Book Review

Russell W. Howell and W. James Bradley, editors. Mathematics in a Postmodern Age; A Christian Perspective. Grand Rapids, MI: William B. Eerdmans Publishing Company, 2001. 407 pp. Paper. ISBN: 0-8028-4910-5. $28.00.

This is an important book for Christian thinkers and in particular is of value to mathematicians attempting to understand their role in the kingdom of God. It attempts to trace a postmodernist trend in contemporary mathematics and offer a critique from a Christian perspective. Although insightful, thought-provoking, and informative, this work has some deficiencies for those accustomed to a biblical-theological approach. Nevertheless, it is carefully researched, thorough, and penetrating in its analysis of current intellectual movements.

This book is written by a collection of authors brought together by the Association of Christians in the Mathematical Sciences. In attempting to answer the question "Why are the theorems of math true?", the authors take us through epistemology, history, culture, God's nature, ethics, artificial intelligence, intelligent design, psychology, and education. Due to the multifarious scope of the material and the diverse authorship, something should be said about each chapter.

The first chapter sets the stage for the inquiry by formulating modernism and postmodernism in terms of mathematics. Is mathematical truth static or changing? Postmodernism attempts to locate mathematics within its cultural milieu with implications for what constitutes adequate proof and what problems are worth solving. Modernism, on the other hand, views mathematics as certain knowledge—in fact, it is knowledge that can be obtained without the axiom of God's existence. Hence, the modernist spirit is grounded in the efforts of natural philosophy to produce an epistemology for autonomous man. The second chapter continues this cultural study by contrasting Greeks, Arabs, Chinese, and Europeans. This discussion is vital as a framework: the mathematician can see his work as part of an evolving intellectual movement which is influenced by cultural factors.¹

The next two chapters deal with God as the eschatological Mathematician (the authors do not use this term!), involved in an eternal felicitous activity of mathematizing, i.e., creating and proving all of mathematics without termination. Chapter three gets pretty technical (there are some bits of mathematical logic) and can be skipped by the non-expert without much loss. But those who stick it out will be rewarded! The fourth chapter deals with aesthetic issues of mathematics and argues that the science proceeds by induction as much as by deduction. One key example is the selection of axioms, which ultimately rests on aesthetic principles—"the simplest explanation is best."

The following three chapters treat the history of western mathematics more thoroughly. The focus is mathematization of the culture. By this, the authors mean the transformation of the ambient culture into something more quantitative—time, calendars, weights and measures, accounting, scales, calibration, experimentation, data collection, analysis, statistics, etc., and on into the information age. It is refreshing to be reminded of this and reflect on how different non-mathematized cultures must have been (maybe getting to church right on time was of less importance to Greeks dependent on the sundial for timekeeping). The key players in the development of western science, such as Kepler, Galileo, Descartes, Newton, and Leibniz, are woven into the fascinating story. Some questions of the appropriateness of using mathematics in the social sciences are raised.

The eighth chapter discusses values in mathematics: is it technique, conceptual framework, or art? Why do we "do the math?" The next four chapters are pure fun: a discussion of artificial intelligence, the possibility of detecting intelligent design, psychological perspectives on mathematical learning, and the mathematical philosophies of constructivism. The conclusion offers a summary to the work: it investigates modern and postmodern views in relation to mathematics; it compares the evolution of mathematics in diverse cultures; it examines ethical issues in undertaking mathematical projects; and considers how "faith perspectives" could shape our thinking on important issues.

It is the issue of "faith perspectives" that is of most concern. Being a work of several contributors, it necessarily suffers from haziness, i.e., it lacks a clear, piercing voice that cries out to the world. It seems that its multifarious character blunts the edge of its analysis. One particularly disturbing case is the discussion of free will versus predestination. The editors suggest that the apparently contradictory nature of these concepts may be due to a perceived tension between completeness and consistency in God's character.² Perhaps an Arminian was on the team.

Much more critical is the fact that their so-called "Christian perspective" differs in no essentials from Judaism and Islam. It is basically Theism plus The Fall. How does the resurrected Christ impact the value of mathematics and its truth? How does a New Creation framework affect the vocation of mathematics? If we now understand "truth" in the way Jesus used it, i.e., eschatological and eternal, then the truth of mathematics is to be understood in terms of the eschatological mathematical activity of God, communicated to us in mere shadows cast down upon our world. How does the crucifixion impact our experience—suffering in mathematics, perhaps? Is mathematics a semi-eschatological activity; is it Kingdom activity? None of these issues are adequately addressed and another book could certainly be written about it.

Nevertheless, this is a great book. Despite the title, it can and should be read by Christian scholars of all ilk. It is to be read over several months in small digestible portions, and will provoke periods of intense, quiet meditation on the deep things of God.

Tucker McElroy
San Diego, California

______________________

¹ As an example of historical factors, consider the geometric flavor of Greek mathematics versus the highly algebraic mathematics that emerged after Descartes. Many more important examples can be found in the book.
² This is one of the most fascinating suggestions of the book. Completeness of a mathematical system has to do with its "power" for proving things, whereas consistency has to do with the avoidance of contradiction. It has been proven that certain mathematical systems cannot (sniff!) have both completeness and consistency. Using this as an analogy for anthropomorphic conceptions of God's character, the editors suggest that a fuller view of God (moving towards completeness) causes a tension with consistency. I quibble with the use of free will/predestination as an appropriate example, since this "mystery" has been adequately resolved (to my knowledge) by Calvin and Jonathan Edwards. The dual nature of Jesus might have been a better choice.