....which mathematicians thought was impossible.

Not exactly one of the more pressing mathematical quandaries of the times.

Total hysteria:

"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 managed to prove a 2,000-year-old theorem that has stumped mathematicians for centuries."

https://news.yahoo.com/2-high-schoolers-theyve-found-145534941.html

Who is Loomis:

https://en.wikipedia.org/wiki/Elisha_Scott_Loomis

Classics in Mathematics link:

https://files.eric.ed.gov/fulltext/ED037335.pdf

On Sunday, March 26, 2023 at 11:44:25 AM UTC-4, Anthony William Sloman wrote:
> On Sunday, March 26, 2023 at 11:08:01 PM UTC+11, Fred Bloggs wrote:
>
> > ...which mathematicians thought was impossible.
> When I got taught math, there were lots of proofs of the Pythagorean theorem, some of them preceding Pythagorus - the Babylonians had one.
> > Not exactly one of the more pressing mathematical quandaries of the times.
> >
> > Total hysteria:
> >
> > "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 managed to prove a 2,000-year-old theorem that has stumped mathematicians for centuries."
> >
> > https://news.yahoo.com/2-high-schoolers-theyve-found-145534941.html
> >
> > Who is Loomis:
> >
> > https://en.wikipedia.org/wiki/Elisha_Scott_Loomis
> >
> > Classics in Mathematics link:
> >
> > https://files.eric.ed.gov/fulltext/ED037335.pdf
> I suspect the confusion here is that Loomis decided that a trignometric proof was impossible while listing several hundred other different kinds of proof. It may be that the kids have proved Loomis wrong and the reporter has misrepresented their achievement, but the assertion as presented here seems to be entirely wrong.

The students' proof relies on the law of sines, making it a trigonometric proof. Loomis merely noted that trigonometry derives from the Pythagorean Theorem and therefore cannot be considered an independent derivation. My first guess is they used some degenerate case construction and then assumed its generality without proof, where a proof was needed. But then again AMS is the last word on theoretical math and didn't discount their work off hand.

I'm pretty sure they didn't use this:

https://en.wikipedia.org/wiki/Law_of_sines

In other news:

The Babylonians discovered their own unique form of trigonometry during the Old Babylonian period (1900-1600BCE), more than 1,500 years earlier than the Greek form.

Written in stone: world's first trigonometry revealed in ancient Babylonian tablet

https://newsroom.unsw.edu.au/news/science-tech/written-stone-worlds-first-trigonometry-revealed-ancient-babylonian-tablet

>
> --
> Bill Sloman, Sydney