The New York Times has a nice article on the recent Communications of the ACM article on P=NP (article at author Lance Fortnow’s site). I had read Fortnow’s article last month, and really liked it. In fact, I am surprised I didn’t blog it: I guess I was too busy worrying about false proofs of P=NP (or not).
The Times article does a good job of summarizing the problem in a non-technical way:
The challenge, in its simplest, but not most understandable phrasing, is to determine whether or not P equals NP. P stands for the class of problems that can be solved in polynomial time, or reasonably quickly. NP stands for the class of problems that can be verified in polynomial time — quickly. If it can be shown that P=NP, then it is possible that the world will be a very different place.
The main thrust of the New York Times article is simply how popular the paper is:
The editors of the journal said they were tickled to have a hit article on their hands.
”I don’t think we’ve ever had an article that started off with this kind of a bang,” said Moshe Y. Vardi, a Rice University computer scientist who is editor in chief of the journal. ”Our e-mail blast went out and thousands of people felt they had to click.”
The author of the article, Lance Fortnow, a computer scientist at Northwestern University McCormick School of Engineering, initially told Dr. Vardi that the article would be a short one. ”Still open,” he writes, was in first reaction to writing about the state of the work on solving the problem.
But the article does point to one possible new direction for attacking the problem:
There remains a glimmer of hope, he noted. An esoteric branch of mathematics known as algebraic geometry may offer an avenue to prove or disprove the problem, which was first outlined by Stephen A. Cook, a University of Toronto computer scientist, in 1971.
That prospect feels a bit intimidating. As Dr. Vardi said, “It’s a bit scary because we have to start learning a very difficult mathematical field.”
Note added As a reddit commentator noted, “algebraic geometry” is hardly “an esoteric branch of mathematics”, so perhaps there is room for improvement in the article.