The Millennium Problems (Basic Books, 2002).
Minesweeper, a computer game, illustrates the P vs. NP problem. To solve it you will have to find a method to answer questions about minesweeper when it's played on a large number of grids. For details go to the Clay Mathematics Institute.
Minesweeper Lecture from the Clay Mathematics Institute
The "millennium problems," have resisted solving for decades. The mind-numbing challenges are important and famous enough among experts that a $1 million reward has been offered for each correct answer. NPR's Scott Simon talks with Stanford University mathematician Keith Devlin about "seven of the greatest unsolved mathematical puzzles of our time."
Devlin's new book The Millennium Problems is what he calls a "tourist guide." He examines the history and nature of each problem, as well as the challenge it represents to the math world. According to Devlin, each "has been around a long time," is "well-known within mathematics" and has "resisted attempts at solution by the best mathematical minds in the world."
The most recent of the seven, the P vs. NP problem was developed in 1970. The Reimann hypothesis, which is concerned with the pattern behind prime numbers, remains unsolved despite first being raised in 1859. Devlin says the Riemann hypothesis is the one problem mathematicians would like to solve "above all."
And Devlin believes it may be solved before the others on the list of seven. He believes the methods developed to solve the Riemann hypothesis will be far more significant than the answer.
Devlin says another of the problems carries "a slight chance that an amateur will solve it." Known as the P vs. NP problem, it has to do with the efficiency of computer systems. It can be illustrated with the ubiquitous computer game "Minesweeper."
The seven millennium problems were chosen by a group of internationally acclaimed mathematicians organized by the Clay Mathematics Institute of Cambridge, Mass. The institute is also offering the reward. But Devlin believes the prize money is secondary to other considerations for those in the running to solve one of the complicated mental tests. "Anyone who wants to solve one of these problems will do it for the glory," he says.
Besides, Devlin believes it might take up to ten years to solve such a problem. For an expert mathematician, that does not represent "a good return on the intellectual ability," he says.
Keith Devlin is the executive director of the Center for the Study of Language and Information at Stanford University. He serves in a slightly less-distinguished role as NPR's "Math Guy."