This is not a game design-related post, nor even a computing-related post, except in a very abstract sense. It is to draw your attention to the fact that a solution to one of the world’s six hardest mathematical problems has been published. It has yet to be checked, and some people believe it may have holes in it, but this is still a very large development in the field.

P!=NP is a statement about the time it would take a computer to solve a certain class of problems: the “NP” class (which stands for “non-deterministic polynomial” if that means anything to you). If it takes a long time to solve a problem from scratch, but a short time to check your solution afterwards, that’s an NP problem. As an analogy, consider a 1,000,000-piece jigsaw puzzle. It may take months or years to complete, but if someone claims they have finished it already, it only takes a second to check if they are telling the truth. The question is whether such problems exist (P!=NP), or whether there is always a simple way to solve them from scratch (P=NP). This question may seem very abstract, but it has a lot of important applications – such as optimising computer networks or creating secure encryptions.

Examples of famous NP problems include the Travelling Salesman problem, which is to find the shortest route through a city while passing everyone’s door at least once (this city may have overpasses and tunnels), the Knapsack Problem, which is how to fit the most value into a knapsack when you have a number of objects of known price and size, and solving many popular puzzles like Sudoku or Minesweeper. The paper at www.hpl.hp.com/personal/Vinay_Deolalikar/Papers/pnp12pt.pdf concerns itself with the Conjunctive Boolean Satisfiability problem, which asks whether a list of logical statements can all be true at once. It asserts that the amount of time it would take a computer to solve such a problem increases very quickly – faster than any polynomial function of the problem’s complexity, in fact. If the proof turns out to be correct, Vinay Deolalikar may just have won a $1 million prize from the Clay Mathematics Institute.

A number of blogs and magazines have already published links to this article. I thought you might be interested as well.