I should point out that (quite to my surprise), I have shown that random mutation combined with selection converges exponentially fast the local "fitness" function. I had thought that the convergence would be only linear.
I'm not particularly gifted in math, but I'm not surprised. I happen to think that learning in brains works along those lines. I also think that learning is an evolutionary process that has a different and faster physical implemenatation. It will be interesting to see if anyone can replicate that functionality in silicon with a clock speed a bit faster than 100 hz.