My email signature includes the quotation, "An equation for me has no meaning unless it expresses a thought of God." What a conversation stopper! Not only do I make the universal claim that God exists (and is personal enough to have thoughts), but the dread mathematical term "equation" is the second word. Surely in this postmodern era I would have enough sense to avoid such a faux pas.
In my defense, the last decade has actually brought a renewed interest in math. John Allen Paulos' book highlighting the "innumeracy" of most adults have been in print for quite a while now, and "holistic" methods of teaching secondary mathematics have aroused no end of controversy among parents and teachers, particularly in California. Andrew Wiles' proof of Fermat's notorious "Last Theorem" (after 300 years) is old news now. Just within the last year, director Ron Howard earned multiple Oscars for his portrayal of the mentally disturbed Nobel Prize-winner John Nash (A Beautiful Mind) and a playwright earned the Tony for Best Play by wrapping a story about family around a putative proof of a famous conjecture (Proof). Christian thought seems a little behind; the few examples include the dubious Bible Code and the more rigorous probabilistic design arguments of Bill Dembski.
Not that this should surprise anyone. Ever since Laplace told Napoleon (perhaps apocryphally), when asked where God was in his equations, "Sir, I had no need of that hypothesis," math has edged away from connections to the Almighty. More and more mathematicians (not to mention philosophers of math) at least pay lip service to one of two notions; either that math is a mere convenient formalism (approximately modernist), or that it is a plastic societal agreement (more or less postmodernist).
Which iconoclast gave me my quote, then? It was Srinivasa Ramanujan, a brilliant Indian mathematician who flourished around World War I and died tragically young. Unfortunately for my quote, Ramanujan also claimed that some of his formulas were given to him in dreams by a minor member of the Hindu pantheon. Should I relent in my quest to be a truly Christian mathematician?
Yet there are Christian mathematicians; in fact, an Association of Christians in the Mathematical Sciences has been active for over two decades. Now Eerdmans has published the collaborative effort of ten of their members addressing the nature of math, the increasing role of mathematics in culture, and many practical contemporary issues. This book, Mathematics in a Postmodern Age: A Christian Perspective (hereafter MPA), brings specifically Christian thought together with informed historical and recent knowledge.
Editors Russell W. Howell and W. James Bradley and the other contributors come to the table with several key shared principles that inform the whole work. First, they assert that our capacity for mathematics is good, as it is created by God, yet they also acknowledge that all our abilities are tainted by the Fall. Out of gratitude for God's gift of redemption, they want to discern God's purposes for math activity; indeed, both in discovering eternal truths and in helping measure and steward the earth, math is part of humanity's creation directive. Within this (rather Reformed) framework, the three main parts of the book treat philosophical issues in the nature of math, math's influence in science and culture, and issue-oriented case studies in mathematics.
The first section emphasizes why many of us study and teach math in the first place. It is true, universal, shows God's order, is challenging, and so on. The first chapter describes the main philosophies of math, but following chapters mold these views in distinctly Christian ways to understand both in what (rigorous, philosophical) sense math can be considered to be in the mind of God (chapter 3) and how to acknowledge the pragmatic component of math (chapter 4).. The latter will be very challenging to any true child of modernity; we find it difficult to admit that effort might have a role in what theorems are considered 'true' by our limited human reason.
Our very human limitations play a larger role in the second section. The role of mathematics in Western culture is sobering. Not just the Pythagoreans (who almost worshiped number) but Greek civilization itself placed pure math and geometry on a near-idolatrous pedestal. In Christian Europe, though, beginning with very worthy ideas of understanding God by understanding the order in his creation, thinkers like Descartes, Newton, and others left a smaller and smaller explicit role for him in it. So much is well known, and well described here. More troubling is the discussion of how over several centuries not only the physical sciences but also to a large extent social science and even the humanities were "mathematized"; that is, quantifiable elements became more and more prominent, with human reason the final arbiter, while anything inaccessible to these methods was jettisoned. Today we see this in how Westerners think of time, space, business, politics, and intelligence. Our authors sketch a response; it condemns the Enlightenment model as the idolatry it is, but calls for a stronger cultural structure for our use of mathematics, so that we do not lose the cultural benefits of our science in the influence of postmodernism. Agree or not, this requires action.
