The fact that evolutionary mechanisms can physically account for the complexity of life on earth seems, well frankly, mind boggling if not preposterous. And there doesn’t seem to be any mathematical model that can explain how random mutations and natural selection results in, for starters, us. Here is how Polkinghorne put it:
"Three or four billion years may seem like a pretty long time for the coming to be of life and the formation of its evolved complexity, but incredibly intricate developments have to be fitted into that period. Someone like Richard Dawkins can present persuasive pictures of how the sifting and accumulation of small differences can produce large-scale developments, but, instinctively, a physical scientist would like to see an estimate, however rough, of how many small steps take us from a slightly light-sensitive cell to a fully formed insect eye, and of approximately the number of generations required for the necessary mutations to occur. One is only looking for an order of magnitude answer, comparable in crudity to the back-of-the-envelope calculations of early cosmologists, but our biological friends tell us, without any apparent anxiety, that it just can't be done. So much of evolutionary argument seems to be that 'it's happened and so it must have happened this way".
From Science and Christian Belief, page 16
So, is Polkinghorne just another mathematician type that doubts evolution? Should he just go take a biology class? Not so fast. Check out how Polkinghorne states the same idea with one important clarification.
"One of the serious questions that many physical scientists wish to ask about a purely Darwinian account of the evolution of life is whether there has been adequate time available to accommodate the amazing variety and complexity of change involved. Three to four billion years may seem a long period, but astonishing things have to have happened, not least in the rapid development of the hominid brain in the space of only a few million years. Is the patient accumulation and sifting of small genetic differences sufficient to accomplish this? Those who ask the question are not querying the idea that natural selection has a role to play, but they simply ask whether it is by itself totally adequate as an explanation. The questioners are not looking for a gap into which to insert the finger of divine intervention, but they may just be seeking a more comprehensive and persuasive scientific account. People like Paul Davies (The Cosmic Blueprint) are very impressed with the remarkable drive to complexity present in cosmic history. Dennett occasionally refers to this time-scale problem, but it seems that neither he nor any other evolutionary reductionist is able to offer a convincing answer to it."
So come on biologists, show us the equations!! You do get marks for the right answer, but unfortunately, to pass this exam you need to write your solution out in full.