News & Opinion | March 27, 2023 2:20 pm

Two Teens May Have Finally Proven This “Impossible” 2,000-Year-Old Theorem

While the Pythagorean theorem has been proven several times over, it's never been done with trigonometry

Mathematics textbook from 1743 year, geometry problem, Pythagorean theorem
The Pythagorean theorem is believed to be around 4,000 years old

Despite it being a fundamental concept in every high school math class, I’m not going to do you the disservice of pretending like I recall any of the details or nuances of the Pythagorean theorem (sorry, Mr. Keller). The gist of it, however, is a2+b2=c2, and while it’s been proven many times over, it’s never been so with trigonometry as it constitutes “circular reasoning” — or an argument that assumes what it’s meant to prove.

That said, per a new report from The Guardian, two high school seniors from New Orleans have purportedly cracked the code doing just that — a feat that mathematicians have believed to be impossible for more than 2,000 years.

Calcea Johnson and Ne’Kiya Jackson of St Mary’s Academy recently presented their findings at the American Mathematical Society south-eastern chapter’s semi-annual meeting in Georgia. Their abstract first points to the “The Pythagorean Proposition” book from 1940, which “flatly states that ‘there are no trigonometric proofs because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem.’”

But, Johnson and Jackson continue, “that isn’t quite true.”

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“We present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry — the Law of Sines — and we show that the proof is independent of the Pythagorean trig identity sin2x+cos2x=1,” the abstract posits. In short, the two say they were able to prove the theorem using the Law of Sines.

Of course, nothing is ever quite as simple as that. They must have their work undergo a “rigorous academic peer-reviewed process,” but experts say — despite not yet being confirmed — Johnson and Jackson’s work is cause enough to celebrate.

“There’s nothing like it — being able to do something that people don’t think that young people can do,” Johnson told New Orleans television news station WWL. “You don’t see kids like us doing this — it’s usually, like, you have to be an adult to do this.”

Although, as an adult who can very much not do “this,” I’m not so sure.