Students discover and publish unexpected proof for 2,000-year-old mathematical theory

[jbycho 754]

Louisiana students Ne’Kiya Jackson and Calcea Johnson wowed their teachers in 2022 when they discovered a new way to prove the 2000-year-old Pythagorean theorem in response to a bonus question in a high school math contest. But that was only the beginning.

A volunteer at their former school, New Orleans’ St. Mary’s Academy, encouraged them to submit their work on the famous mathematical theory to a professional conference, and in March 2023 they became the youngest people to present at the American Mathematical Society’s Southeastern Sectional conference in Atlanta. Their appearance elicited a wave of media coverage, including a spot on “60 Minutes.” The pair also received symbolic keys to the city of New Orleans and a shout-out from Michelle Obama.

Now Jackson and Johnson, who started college last year, have notched another achievement: authoring an academic paper detailing their original proof — plus nine more. Their work published Monday in the scientific journal American Mathematical Monthly.

Experts described Jackson and Johnson’s approach as particularly challenging because trigonometry as a field is essentially based on Pythagoras’ theorem; thus using trigonometry to prove the theorem typically requires what mathematicians call “circular reasoning.” However, the new proofs aren’t circular, according to the study.

“None of the theorems we use in our proofs … have already assumed the Pythagorean theorem to be true,” the authors wrote in the paper.

Tom Murdoch, an honorary professor at the University of Bristol’s School of Mathematics in the United Kingdom, described the study as “impressive.”

“I think what’s intriguing about it (this study) is that a lot of people thought it was impossible,” he said.

“Trigonometric functions are based on sine and cosine, which are expressed as ratios of certain lengths of a right-angled triangle. It’s quite easy to get into a circular argument, and what’s so appealing about this is they found a line of argument using sine and cosine that doesn’t assume Pythagoras is true,” he added.

Jackson and Johnson’s study outlines five new ways of proving the theorem using trigonometry, and their method reveals five more proofs for 10 total. The pair presented only one of the proofs at the 2023 conference, meaning that nine are totally new.

https://amp.cnn.com/cnn/2024/10/29/science/teens-pythagorean-theorem-study

[kilroy69 1,247]

This is freaking awesome and the type of thing I want to see plastered all over the news instead of stupid politics. 

[RaiderHaters Revenge 4,345]

That’s amazing 

[RaiderHaters Revenge 4,345]

Well written story. No need to even point out they are black or women. Just smart people 

[jbycho 754]

13 minutes ago, RaiderHaters Revenge said:

Well written story. No need to even point out they are black or women. Just smart people 

Didn't think of that. Good call. Normally these articles are flooded with minority praising. 

[jerryskids 6,790]

Quite impressive!  I've got the link to their actual paper open and plan (hope?) to make some sense of it.   

[RaiderHaters Revenge 4,345]

2 minutes ago, jerryskids said:

Quite impressive!  I've got the link to their actual paper open and plan (hope?) to make some sense of it.   

oh nice post it!

 

[jerryskids 6,790]

39 minutes ago, RaiderHaters Revenge said:

oh nice post it!

 

https://www.tandfonline.com/doi/full/10.1080/00029890.2024.2370240#d1e136

[Mike Honcho 5,269]

41 minutes ago, RaiderHaters Revenge said:

oh nice post it!

 

https://www.tandfonline.com/doi/full/10.1080/00029890.2024.2370240#d1e1821

43 minutes ago, jerryskids said:

Quite impressive!  I've got the link to their actual paper open and plan (hope?) to make some sense of it.   

Good luck with that...I'm just like  looking at it.  Been way too long for me to remember 1/1000th of the math.

[frank 2,302]

How could you have a circular argument in trigonometry?

[RaiderHaters Revenge 4,345]

54 minutes ago, Mike Honcho said:

https://www.tandfonline.com/doi/full/10.1080/00029890.2024.2370240#d1e1821

Good luck with that...I'm just like  looking at it.  Been way too long for me to remember 1/1000th of the math.

Pier reviewed and they nailed it. I never thought to look at it that way but always found it weird that it was circular logic 

[RaiderHaters Revenge 4,345]

Just now, frank said:

How could you have a circular argument in trigonometry?

Try the square peg 

[frank 2,302]

2 hours ago, jbycho said:

Jackson and Johnson’s study outlines five new ways of proving the theorem using trigonometry, and their method reveals five more proofs for 10 total. The pair presented only one of the proofs at the 2023 conference, meaning that nine are totally new.

This much checks out at least.

[Patented Phil 1,469]

3 hours ago, RaiderHaters Revenge said:

Well written story. No need to even point out they are black or women. Just smart people 

Well, except for the 60 Minutes and Michelle Obama part.  That was a dead giveaway.