World-famous mathematician G. H. Hardy took public pride in touting the purity of pure mathematics [1,2] and in deprecating applied mathematics as “ugly” and second rate. That Hardy was, as the phrase goes, “on the wrong side of history” is an understatement that is, in particular, borne out by the applicability of his own work. (See, for instance, the Hardy-Weinberg theorem or law for the persistence of genotypes. Some of Hardy’s work on number theory is also deeply embedded and widely scattered in today’s computer, data encryption, and data communication technologies.) And, to kick the straw-man argument while it’s down, I’ll quote the review [3] of Hardy’s “Apology” by Nobel chemist--and no mean mathematician--Frederick Soddy: “From such cloistral clowning the world sickens.” (I hasten to add that my admiration of Hardy remains undiminished, as it is his mathematics--not his comparative “sociology” of mathematics within the human condition--that endures. Though it’s not for me to speak for all, Hardy was, and is, by no means a straw man.)

With applied mathematics’ honor intact, the mindset engendered in me by the subtitle of this book, “Mathematics for Key Technologies,” was to expect an advanced and more general treatise along the lines of Garnier and Taylor’s book [4], which is a pedagogic, hands-on, active-reading book at the contextually elementary level, aimed at students and non-specialist professionals. I say all this under the non-judgmental, non-critical assumption that others may extrapolate the (sub)title of the book under review the way that I did sight-unseen, and be interested in the present book as the alluded-to advanced general treatise, having lots of equations and derivations from discrete and continuum mathematics.

This book is of a different species; it is a collection of contemporary papers and “showcases,” which are collections of figures, photographs, and other material, supplemented by (what I call) extended captions comprising explanatory text of “success stories” of applied mathematics. There are 11 editors and over 100 (co-)authors of articles and summaries of mathematics applications in the life sciences; various species of networks; mathematical aids to production; electronic and photonic devices; finance; visualization; and education. The introduction, by two of the editors, reveals that “Matheon [is] a word invented by students of [Berlin’s] University of the Arts [my translation from the German]” for the name of a ‘mathematical research center in Berlin [to stand for] creative application-driven research in mathematics aiming at an interdisciplinary and cooperative solution of challenging problems in key technologies.” Matheon was established in 2001 and was funded for the 12 years ending May 2014 by the German Science Foundation (DFG). The 2001 Executive Summary of goals included the DFG’s “giving a strong push to the role of mathematics” in the interactive and “transversal” process among sciences and between science and mathematics. The editors state that “this book proves that these promises were kept and that solutions to most of the detailed goals ... were delivered.” Matheon will also survive post-DFG as the Einstein Center for Mathematics (ECMath) in Berlin.

I say, with the reluctance of revealing wishful get-rich-quick thinking at an advanced age, that what first caught my eye in this book’s brochure was Section E, “Finance,” comprising three articles and two “showcases.” My manifestly unrealizable wish is for a mathematical philosopher’s stone in the field of finance, where psychology and free will are added to the difficulties of modeling. (I hasten to add that the Matheon book does not purport to offer this.) Two books by a famous quant [5,6], and the publicity of the 2012 London Interbank Offered Rate (LIBOR) scandal, sharpened my latter-day interest here. What comes out loud and clear is that both the Black-Scholes equation and LIBOR interest-rate modeling (Showcase 17 in the Matheon book) comprise, to say the least, mathematics that is worthy of study and mastery, with results of application to be judged empirically.

I’ll refrain from eye-glazing enumeration of paper and showcase titles, but will point out the very high quality of editing and production of this book. The flow is as good as can be achieved by 11 editors and 100-plus authors, and the illustrations are simply stunning. The book makes a case “by construction” for mathematics that in a “more perfect” world would never have to be made. It makes this case with a relatively sparse number of mathematical expressions per unit text, and a set of authoritative references to the literature and to computing tools in the various fields.

I think that the optimal placement of this excellent book is as a report writ large to potential funding agencies for research at the Einstein Center, and, of course, in technical and scientific libraries. Mathematics libraries no longer under Hardy’s spell will also benefit greatly from its presence.