US teens say they have new proof for 2k-year-old mathematical theorem | Hacker News Reader

US teens say they have new proof for 2k-year-old mathematical theorem

theguardian.com

14 pointshackernj10 comments

Kudos for the kids for putting in the effort. However, without seeing any details (and no experts were cited in the article!) I would assume what was done was rather trivial. I suppose if you define the trigonometric functions using power series you could probably arrive to the result rather easily. I didn't work out the details, but that would seem like an alternative way to get a handle to these functions without using any geometric ideas.

Edit: so they refer to a book by a math PhD for the claim that there is no trigonometric proof. The book is rather old, so maybe the information is outdated, but it does suggest it's maybe not entirely trivial.

Edit2: wait, wouldn't this just boil down to showing that sin^2 x + cos^2 x = (isin x + cos x)(-isin x + cos x) = e^(ix)e^(-ix)=1?

Surely you'd have to do a bit of work with the series to be able to write that, but looks like standard calculus.

Edit3: ok, so I dug a bit deeper and found that the book that is cited claims as a fact that you cannot prove Pythagorean theorem using trigonometric functions, since to use trig. functions you need Pyth. theorem. This is not true, if you start with series expansions. So I wonder if the story is that the kids relied on the book as a fact, did some calculus and proved their theorem. The teachers, not being mathematicians, took the book as face value as well (and here's where the mistake happened) didn't consult an actual expert before speaking to the press. Still, I'd say pretty nice job from the kids to actively pursue a mathematical problem, hopefully next time with a proper supervisor.

So we don't know if anyone at all has reviewed their proof, do we? Sounds like at this point they are just claiming something.

I guess it will become interesting once it's actually reviewed.

Which is good! They're backing that claim by submitting it for peer review. It may seem like they're leapfrogging the process by getting published in the Guardian before getting validation but: a. The Guardian is promoting them, not the students themselves, I believe. b. It's genuinely impressive that high school students worked out a proof, (for something so common like the Pythagoreas theorem!) that wasn't immediately rejected on first sight by professionals. Even if is eventually rejected, getting to this point is worth noting and appreciating.

Oh that's the bit I was missing: so professionals did see the proof and did not reject it right away, is that right?

It was not clear to me if they just submitted their work or actually presented it already.

Do undergraduate mathematics journals ever desk-reject sincere attempts?

Let me introduce Eleftherios Argyropoulos, a Greek mathematician, currently alive who has invented 520 different theorem proofs on the subject, and most likely counting...

You can check out his books, a brief excerpt of him, it is in Greek tho. https://yewtu.be/watch?v=JaaDmEMsum4

There's a little more information in this Reddit thread [1]. In it someone references an earlier work by Jason Zimba [2].

[1] https://www.reddit.com/r/math/comments/11zptjo/an_impossible...

[2] https://forumgeom.fau.edu/FG2009volume9/FG200925.pdf

The are many trigonometric proofs of the theorem.

https://www.cut-the-knot.org/pythagoras/

I wonder if they used ChatGPT?

The AMS can't stop getting high off their own farts

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