter 2022–23
2ヶ月それぞれが独立して証明を見つける。
Mar 18, 2023
アトランタアメリカ数学会で「ピタゴラスの不可能な証明」を発表。
Late Mar 2023
バイラルWWL-TVのレポートが拡散し、数日以内に全国放送される。
Apr 2023
市の鍵ラトーヤ・カントレル市長から授与され、ルイジアナ州上院から表彰される。
May 2023
卒業カルセアがセント・メアリーズ高校の2023年卒業生総代に。
Aug 2023
大学入学カルセアがLSUに、ニキヤがザビエル大学ルイジアナ校に入学。
Feb–May 2024
査読2月に論文受理、5月に採択。
May 5, 2024
60 Minutesビル・ウィテカーによる特集。後にチャールズ・バークレーが学校に100万ドルの寄付を約束。
Oct 2024
出版『アメリカ数学月報』に「ピタゴラスの定理の5つまたは10の新しい証明」が掲載。
Nov 2024
EBONY Power 1002人がSTEM分野の先駆者として称えられる。
Aug 2025
アップデートCBSが、カルセアがLSUに、ニキヤが薬学部に在籍していることを報告。

Visual story: Calcea Johnson on camera

ABC News、2023年3月:インタビューを受けた2人の高校生

60 Minutes、2024年5月:ビル・ウィテカーのレポートを含む全編

人物国節目年齢 / 記録
Calcea Johnsonアメリカ合衆国ピタゴラスの定理の新しい三角法による証明 (ニキヤ・ジャクソンと共同)17
Blaise Pascalフランス「神秘的な六角形」の定理を発表16
Terence Taoオーストラリア国際数学オリンピックで金メダル13
Ruth Lawrenceイギリスオックスフォード大学に入学、13歳で首席卒業12
Daniel Larsenアメリカ合衆国カーマイケル数に関する新しい結果を証明17
Hannah Cairoバハマ / アメリカ合衆国溝畑・竹内予想を否定17

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.”

カルセア・ジョンソンとニキヤ・ジャクソンは、数学者が記録以上に重んじることを成し遂げた。それは、誰もが信じていた命題に対し、高校生が使える道具で真に新しい証明を見つけたことである。その証明は精査され、査読を経て、彼女たちの名前だけで出版された。

この物語は、功績がいかに簡単に歪められて伝わるかも示している。一部の見出しは「2,000年来の難問解決」と誇張し、一部の心ない人々は彼女たちの功績であることを否定した。しかし、古い教科書で不可能とされた問いに対し、高校生が答を見つけ出したという事実は、それだけで十分に印象的なものである。

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?

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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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