I came across an article published in Science "Memcomputing NP-complete problems in polynomial time using polynomial resources and collective states", which makes some pretty astonishing claims.
Memcomputing is a novel non-Turing paradigm of computation that uses interacting memory cells (memprocessors for short) to store and process information on the same physical platform. It was recently proven mathematically that memcomputing machines have the same computational power of nondeterministic Turing machines. Therefore, they can solve NP-complete problems in polynomial time and, using the appropriate architecture, with resources that only grow polynomially with the input size.
I would dismiss this off the bat as non-serious, given the strong nature of the claims, if it weren't for the fact that this was published in Science, and that related material by some of the authors was published in Nature Physics, in an IEEE journal and in Physics Review E, all of which are reputable peer-reviewed publications that wouldn't let such claims get published without them being serious.
So is it true? Can these people solve NP-complete problems in P-time using their model?