Throughout the history of humanity there were certain “facts” considered proven and established “laws of nature” universally known to be absolutely known to be correct, until they were subsequently discovered to be wrong. Everyone knew time and space were fixed. Einstein proved they were relative. Einstein “proved” nothing could travel faster than light. Since then physicists discovered photons and pulses sometimes can break light speed; then in 2011 CERN observed subatomic particles traveling faster than the speed of light. Everyone including our most brilliant computer scientist, renowned mathematicians and Homer Simpson has been trying to find out if P ≠ NP. No one yet has been able to collect that million-dollar prize offered by the Clay Institute, and it is not because of a lack of trying.
The question of whether or not P = NP hinges upon if there is a simple executable algorithm that will provide a simple resolution to exceedingly complex problems. Right now, we do not have such an algorithm. That does not mean that one does not exist. The other facet to this problem is our technology. Technology is constantly advancing. Algorithms that would have taken weeks to compute twenty years ago now take seconds. This means that the number of “unsolvable” problems is growing smaller every day. Likewise, in the process of seeking a solution to P ≠ NP we are discovering new, more efficient algorithms. As Cameron and Tracey Hughes point out in their article “A Way You Could Use P ≠ NP”, “This is one of those things where it’s not so much the destination as the journey.”
Hughes, Cameron and Tracey Hughes. "A Way You Could Use P ≠ NP." 01 09 2010. Dr. Drobbs Bloggers. 2012 06 2012
Mick, Jason. "CERN Physicists Observe First Faster-Than-Light Long-Distance Travel." 26 09 2011. Daily Tech. 17 06 2012
Moskowitz, Clara. "Strange Particles May Travel Faster than Light, Breaking Laws of Physics." 22 09 2011. Live Science. 17 06 2012