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Pair of teens may have found proof for 2,500-year-old Pythagoras’ theorem

Fun VLOG April 08, 2023
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. Calcea Johnson and Ne?Kiya Jackson, who are students of St Mary?s Academy, recently gave a presentation of their findings at the American Mathematical Society south-eastern chapter?s semi-annual meeting in Georgia. They were reportedly the only two high schoolers to give presentations at the meeting attended by math researchers from institutions including the universities of Alabama, Georgia, Louisiana State, Ohio State, Oklahoma and Texas Tech. And they spoke about how they had discovered a new proof for the Pythagorean theorem. Illustration showing megaphones screaming stats and numbers How to read the news like a mathematician ? from the budget and HS2 to Covid and sport Read more The 2,000-year-old theorem established that the sum of the squares of a right triangle?s two shorter sides equals the square of the hypotenuse ? the third, longest side opposite the shape?s right angle. Legions of school 11907481 Two New Orleans schoolgirls say they have discovered new proof for the Pythagorean theorem
Ne’Kiya Jackson, left, and Calcea Rujean Johnson found the proof as part of a maths contest their school held for over the Christmas break (Picture: WWLTV)

A pair of high school students in the US have stunned mathematicians around the world after seemingly finding a new proof for Pythagoras’ theorem.

Ne’Kiya Jackson and Calcea Rujean Johnson made the discovery when they answered a ‘bonus question’ which was set as part of a maths contest over their school Christmas break.

The two students from St Mary’s Academy in New Orleans recently presented the proof to a regional meeting of the American Mathematical Society, where they were encouraged to submit it to a peer-reviewed journal.

While the proof has not been released to the public yet, it has got plenty of chins wagging in the academic world.

Many people will remember being taught Pythagoras’ theorem in their high school maths classroom.

It says that if you add together the squares of the two shorter sides of a right-angled triangle, you’ll get the square of the longest side, which is also called the hypotenuse.

The theorem – which can be written out as the equation a2+b2=c2 – is one of the most famous in geometry, and has everyday uses such as calculating the distance between the corners of a rectangle.

But over the centuries, mathematicians have struggled to find a definitive proof for the theorem which would not only show that it works, but explain why it does.

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. Calcea Johnson and Ne?Kiya Jackson, who are students of St Mary?s Academy, recently gave a presentation of their findings at the American Mathematical Society south-eastern chapter?s semi-annual meeting in Georgia. They were reportedly the only two high schoolers to give presentations at the meeting attended by math researchers from institutions including the universities of Alabama, Georgia, Louisiana State, Ohio State, Oklahoma and Texas Tech. And they spoke about how they had discovered a new proof for the Pythagorean theorem. Illustration showing megaphones screaming stats and numbers How to read the news like a mathematician ? from the budget and HS2 to Covid and sport Read more The 2,000-year-old theorem established that the sum of the squares of a right triangle?s two shorter sides equals the square of the hypotenuse ? the third, longest side opposite the shape?s right angle. Legions of school 11907481 Two New Orleans schoolgirls say they have discovered new proof for the Pythagorean theorem
The two teenagers have been asked to submit their proof for peer review (Picture: WWLTV)

Previous proofs have almost entirely avoided using trigonometry, as one of the discipline’s fundamental equations is itself largely built around Pythagoras’ theorem – meaning they would be ‘circular’, looping back round to themselves.

Ne’Kiya and Calcea’s proof uses a different trigonometry equation that avoids making it circular, and it may be among the first to do so.

In the abstract for their talk to the mathematical society, the two teenagers write: ‘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.’

Despite the fact their work is not available publicly, a YouTube channel called MathTrain deduced it from the slides projected behind them in pictures released by their school.

@mathandcobb

A few of you have tagged me to talk about this new proof of Pythagoras so here is my take and an explanation of what we think the proof is! Very exciting and big congrats to Ne’Kiya Jackson and Calcea Johnson!! And thanks to MathTrain for the reconstruction of the proof. More details need to be added but here you can find a sketch! #math #mathtok #pythagoras #pythagoreantheorem #proof #trigonometry

♬ original sound – Álvaro Lozano-Robledo

It was then picked up by Álvaro Lozano-Robledo, a mathematics professor at the University of Connecticut, who described how it works on his TikTok.

He said the new proof ‘does seem to be a big deal’ due to its clever use of trigonometry, and added seeing teenagers coming up with something ‘really important and fantastic’ was ‘so invigorating’.

Catherine A. Roberts, the executive director of the American Mathematical Society, said: ‘Following their conference presentation, their next step would be to look into submitting their work to a peer-reviewed journal, where members of our community can examine their results to determine whether their proof is a correct contribution to the mathematics literature’.

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