why should it be trusted?

[Jordan Dimov]

>Perhaps it is you who should do so.  Showing a problem to be
>asymptotically Omega(N!) or Omega(N^N) (or Theta of either) is
>effectively proving it to be NP-hard--that is, it grows in
>non-polynomial time.

Probelms are not asymptotically Omega(N!) or Omega(N^N).  Solutions are.  
I don't believe anyone has ever proved that an NP-hard problem can not be
solved in polynomial time.  Not being able to solve a problem in
polynomial time with current techniques does not make it unsolvable.  MIT
people always surprise me.