Sputnik, the very first artificial satellite, was launched from Kazakhstan almost a half-century ago. This unexpected event sent shockwaves through the US’s math-science public education establishment. George Hacken was in high school, and was lucky enough to pass the exam for a Sputnik-inspired extracurricular IBM/Joe Berg Foundation course in discrete math (whose textbook was Kemeny, Snell, and Thomson’s Finite mathematics). As must be true of many CR readers, he never got over it, that is, over logic and discrete math.

He majored in physics (AB and PhD) at Columbia, where he stayed on as a researcher until 1976, and enjoyed with fellow students and post-docs the reflected glory of his thesis sponsor’s 1975 Nobel Prize. (Professor James Rainwater had him pegged from the beginning as a computer geek, and George did his best to be useful as a discrete math, computational complement of his awesome physico-geometric intuition.)

His first program (1962, Fortran II, IBM 1620) was a multidimensional constrained minimization problem; it was a lesson par excellence in the downright practicality of trying to “get it right the first time” — a personal augury of formal methods. The year 1976 saw another defining moment: he serendipitously came upon E.W. Dijkstra’s A discipline of programming. He had, by then, written approximately 5,000 programs, the later ones for a special, scientific model of the IBM 360, the 44, and all in connection with physics research. Dijkstra’s masterpiece changed his life, as it changed the lives of many others.

Career progression, not necessarily logical but certainly chronological, saw computing venues in telephone company rate-structure calculations; computations of credit card delinquency risk; flight simulation; factory-automation and sawmill process control; radiation-dosimetry safety-critical database work; and railroad-car brake control. These projects were followed by a 15-year aerospace defense stint at Singer-Kearfott/Plessey/GEC-Marconi, where embedded computers effected guidance, navigation, and control, and command, control, communications, and intelligence. There was also a concurrent activity as adjunct professor of computer science at William Paterson University.

Great respect for the expertise of the late Austin J. Maher (his boss and mentor at Singer-Kearfott) led to Hacken’s minimal resistance in joining Maher and the Council of Defense And Space Industries (CODSIA) government industry group in the collective creation of DoD-Std-2167, Defense System Software Development, which is fairly characterized as one of the precursors of the Capability-Maturity Model (CMM). This was a most natural segue, seven years later, into the job as CMM process lead in the company’s GEC-Marconi incarnation.

Seven years ago, Hacken started his current job as Senior Director of Vital [a.k.a. Safety-Critical] Systems Integrity at MTA/New York City Transit, where formal methods are being applied in the design, certification, and implementation of processor-based train control technologies. A most rewarding part of his job is the creation and execution of an in-house safety-critical systems design and certification course. He is, in addition to being an ACM and IEEE member, greatly informed by membership in the New York Academy of Sciences, Sigma Xi, and the American Mathematical Society.

By the way, he was born in Kazakhstan, but that’s another story.

Learning L^{A}T_{E}X (2nd ed.) Griffiths D., Higham D., SIAM-Society for Industrial and Applied Mathematics, Philadelphia, PA, 2016. 113 pp. Type: Book (978-1-611974-41-6) T_{E}X, pronounced “tek,” and its considerable elaboration L^{A}T_{E}X (“la’tek”), are mathematical typesetting systems [1,2] that hardly need introduction; they are the transformative work of ...

Jun 12 2017

Mathematics without apologies: portrait of a problematic vocation Harris M., Princeton University Press, Princeton, NJ, 2015. 464 pp. Type: Book (978-0-691154-23-7) A long time ago, a friend and fellow undergraduate math major said of a world-famous professor at our university, “He doesn’t teach you any math; he teaches you what it means to be a mathematician.” The enthralling book under rev...

Jun 5 2017

Elements of mathematics: from Euclid to Gödel Stillwell J., Princeton University Press, Princeton, NJ, 2016. 440 pp. Type: Book (978-0-691171-68-5) Stillwell, the author of this exceptional work, states: “This book grew from an article I wrote in 2008 for the centenary of Felix Klein’s Elementary mathematics from an advanced standpoint” [1], and that “what is ne...

Feb 28 2017

Summing it up: from one plus one to modern number theory Ash A., Gross R., Princeton University Press, Princeton, NJ, 2016. 248 pp. Type: Book (978-0-691170-19-0) I am not an official number theorist, like most in the target readership of this intriguing book, but I do belong to the set of “math enthusiasts of all backgrounds” for whom this book was written....

Jan 26 2017

Computer science: an interdisciplinary approach Sedgewick R., Wayne K., Addison-Wesley Professional, Upper Saddle River, NJ, 2016. 1168 pp. Type: Book (978-0-134076-42-3), Reviews: (2 of 2) I’ve decided to say here at the beginning that this book is outstanding and that it has my highest recommendation, both for self-study and as a text for undergraduate students who are serious about computing. The book’s content, organi...

Dec 2 2016

Reactive Internet programming: state chart XML in action Barbier F., Association for Computing Machinery and Morgan & Claypool, New York, NY, 2016. 241 pp. Type: Book In choosing this book to, in Nobel laureate J.D. Watson’s words, “read around [my] subject” [1], laureate Richard Feynman’s expressed truism, namely that “the same equations have the same solutions,” came to min...

Sep 26 2016

Completeness and decidability results for CTL in constructive type theory Doczkal C., Smolka G. Journal of Automated Reasoning 56(3): 343-365, 2016. Type: Article The following sentence from the rather demanding introduction to this quite demanding paper reveals common ground between us users of formal methods and the expert authors of this paper: “Given the practical importance of CTL [computation tr...

Jul 15 2016

Uncertainty quantification: theory, implementation, and applications Smith R., SIAM, Philadelphia, PA, 2013. 401 pp. Type: Book (978-1-611973-21-1) One century-old first-year calculus problem posed by a teacher of that era (and many teachers thereafter) is this: Given a square of side s, what is the approximate change in its area if s is changed by the sm...

May 20 2016

Mathematics++: selected topics beyond the basic courses Kantor I., Matousek J., Šámal R., American Mathematical Society, Boston, MA, 2015. 343 pp. Type: Book (978-1-470422-61-5) This fascinating book “was conceived while the authors were teaching PhD students in theoretical computer science and discrete mathematics.” The preface conveys computing science as “one of the most mathematical fields besides ma...

May 10 2016

Reliability of safety-critical systems: theory and applications Rausand M., Wiley Publishing, Hoboken, NJ, 2014. 466 pp. Type: Book (978-1-118112-72-4) My current venue (of 16 years and counting) continues to afford me the privilege of working with worldwide and world-class engineering firms in ensuring that their designs of such computer-driven control systems as communication-based train-contro...