The final section is a smorgasbord of contemporary issues. As a newer teacher of math, I want to know what role rote processes have compared with group projects; chapter 12 chronicles recent battles over math standards involving just such issues. Being at a research-oriented department, I appreciate the proposed Christian response here, which affirms centering the learning environment on the student (as made imago Dei), humbles us in recognizing we cannot know everything (even in math), and criticizes recent theory claiming students are autonomous learners (God is our source). Similarly, chapter 11 reviews psychological research that examines how we learn more abstract concepts, while insisting (against usual research bias) that this window to learners is limited. Other sections readers of this journal will want to take note of include a synopsis of the mathematical aspects of Intelligent Design theory and the limitations of artificial intelligence.
And it is all readers of this review who can read this book profitably. Certainly Christian mathematicians should be reading MPA, as the essentials in math history and philosophy are covered in the acknowledgement of Christ as Lord. However, the issues raised are of general interest; the latter chapters could almost be published as separate, cost-effective pamphlets. I have already mentioned the call for change in the over-mathematization of Western culture. Social scientists should start formulating wise rules for the use of quantification in their disciplines; business and government leaders likewise can take this advice to heart, before we destroy our institutions with too much (or too little) math. That's not all, though. Historians will gain good examples from the comparison of math in ancient Greece, medieval Islam, and pre-colonial China. Teachers and parents can start to discuss secondary math reform responsibly using this resource; mathematicians of any (or no) religion can finally start to understand their Christian colleagues.
The book's success at engaging postmodernism responsibly is noteworthy, and is in line with the larger Christian trend of discarding the bad from the Enlightenment project and affirming the positive about postmodernity. When that does not suffice, each chapter has suggestions for improvement. It is a little disappointing (especially so in the last part, concerning contemporary issues) that the "Christian response" in each chapter was relegated to the end; in contrast with the rhetoric of the introduction and conclusion, it leaves the reader feeling that Christians can only react to trends in culture, not start new, positive ones.
Be aware; some familiarity with general logic or philosophy is helpful in the denser chapters on the nature of math, and although MPA makes no specific claim to be a systematic history or philosophy of math, it is detailed enough that some readers might take it to be one. There are plenty of stellar references included on both counts; use them!
What is the upshot for me, then? After good descriptions, well-reasoned blows at much that is bad, and good suggestions for the future, MPA outlines a program for a lot of future Christian thought in math in an exciting conclusion. For a young Christian mathematician who delights in knowing the mind of God, that means there is a lot to look forward to.
Karl-Dieter Crisman is a doctoral student in mathematics at the University of Chicago. His work this year is supported by a departmental grant from the National Science Foundation.
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Books & Culture Corner appears Mondays at ChristianityToday.com. Earlier Books & Culture Corners and Book of the Week include:
Getting Beyond Victimology | A provocative collection of essays for "the black silent majority." (Feb. 3, 2003)
Strange Bedfellows | Christopher Hitchens and Christopher Caldwell collaborate on a collection of political writing. Has the millennium arrived unnoticed? (Jan. 27, 2003)
Encounters of the Gods | Christianity and Native American religion in early America. (Jan. 20, 2003)
Books Present, Books Past, and Books to Come | Plus: A new format for this column. (Jan. 13, 2003)
Double Indemnity Meets Dead Souls | A conversation with novelist Richard Dooling. (Jan. 6, 2003)
Books of the Year | The top ten. (OK—make that twelve.) (Dec. 30, 2002)
Entertain Us | Nirvana, Pearl Jam, and the rapture of distress. (Dec. 16, 2002)
Boys Will Be Boys | A new book by a leading Christian feminist scholar inadvertently reveals the flawed assumptions underlying much talk about "flexibility" in gender roles. (Dec. 9, 2002)
Street Cred | Dave Eggers: The portrait of an artist as a … what? (Dec.2, 2002)
Epicurus'—and Darwin's—Dangerous Idea | How we became hedonists. (Nov. 18, 2002)
Weird Science? | A Darwinian debate continues. (Nov. 11, 2002)
Of Moths and Men Revisited | A Darwinian debate. (Nov. 4, 2002)
Angels in Heaven | A game that's more than a game. (Oct. 28, 2002)
Number One with a Bullet | America's foist family as a tool for evangelism. (Oct. 21, 2002)
Train Up a Child | Helping children to become intimately familiar with Scripture. (Oct. 14, 2002)
Acting Like Those 'Evangelicals' | Guilty as charged? (Sept. 30, 2002)
Ugly Evangelicals | Is this us? (Sept. 23, 2002)
Herbie Goes Bananas | The rise and fall and rise and fall and rise of the VW Beetle. (Sept. 16, 2002)
So Far, So Near | A graduate of Murree Christian School in Pakistan, the site of a deadly assault by Islamic terrorists in August, reflects on his growing-up years, on what has changed in the interim, and on the beleaguered Christian community in Pakistan (Sept. 9, 2002)