Edit: so with this in mind, is it safe to say that the NSA's mathematicians are probably the few individuals in the world most interested in this recent development ? Or, are there other types of problems out there that this proof attempts to address? (Commercial etc)
Cryptography is a perverse example where you want to create very hard problems (if not impossible) for others to solve while having some means of keeping the problem easy for yourself and individuals you trust.
If we had some easy way to solve problems in NP though, I bet there would be tons of productive applications. I'll quote a friend of mine:
"That would transform life on earth, and multiply our technological development rate by a factor unimaginable.
There's no way of even estimating what could happen if that problem were solved, unless the polynomial conversion made the problem impossible.
....It would also solve the protein-folding problem and all of the quantum state problems. Money is nifty; immortality and a possible stardrive don't suck. The NP problem is the current barrier to human science. 'There's no way to simulate that' is a constant refrain around here."
An interesting way of looking at it is that a valid proof that P != NP would be a kick in humanity's balls comparable to Gödel's incompleteness theorem.
Well, if the opposite had been proven, P = NP, there would be titanic commercial opportunities, but it seems to be the opposite (as most people suspected).
no, a proof that P!=NP would most likely have no immediate consequences for engineering ("practical") applications to anyone, the people most interested in resolution of P vs NP are complexity theorists and other theoretical computer scientists
Edit: so with this in mind, is it safe to say that the NSA's mathematicians are probably the few individuals in the world most interested in this recent development ? Or, are there other types of problems out there that this proof attempts to address? (Commercial etc)