The text you quote is not even part of the article.
But it is related to text that precedes my quote:
> One of the problems the two friends looked at was a version of a century-old unsolved question in geometry.
> “The problem is so easy to state and so easy to understand, but it’s really hard,” said Elizabeth Denne of Washington and Lee University.
> It starts with a closed loop — any kind of curvy path that ends where it starts. The problem Greene and Lobb worked on predicts, basically, that every such path contains sets of four points that form the vertices of rectangles of any desired proportion.
Emphasis mine. The article explicitly describes the problem they solved, only to later point out that they actually solved a different problem.
Oh my god here, is the same qualification near the top of the article.
> One of the problems the two friends looked at was a version of a century-old unsolved question in geometry.
On every Quanta article there's always someone welching about some gotcha they think they've found that just demonstrates how trash Quanta's popularizations of mathematical topics is. But whenever I read the article in question it always turns out that the writers and editors over there somehow manage to thread the needle in making their material accessible without being mathematically inaccurate. Vague, yes, but that's why they link to the research in question because it's a pop article not a journal publication.
You edited your comment to add another objection. It is equally insubstantial unless you dug through the paper yourself and demonstrated that the transformation applied could not reasonably be called a rotation.
> Oh my god here, is the same qualification near the top of the article.
>> One of the problems the two friends looked at was a version of a century-old unsolved question in geometry.
Did you read past the first sentence of my comment?
> You edited your comment to add another objection. It is equally insubstantial unless you dug through the paper yourself and demonstrated that the transformation applied could not reasonably be called a rotation.
I disagree. The article strongly implies that the transformation applied could be called a rotation, and I see no particular reason to doubt that. ("The Möbius strip can be rotated by any angle between 0 and 360 degrees, and he proved that one-third of those rotations yield an intersection between the original and the rotated copy.")
But I very much object to the article's idea that I should help myself think about a rotation that only changes point values along a single dimension by visualizing an entirely unrelated transformation. How is that supposed to help?
Emphasis mine.