91–100 of 287 posts
I don't get how this is "new" or "novel" ? it seems to me the law of cosine (or al kashi's theorem) we study this in high school in France ... https://en.wikipedia.org/wiki/Law_of_cosines
[1] https://www.cs.utexas.edu/~EWD/transcriptions/EWD09xx/EWD975...
[flagged]
[flagged]
I remember reading a book in high school and realizing there could be other ways to prove things that I had been taught only one way. One that particularly stood out later was using a rotating fishtank to prove the pythagorean theorum. A good friend of mine was so delighted by the example I gave him a copy of the book I found it in. https://press.princeton.edu/books/paperback/9780691154565/th... ) The relevant sectio…
> In his “Mathematician’s Lament,” Paul Lockhart describes how school cheapens mathematics by robbing us of the questions. We’re not just asked, hey, how much of the triangle takes up the box?
> That’s a puzzle we might delight in. (If you drop a vertical from the top of the triangle, you end up with two rectangles cut in half; you discover that the area inside the triangle is equal to the area outside.)
[flagged]
I’ve had similar thoughts in the past but figured out I personally do better when I channel the doubt into excitement for anyone’s’ potential claim.
I’m happy that a human—or humans, in this case—believe(s) they have discovered a novel way to do something and want to share it with the world.
That doesn’t mean I take the claim at face value, I don’t, and want to wait for secondary confirmation. But it’s true that I no longer worry if I’m hearing about something because of an agenda…because I know I am, in all cases.
So I skip that part and just stick with the hopeful awe.
On my phone at a restaurant right now so I'm not looking it up but this was previously in a published paper in 2009. Not to rain on their parade: this is a great start for a couple of math prodigies, but they didn't quite discover a new proof.
On the Possibility of Trigonometric Proofs of the Pythagorean Theorem
Jason Zimba
Abstract. The identity cos2 x + sin2 x = 1 can be derived independently of the Pythagorean theorem, despite common beliefs to the contrary.
By now we should have already expected that AIs like LLMs are able to create unique proofs and new solutions to existing unsolved mathematical problems. They still haven't after years of hype and not even one single mention of buzzwords like 'LLMs', 'AI', 'GPT', etc in this thread. I'll tell you why:
The difference is those teenagers were able to clearly explain the process of deriving this proof transparently with the proof itself being (and still is) subject to intense scrutiny even by experienced mathematicians, going against what was thought to have been 'impossible'. Unlike the finest of LLMs and AI models which just repeat the same nonsense it has been trained on and confidently outputs more nonsense, whilst many celebrate this sophistry as a so-called 'breakthrough' even when it cannot transparently reason with its own decisions.
It goes without saying that these teenagers are very intelligent in mathematics to create this proof as it is not straightforward to just 'generate' it, given that it requires an amount of creativity AND originality that not even ChatGPT or LLMs in general can bullshit it's way around and will still tell you that it is impossible.
That proof is the true breakthrough; not magic AI black-boxes that spit out nonsense.
[flagged]
> This is the Louisiana education system in the USA, a state which is rather notorious for having sub-par education What does this have to do with anything? Exceptional people come from absolutely anywhere, and seek to learn on their own. It's as true in Louisiana as it is in Massachusetts. Ken Thompson was born and (at least partly, afaik) raised in Louisiana, for example. Are we all just dumb people using a dumb pe…
For example, look at LAMP High School[0] or Mountain Brook[1] in Alabama. One is listed as the 17th top school in the US, the other produced 3 Rhodes scholars. Both consistently rank very high on the lists of top schools in the US. And there are quite a few other pretty academically great schools in that state, just ranked a bit lower (but still as some of the best schools in the country).
I have read about this proof for a bit and this is the first write-up that gives the slightest details. The phrase "using trigonometry" is confusing. What they do is assume functions sine and cosine exist, as normally defined, as ratios of triangle values, without assuming these have the various Pythagorean-theorem derived properties. They then construct an infinite series of nested triangles and use the formula for…
Agreed "using trigonometry" is potentially misleading. After reading the proof, the only 2 senses in which "trignometry" is being used are:
1. The term "sin a" is used to denote the ratio opposite / hypotenuse. But this can be considered a purely notational convenience. They could have called it "foo a" and nothing would change, or they could have inlined the referred-to ratio everywhere.
2. The law of sines is required. But the proof of this law [1] also boils down to nothing more than the ratio definition and some algebra.
So afaict no circular logic is being used, but at the same time it doesn't seem to be doing anything previously thought to be impossible, unless there was a previous belief that the law of sines could not be used in a proof, which would be a strange belief to hold. I see it simply as a creative, unexpected proof.