Brian Davies was my Tutor and I am due to hear him lecture on this subject in May, although I never became a practising Mathematician or Scientist. I have read a great deal about science, maths and physics in particular, including Roger Penrose's books. So it was very interesting to read the alternative view, very much against most of the popular theory of everything which I would categorise as 'science can explain everything'.
Although very well argued one is, inevitably perhaps, left with an impression of negativity. I found myself thinking, OK that's what science isn't, how about telling us what it is.
Nevertheless it was a good and fairly easy read, well and concisely argued as I would expect. I would put it on the must read list of anyone interested in the philosophy of science whether they agree with the conclusions or not.