The "unreasonable effectiveness of mathematics in the physical world" as E.P. Wigner once called it is an very interesting and forgotten problem which is now a hot topic of philosophical speculation (Max Tegmark's recent article in Scientific American called "Parallel Universes" is a good introduction to the way physicists are trying to unravel it). But Mark Steiner's misleadingly titled book is not about this subject at all! Though he mentions Wigner's query --- and idiotically faults him for only counting the successes of math in physics, as if any or all of the "failures", none of which he identifies, would make the successes less surprising! --- the book turns out to be little more than a diatribe aiming to show that physicists, since Maxwell, have been (sin of sins!) resorting to "anthropocentric" reasoning! He identifies two "strains" of this dangerous trend which he calls "Pythagorianism" and "Formalism" and he gives some anedoctical historically unfounded episodes which he diagnoses as examples of either of these nasty habits suggesting this shows some sort of reasoning in bad faith (ah ha!). It is clear from the text that Steiner has no background in contemporary physics and his examples rely on what he heard from other people and was quite unable to digest. But his real failings are, however, as a philosopher who seems as completely unaware of the recent debates
which animate the Philosophy of Physics as, for that matter, of any Philosophy of Math this side of Frege! Perhaps the most glaring misaprehension in this book is his unquestioned assimilation of Pythagorianism --- the belief that the ultimate components of the world are mathematical entities, as he puts it) with anthropocentrism (the notion that human interests, values, concerns must take center stage in any explanation). The fact is that 99% of all working physicists (and mathematecians) subscribe, consciously of unconsciously, to some variety of platonist realism which places mathematical essences in a realm transcendent of human concerns or mental categories of any sort!
Rather than facing this obvious fly in his ointment Steiner merely states: "but this is not a book about Platonism." which apparently is good enough reason for him to ignore its existence! (If you are wondering, his indictment of "nominalism" is not more convincing...). In all a real waste of time and paper.