P is not equal to NP. Seems simple enough. But if it's true, it could be the answer to a problem computer scientists have wrestled for decades. Vinay Deolalikar, who is with Hewlett-Packard Labs, has sent to peers copies of a proof he did stating that P is not equal to NP. Mathematicians are reviewing his work now—a task that could go on for a long time. If he's correct, Deolalikar will have figured out one of the Clay Mathematics Institute's seven Millennium Prize Problems, for which they give $1 million prizes. (Grigory Perelman won one of the seven for solving the Poincaré conjecture, but turned down the money last month.) What's all the hubbub? First, an explainer:
The P versus NP question concerns the speed at which a computer can accomplish a task such as factorising a number. Some tasks can be completed reasonably quickly – in technical terms, the running time is proportional to a polynomial function of the input size – and these tasks are in class P. If the answer to a task can be checked quickly then it is in class NP [New Scientist].
