To be fair to yourself, would you reject it if it were a proof of something you agreed with?
If they had gone out and 'proven' mathematically that sentient robots ARE possible, I'd be equally skeptical - not of the conclusion, but of the validity of the proof, because the core of the question is not mathematical in nature.
Based on Tononi's earlier work on Integrated Information Theory, apparently, Maguire et al. have come up with a formulation of consciousness as a lossless integration of information that requires noncomputable functions, which implies that consciousness cannot be modeled computationally.
http://www.newscientist.com/article/dn25560-sentient-robots-not-possible-if-you-do-the-maths.html
I'm personally skeptical of this, but their paper (seen here: http://arxiv.org/abs/1405.0126v1) has some impressive looking formal mathematical proofs that I will admit I lack the mathematical competence to judge the veracity of. Anyone with greater mathematical acumen want to take a look?