I liked this ( http://www.newscientist.com/article/dn19287-p--np-its-bad-news-for-the-power-of-computing.html ):
His argument revolves around a particular task, the Boolean satisfiability problem, which asks whether a collection of logical statements can all be simultaneously true or whether they contradict each other. This is known to be an NP problem.
Deolalikar claims to have shown that
there is no program which can complete
it quickly from scratch, and that it
is therefore not a P problem. His
argument involves the ingenious use of
statistical physics, as he uses a
mathematical structure that follows
many of the same rules as a random
physical system.
The effects of the above can be quite significant:
If the result stands, it would prove
that the two classes P and NP are not
identical, and impose severe limits on
what computers can accomplish –
implying that many tasks may be
fundamentally, irreducibly complex.
For some problems – including
factorisation – the result does not
clearly say whether they can be solved
quickly. But a huge sub-class of
problems called "NP-complete" would be
doomed. A famous example is the
travelling salesman problem – finding
the shortest route between a set of
cities. Such problems can be checked
quickly, but if P ≠ NP then there is
no computer program that can complete
them quickly from scratch.
