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Comment by oceansea | Hacker News Reader

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You took this thread on an offtopic flamewar tangent, which breaks the site guidelines. We ban accounts that make a habit of this, so please don't do it again.

You also threw in nasty regional flamebait and crude name-calling. Those things are also not allowed here.

If you'd please review https://news.ycombinator.com/newsguidelines.html and stick to the rules when posting to HN, we'd appreciate it.

I have a PhD in math and I have no idea what you are talking about. This is a proof.

There's no actual requirement for a proof to give you a "why." The steps just all have to be be logically correct and not accidentally, eg, assume what is to be proven.

Lots of proofs are basically unhelpful at giving you a "why," that doesn't disqualify them from being a proof.

I was using Stanford’s definition. https://web.stanford.edu/class/archive/cs/cs103/cs103.1202/l...

That definition (as interpreted by you) would appear to, at the very least, preemptively disqualify any proof by exhaustion ("it's true because we brute forced all the possibilities and didn't find any counterexamples"), which is a perfectly valid proof method.

https://en.m.wikipedia.org/wiki/Proof_by_exhaustion

"All the steps are valid but it doesn't explain anything and I'm dissatisfied" is not an argument against a proof's validity. Sometimes the argument is just "A implies B implies C implies D implies E implies P, QED" and as long as you are convinced that each step is valid, you've got to take the proof itself as valid, even if the gestalt isn't satisfying.

That is not Stanford's official definition. That is the definition from one of their Computer Science lecturers.

I can't speak to it's accuracy but I would imagine better sources exist.

That's a misc slideshow from a class, not a formal definition.

"A mathematical proof is an argument that demonstrates why a mathematical statement is true, following the rules of mathematics."

yes, and?

The proof does indeed seem to demonstrate a^2 + b^2 = c^2 from first principles. If you have specific problems with assumptions the proof is making you should state them; as it is it’s unclear what problem with the proof your post is responding to.

I can't see how your claims relate to the article involved. The proof that's described uses a construction of infinitely many triangles and the formula for the sum of a geometric series, so it basically is a proof in it's form, whether it's correct or uses circular logic is another question but not it's merely a demonstration of properties (which is one way student proofs often fail but I don't see that here).

Can you elaborate on what is a proof in your opinion? Having a degree in applied physics and mathematics from MIPT I’m struggling to understand your point. It does look like a proof of the theorem to me.

https://web.stanford.edu/class/archive/cs/cs103/cs103.1202/l... I am using Stanford University’s definition.

Ok, I have read the first 20 slides for a CS class at an institution from which I have a degree. I feel no closer to understanding why it is relevant.

Can you specify which step in the "new proof" is wrong, unproven, or tautological (itself requires the Pythagorean theorem)?

The simplest reason why it is explanatory as defined in your cited reference is that the Euclidean distance is defined by the hypotenuse of the triangle, that triangle (and similar triangles by construction) have ratios which are also similar, the distance along a side is the sum of those distances in an infinite series, the series expansions of sin and cosine are known along with the law of sines and are independently (from the Pythagorean) proven.

You're pointing at a document without specifying what precisely in that document would indicate that the argument (which is presented only as an outline and extrapolation of the students' work) does not constitute a proof. If you're going to attempt to prove something, do try to use at least a modicum of rigor.

Apparently there are some university math professors such as Lozano-Robledo who disagree with you.

I can't say if their proof will hold up under real peer review but I hope it does.

I can't see it failing to pass muster.

It's more complicated than most proofs of Pythagoras's theorem I know, but it's still simple enough that several people have reconstructed it from just a diagram and some basic notes on how it should work. For so many people to have now independently reconstructed it without anybody finding issues is a clear indication that, even if the way they wrote it up has mistakes, the core ideas are solid.

> 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 person's language and OS?

A lot of people also don't realize that, even though schools in states like Alabama and Louisiana on average perform poorly on primary education metrics compared to other states, each one of the states almost definitely has at least one absolutely great high school that is extremely competitive on a national level in academics.

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).

0. https://en.wikipedia.org/wiki/LAMP_High_School

1. https://en.wikipedia.org/wiki/Mountain_Brook_High_School

There’s even people from the state that read this forum now and then

Indeed. I’d like to add the Louisiana School for Math, Science, and the Arts as another example of a great high school. https://www.lsmsa.edu/

I’m a grad student at Tulane in New Orleans I was being sarcastic

I understood that you were being sarcastic. I should have said I loved your comment and thanked you for it as someone who was born and raised in New Orleans.

Excellent points, I am not sure why you were flagged as dead.

It was an obvious flamewar comment, which is against the site rules, plus name-calling, which is also against the site rules, plus nitpicking in an aggressive way. That's not what HN is for.

https://news.ycombinator.com/newsguidelines.html

Because they are wrong? Read the article.

> to make a proof of it would be to show why a^2 + b^2 = c^2

That's what the article shows as a final step. And it outlines what assumptions are made and how the final step is demonstrated. I have no idea what OP is rambling about.

Yeah, they made a symmetry argument, a series expansion argument, and a law of sines argument. None of those require the Pythagorean Theorem and are all separately proven. There may be a reason that it's wrong (I'm not a mathematician but the article's author is).

So, they showed why the sum of squares is true for the hypotenuse of a triangle. It's even an exact proof rather than a limit argument. That I could follow the steps, and other mathematicians seem unaware of this combination of tools makes it seem relatively novel.

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