Equations from God: Pure Mathematics and Victorian Faith (Johns Hopkins Studies in the History of Mathematics)
Daniel J. Cohen
Johns Hopkins University Press, 2007
256 pp., $55.00
God & Math
There are other oddities. Cohen writes, "Students at his school in the late 1830s recalled that [George] Boole had drifted from the Church of England, reading from the Greek Bible rather than the authorized Church of England version." This piece of information is so incomprehensible it must be garbled. The only sense in which a translation was authorized was for the public reading of Scripture during an Anglican church service, and—so far from competing with the Greek original—the whole point of authorizing a translation was to ensure that it accurately reflected it.
Tellingly, Cohen insists in an endnote that the Bible teaches that the value of π is precisely 3, despite conceding that not a single person committed to the truthfulness of Scripture has ever been troubled by this alleged fact: "Biblical literalists never objected to the advanced mathematical conclusions about π ."
Cohen accurately and usefully reveals the way that professional mathematicians drove out the amateurs and secured the discipline as their own exclusive preserve. They banished puzzle-solving, relocated discussions to dry and technical journals, and generally attempted to make mathematics appear as boring as possible to the wider public. In this endeavor we must credit them with some enduring success.
Bloody-minded amateurs get the beating they deserve in Equations from God. A group of them refused to accept that π is transcendental and thus that there is no circle-squaring solution. James Smith, for example, "cut pieces of cardboard and copper into circles and squares of different sizes, weighted them, and compared the sums." He announced that π was exactly 3 1/16. Again, in order to make his narrative neater, Cohen asserts that these amateurs were motivated by a conservative religious perspective. The evidence given in his own account, however, indicates the opposite: from what one reads here, it seems clear that for figures such as James Smith, mathematics actually served as a substitute religion. Their tone-deaf, common-sense instincts (for example, John A. Parker's insistence that "infinite" is a woolly-headed concept) are no less damning for traditional theological claims.
Following a standard Victorian loss-of-faith narrative arc, Cohen's book ends with the complete defeat of an idealist or Platonic notion of mathematics. In keeping with this version of events, the last word is given to the atheist philosopher and mathematician Bertrand Russell. It is therefore rather startling to pick up Mario Livio's Is God A Mathematician? Livio, an astrophysicist working for the Hubble Space Telescope Science Institute, makes it clear that the Platonic view is very much a live one among contemporary mathematicians. His book explores the question of whether math is discovered (and thus reveals, as it were, divine thoughts—the Platonic view) or is merely a human construct (the formalist view), while at the same time offering a lively account of the history of the discipline that explains mathematical concepts clearly and cogently for non-specialists.
Here is Livio on the beginning of thinking about what we now call irrational numbers: "One of the Pythagoreans … managed to prove that the square root of two cannot be expressed as a ratio of any two whole numbers. In other words, even though we have an infinity of whole numbers to choose from, the search for two of them that give a ratio of √2 is doomed from the start." It could be the title of a new James Bond film: Infinity Is Not Enough. Or, as Buzz Lightyear would say: "To infinity and beyond!" (These cracks are my own, but if you do not like them, then you will probably find some of Livio's attempts to write for a popular audience irritating: he says our response to Newton's Principia should be "Wow!", illustrates the utility of probabilistic thinking with a reference to "gold diggers who marry for money," recurringly quotes Woody Allen, and much more.)
Livio has a flair for enlivening and humanizing his narrative through personal anecdotes about great mathematicians. René Descartes, for example, was prompted into his intellectual journey through mystical dreams in which, among other scenes, "An old man appeared and attempted to present him with a melon from a foreign land." (Although psychoanalytical interpretation now reveals this to have been sexual in nature, Descartes innocently mistook it for a summons to the pursuit of knowledge through reason.) Readers may also be reassured to learn that tossing a coin is indeed a fair way to determine which team gets to choose whether or not it will kick off at the start of a football game. In an unhurried quest for empirical knowledge, the statistician Karl Pearson tossed one coin 24,000 times in a row. (It came up heads 12,012 times.)