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“A Mathematician’s Apology” is a slightly better than decent read, but it certainly isn’t great. Probably the two most interesting aspects of the book are the philosophical forays and Hardy’s own psychology. As an apology for mathematics, it’s one the verge of sorry. It really is more of a mathematicians’ apology than an apology for mathematics. Moreover, it is more of an apology for a mathematician, videlicet, Hardy, than it is a mathematicians’ apology, thus the psychological remark. It is very difficult to make this aspect of the text more obvious, unless one were to have a relatively close friend, such as C.P. Snow, write a pseudo-psychoanalytic preface, as the publisher has. Some aspects of the text are downright bizarre, which may make it all the more interesting to some readers. For instance, the terms in which Hardy wants to talk about “utility,” in relation to mathematics’ utility, will induce some amount of thought, though, I am sure, many will find some such oddities in Hardy’s views not worth expression. Rather unfortunately, I think the text is a bit too short for Hardy to have effectively communicated the value and veracity of the distinctions he tries to draw. Nonetheless, there is some merit to what he says, on the basis of what he does say.
I think the disappointment for me has been the Victorian and Edwardian British mentality of Hardy’s apology: doing mathematics for the sake of distinction, as tradition affords, is a horribly weak point to make. Perhaps it is this mentality that leads him to an elitist sounding lamentation that resurfaces throughout, not to mention is bitter sadness in, at, and with life. How such sociological considerations fit with his strong Platonism is beyond me (e.g., he refers to the Platonic position on mathematics “realism,” as opposed to “idealism”). Claiming that mathematicians are more in touch with reality than physicists requires quite a bit more discussion than Hardy gives.
All these frustrations considered, there are some really beautiful points that he makes, and I think it is more those beautiful nuggets than anything that have garner the book such acclaim. Ultimately, if I could, I would rate the book a 3.7 or 3.8 stars, because it certainly is one of those books I’d recommend to someone of sufficient interest in math, philosophy of math, scientific biographies, psychology in science, etc. I did experience a considerable amount of pleasure in reading it in some places within the text, but there were certainly stretches where the psychological pathology and the rants were a bit much. It is certainly suitable for high school students, especially the advanced ones, for college students, and at-large intellectuals. I wish, however, it weren’t in the Great Books of the Western World. I definitely think it doesn’t deserve to be.