In The Art of Computer Programming (Volume 1, 3rd Edition, Page 6), Knuth states that "there is an algorithm that determines whether or not the game of chess can always be won by White if no mistakes are made.  Yet, it is a safe bet that we will never in our lifetimes know the answer; the algorithm requires fantastically large amounts of time for its execution, even though it is finite."

I asked Knuth how long he thought it would be until there exists a computer to execute that algorithm.  Click here to listen to Knuth's response.