- Two US high schoolers believe they have cracked a mathematical mystery left unproven for centuries.
- Calcea Johnson and Ne'Kiya Jackson looked at the Pythagorean theorem, foundational to trigonometry.
- The American Mathematical Society said the teenagers should submit their findings to a journal.
Two high school seniors from New Orleans think they have achieved a feat of mathematics which has stumped experts for 2,000 years.
Their work got Calcea Johnson and Ne'Kiya Jackson far enough to present their findings to researchers, per an interview with local TV.
It concerned the Pythagorean theorem, a staple of high school math lessons which defines the relationship between the three sides of a right-angled triangle, expressed with the formula a2+b2=c2.
Johnson and Jackson claim to have broken new ground by proving the theorem using trigonometry (it has already been proved extensively by other means).
This is difficult because much of trigonometry itself is underpinned by the theorem.
In the abstract presented by Johnson and Jackson last week, the two teenagers gestured to this. They noted that the 1940 book "The Pythagorean Proposition" "flatly states" that there are no trigonometric proofs because they are "based upon the truth of the Pythagorean Theorem."
They countered in their work that the claim "isn't quite true." The two claimed they were able to prove the theorem using the Law of Sines, another principle of trigonometry which does not rely on the Pythagorean theroem.
When the American Mathematical Society met in Georgia last week, Johnson and Jackson were the only high schoolers at the meeting, according to New Orleans television news station WWL.
Their claim has not gone through the rigorous academic peer-review process — or been confirmed by other experts in the field.
Similar claims have also been made before by professional academics, both in a published journal and via the pre-print service arXiv.
Catherine Roberts, executive director for the American Mathematical Society, encouraged the young mathematicians to submit their findings to a journal where it can be assessed.
She said the society "celebrates these early career mathematicians for sharing their work," The Guardian reported.
"Members of our community can examine their results to determine whether their proof is a correct contribution to the mathematics literature," Roberts said.
In an interview with WWL, the students said they were excited just to be a part of the process.
"There's just nothing like being able to do something that people don't think young people can do," Johnson said, "A lot of times you see this stuff, you don't see kids like us doing it."
Correction: March 27, 2023 — An earlier version of this story misstated the nature of Johnson and Jackson's claim. Johnson and Jackson claim to have broken new ground by proving the Pythagorean theroem by means of trigonometry, not by proving it for the first time. The story was also updated to clarify language around the concept of mathematical proof and to note that previous, similar claims exist. We are grateful for the mathematicians who wrote in to set us straight.