11 August 2010

when a proof becomes a proof

Just this week, a researcher at HP labs named Vinay Deolalikar has claimed to solve the P ≠ NP problem. It has been conjectured long ago that P ≠ NP, and probably every researcher in algorithms, signal processing, and computer science has some work that relies on the belief that P ≠ NP, so if he has proved it there will be world wide celebrating. It is also one of the Clay Math prize problems, so (again, if the proof is accepted) Deolalikar will win the million dollar prize.

What I find so exciting is now the process of accepting or rejecting the proof as a community of researchers. This blog post discusses possible issues in the proof that have been raised by various computer scientists and mathematicians. Hopefully this process will help the public understand something about the way that math and research really works-- as that blog quotes from mathematician Yuri Manin, "A proof only becomes a proof after the social act of accepting it as a proof." Engineering, science and even math are social endeavors in many ways, but the most important is that ideas only begin to impact the world when the whole community begins to understand and accept them. The point in time when the community embraces the ideas, and begins to voice the implications enthusiastically, is the point at which the idea really guarantees its spot in the library of scientific knowledge.