Prime Obsession: by John Derbyshire.

The book and the style of writing are maddening, especially coming from a professional in the field - as often as not one wishes one could do more than raise eyebrows in a civilised manner and simply bop the fellow one on head, hard. It is bad enough he downplays or speaks degradingly of his professional colleagues in general, although not anyone in particular. He also refuses to provide extremely simple proofs claiming "that way lies madness" thus depriving non professionals of an opportunity of being charmed with the beauty of the subject of Mathematics. Why he feels the need so desperately to kowtow to idiots by disparaging the subject, the profession, the people in the profession, and so on, is difficult to comprehend for anyone unfamiliar with the atmosphere in general from early schools to colleges to universities - indeed generally any institutions short of stature compared to, say, Princeton or thereabouts - where jocks are worshipped and those capable of thought are abused verbally and in almost every other way beginning with epithets such as nerd, geek et al (and then comes the resentment against other cultures that actually do study, worship knowledge, and reap benefits of intelligence era in work and employment); but still, he need not have assumed the reader of such a book would have the same idiot bully attitude or that he would be stoned to death if he did not disparage his subject and badmouth it.

All that is bad enough, but having gone through the book it is far more maddening to find extremely important clues missing, almost as if he is afraid a stray reader might solve the Riemann hypothesis while reading this if he provided the important clues. He covers his back by mentioning that Mathematicians do handwave and leave gaps that are expected to be filled by the audience, but those are the sort that are more obvious, and one is not expected in the course of a lecture or a series of lectures in the subject to know why a sum of an infinite series of powers of positive integers becomes zero at negative even numbers even if the said sum can be shown to equal an infinite product of inverse terms involving primes, all primes. If one is needled, one has to go through the book over and over to find somewhere hidden in a corner a mention that a third expression for the same function is a product including sine function with half pi integer multiple, but if he has given why the third expression is equal to the other two infinite ones, one a sum and another a product, that is far too well hidden - or one has missed it due to some miracle.

All this exasperation and the double wish the book generates, one regarding going into the subject and another about bopping the fellow a few times on the head, still strangely enough does not do away with the fact that the book is very worth reading for someone not already deep in the subject. For those very familiar with all the mathematics herein I suppose the history nevertheless is extremely interesting. One does feel an immense sense of gratitude to all those great geniuses for not bending their minds to reap immediate rewards for personal benefit.