Phil Plait gets it wrong
But when you start to approach the speed of light, or deal with masses that are very large, Newton’s math breaks down. It doesn’t work.
This is wrong, completely so. Newton’s math works just fine – it simply doesn’t give the correct answers, because Newton’s laws don’t hold over those domains. Newton couldn’t have known that – his theories were correct to the limits of measurement of his day – but he was, in fact, incorrect about how the world works.
Relativity may also be shown to be wrong. That would be quite impressive. But not through merely manipulating mathematics. It’s conceivable that a better mathematical description could be found, one that would clear up the problems of unifying General Relativity and quantum mechanics, for example. Every time we make an observation we admit the possibility that the resulting evidence may overturn existing ideas, though, and Einstein’s great work is not spare this standard.
It has been said that scientists must sacrifice their children if the evidence demands it. It’s not talking about human sacrifice, of course, but a very human sacrifice. As much as I love ol’ Albert, if the evidence shows his ideas don’t work in some domain, out they go!