Did High Schoolers Just Make a Major Math Breakthrough?

From NOTICE News Daily for March 28, 2023

Have two high school seniors solved a major math mystery? They might have proven the Pythagorean Theorem after 2,000 years.


“Two New Orleans high school seniors who say they have proven Pythagoras’s theorem by using trigonometry – which academics for two millennia have thought to be impossible – are being encouraged by a prominent US mathematical research organization to submit their work to a peer-reviewed journal.” >> Full story from The Guardian


If you’ve taken trigonometry, you definitely know the formula. A squared plus B squared equals C squared, known as the Pythagorean theorem, is a formula that’s been used for 200 years to calculate the length of a right triangle’s hypotenuse. It’s long been accepted that trigonometry can’t be used to prove the Pythagorean theorem. That’s because the Pythagorean theorem is the basis for all trigonometry – so using trigonometry to prove it is called ‘circular logic’. Circular logic is basically trying to prove an argument, using the argument itself. But, two high school seniors say they’ve figured out how to do just that.

Calcea Johnson and Ne’kiya Jackson from New Orleans say they’ve found the first proof of the theorem using trigonometry, without resorting to circular logic. Instead, they used the law of sines to prove the Pythagorean theorem. The law of sines is used to find the missing length of a triangle in a way that’s independent from the Pythagorean theorem. Their discovery was so significant, they were invited to present at the American Mathematical Society’s semi-annual conference, and they were the only high schoolers present.

Sound: “It’s an unparalleled feeling honestly because there’s just nothing like it, being able to do something that people don’t think that young people can do.”

The girls found the proof after a teacher challenged them to it.

Sound: “Our slogan is there’s no excellence without hard labor so they definitely push on that. And we have really great teachers.”

The executive director of the American Mathematical Society said she encouraged the girls to have their proof reviewed, after which, it could end up in textbooks.