I don't think the article gives enough details for the case to be made but then if it did I probably wouldn't understand it.
https://www.quantamagazine.org/mathematicians-measure-infinities-find-theyre-equal-20170912/
Yes it does. It says that it's been proved.
What it doesn't do is give you enough detail to verify that for yourself. But then it couldn't. If you or I or anybody here had the mathematical tools to b able to verify the proof, we would be reading the original paper, not this article.