In order to understand these crimes...we must consider the stock-in-trade of the mathematician, for all his speculations and computations tend to emphasize the relative insignificance of this planet and the unimportance of human life...He deals in abstruse and apparently contradict'ry speculations which the average mind can not even grasp. He lives in a realm where time, as we know it, is without meaning save as a fiction of the brain, and becomes a fourth coordinate of three-dimensional space; where distance is also meaningless except for neighboring points, since there are an infinite number of shortest routes between any two given points...In this realm of the modern mathematician, curves exist without tangents. Neither Newton nor Leibnitz nor Bernoulli even dreamed of a continuous curve without a tangent -- that is, a continuous function without a differential co-efficient. Indeed, no one is able to picture such a contradiction -- it lies beyond the power of imagination. And yet, it is a commonplace of modern mathematics to work with curves that have no tangents...[Now he relates some of the odder features of general relativity.] These are not paradoxes of logic,...they're only paradoxes of feeling. Mathematics accounts for them logically and scientifically. The point I'm trying to make is that things which seem inconsistent and even absurd to the lay mind are commonplaces to the mathematical intelligence. [And now the point:] Is it surprising...that a man dealing in such colossal, incommensurable concepts...might in time lose all sense of relative values...? ...In his heart he would scoff at all human values, and sneer at the littleness of the visual things about him."

For anyone interested in relativity theory and convoluted detective stories, this "takes the biscuit."

Mathematically, I rank quite low so I can not comment on that part of the content. However, I like the 1930 film with Basil Rathbone as Vance, and you can see it on Turner Classic Movies from time to time. In fact I've just requested they show it again, on their website; I shall re-read my paperback for the math. Thanks.