No GR is not wrong. We've verified it's predictions experimentally to a high degree of precision. If these guys have got something - which they probably don't - then that will be a refinement of GR. Just as GR refined Newtonian gravity (though by a LOT in that case). We're all expecting that GR and QM will be refined, as the two don't play well together.
I agree.
I'd like to see people take the same attitude to other topics. But then, I often don't get everything I want. Why should this be different?
I'd be surprised that a couple of mathematicians did it though.
Why? Because physicsts are smarter?
I also have doubts about such theories, but mainly because while evidence is aplently, in the last 150 years, the major breakthroughs like this, have come from someone sitting down trying to marry 2 different known sets of equations, and in the process, realise that our science has been based on certain assumptions, like that space HAS to be Euclidean. Once the equations were recalculated without said assumptions, then the new equations made strange predictions of new entities that no-one had thought could exist, that turned out to be real, and found repeatedly by experiment, and the equations themselves turned out to be far more accurate than the previous equations.
That being said, I suspect that it depends on how they've developed these new equations. If they have simply asked the question "What if not all energy and not all matter is positive?" and recalculated Einstein's equations, allowing for the possibility that some matter is negative and some energy is negative, then we'll find one of 2 things:
1) All matter and all energy is positive anyway, just like we assumed. Then their equations would be as accurate than Einstein's, but no more, and no less, either.
2) Some matter and some energy is negative, and a substantial enough amount of that, that there is a detectable difference in our experimental results. Then their equations would be more accurate than Einstein's.
However, if this is just pure guesswork, someone just trying to come up with a way to make themselves into another Einstein, then it'll probably come to nothing.