Why the ad hominem? I have nothing against the mathematicians or their work. I don't even know the math; that's why I'm reading the article. And I'm just trying to wrap my head around the article's explanation and trying to figure out why its premise seems inconsistent with my understanding. The problem is more likely somewhere in my understanding, so I posted it here in case somebody could clarify whether/what I'm misunderstanding of the difference between what we've called "equality" and what they're calling "equivalent", given neither of them seems to necessarily mean "exactly the same".