Well, undecidability, maybe no. But provability - yes. There are plenty of algorithms that yield results, but we haven't the faintest idea why. The models don't fit into regular mathematics or at least not any mathematics that we understand or have developed yet. I am talking about neural nets and genetic algorithms. Say a sample neural net/genetic algorithm can be trusted and 'verified' to result in a useful solution perhaps 90% of the time, measured on a large amount of tests. How are you going to prove mathematically that this 90% will hold over time, if you don't even know how to describe the solution (the solution is developed by the program itself over time). It's inherent to chaos theory that you cannot predict what will happen at that level of 'randomness'. But please prove me wrong! (pun intended)
