Initially hailed as a solution to the biggest question in
computer science, the latest attempt to prove P ≠ NP – otherwise
known as the "P vs NP" problem – seems to be running into
trouble. Two prominent computer scientists have pointed out
potentially "fatal flaws" in the draft proof by Vinay Deolalikar
of Hewlett-Packard Labs in Palo Alto, California. Since the
100-page proof exploded onto the internet a week ago,
mathematicians and computer scientists have been racing to make
sense of it. The problem concerns the speed at which a computer
can accomplish a task such as factorising a number. Roughly
speaking, P is the set of problems that can be computed quickly,
while NP contains problems for which the answer can be checked
quickly. It is generally suspected that P ≠ NP. If this is so,
it would impose severe limits on what computers can accomplish.
Deolalikar claims to have proved this. If he turns out to be
correct, he will earn himself a $1 million Millennium prize from
the Clay Mathematics Institute in C