Science in the Looking Glass

A stimulating overview of science by a mathematician who is sceptical about the ultimate reach of mathematical theories. Even if such theories provide highly accurate predictions we should not conclude that such theories are true or that Nature is governed by mathematics. He predicts that the scientific theories that may be around in 10,000 years may be the least mathematical like evolution and plate tectonics. The scope of the book is impressive and the discussion well informed in all areas, even those beyond the author's immediate area. He begins with perception and language, moving on to theories of mind, arithmetic, mathematics, mechanics and astronomy, probability and quantum theory, and evolution; then, in the last two chapters, a critique of reductionism in favour of multi-level analysis and a discussion of some broader philosophical issues. He sees science as providing a series of different views, with each window giving an equally valid view of the same reality. An impressive and highly readable work for the general reader but one which will also challenge the author's colleagues, especially self-confessed Platonic mathematicians.