Timothy Larsen

God & Math

Oil and water, or gin and tonic?

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Although Cohen is certainly right that amateurs were deliberately and successfully squeezed out of the discipline, even this generalization has at least one exception. For the whole of the 20th century hitherto, mathematicians had accepted a table of 43 non-alternating knots of ten crossings. Then, in 1974, a New York lawyer, Kenneth Perko, discovered that two of them were identical while experimenting with ropes on his living room floor.

As to the question energizing the book, Livio quotes numerous 20th- and 21st-century mathematicians who believe in the Platonic view. In the folksy articulation of contemporary mathematician Martin Gardner: "If two dinosaurs joined two other dinosaurs in a clearing, there would be four there, even though no humans were around to observe it, and the beasts were too stupid to know it." Bolstering this conviction is what Nobel laureate physicist Eugene Wigner famously called "the unreasonable effectiveness of mathematics." If mathematics is merely a human construct, why do scientists keep discovering that nature conforms to these invented games? This is most strikingly brought home through the predictive powers of mathematics.

Livio is at his best demonstrating in breathless wonder how again and again, work in pure mathematics has subsequently found a practical application. In what was almost a self-parody of an academic, the mathematician G. H. Hardy boasted: "No discovery of mine has made, or is like to make, directly or indirectly, for good or ill, the least difference to the amenity of the world." He spoke too soon: the Hardy-Weinberg law is now used by geneticists to study the evolution of populations.

At the end of the book, Mario Livio weighs in on the dispute to pronounce magisterially: "Our mathematics is a combination of inventions and discoveries." This rather pedestrian sic et non does not seem to warrant its excited italics. Nevertheless, Livio himself humbly and astutely observes that perhaps mathematicians are not the people best equipped to address the question. Moreover, whatever one thinks of Livio's own answer, his book is of considerable worth as a history of mathematics and as a clear introduction to mathematical ideas and philosophical perspectives on the discipline.

All that remains is for me anti-climactically to pronounce my own view: If two dinosaurs joined two other dinosaurs in a clearing, even if there were no humans to generate theological ideas, and the beasts were too stupid to discern it, there would still be the mind of God.

Timothy Larsen is McManis Professor of Christian Thought at Wheaton College. He is the author most recently of Crisis of Doubt: Honest Faith in Nineteenth Century England (Oxford Univ. Press), and is at work on a book about the Bible in the 19th century.

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