I haven't read that particular book of Dawkins, but I have encountered a mathematical argument I find somewhat troubling, though I don't have the background to really examine it in depth.
It's discussed in this interview here:
https://youtu.be/noj4phMT9OE
Essentially the number of possible configurations of the sequence of a piece of genetic code required to produce the instructions for producing a usable protein are something like 10^77 to 1. The state space is filled with an astronomical amount of unusable junk.
The next part of the argument hinges on the Cambrian explosion. They claim that mathematically there isn't enough time for life produce enough trials to give rise to the amount of species seen during that period given the duration of the period and the sheer number of combinations life has to try in order to find viable ones.
They sort of say that Darwin was like Newton. A good enough explanation of a large portion of observable phenomenon, but it breaks down at the edges and a new theory is needed.
They seem to want to fill it with Intelligent Design. I'm an atheist myself, so I don't feel compelled to fill it with the god of the gaps, so to speak. But I'm finding it hard to accept Darwin as the whole answer.
Does Dawkins book address this? Is there any book that addresses this?