Daniel Cohen, an assistant professor of history at George Mason University, wants to illuminate the religious history behind the odd academic phenomenon that most of us have experienced: mathematicians humbly belittling and trivializing the nature and parameters of their discipline. Cohen quotes Bertrand Russell in a typical backhanded grand gesture: “Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true” (181).

Cohen succeeds in showing that this rhetoric of humility has roots in the hopes of George Boole (1815–1864) and Augustus De Morgan (1806–1871) to use mathematical logic in the service of true religion. Symbolic logic, Boole believed, would strip the ambiguities and inconsistencies present in religious dialogue and point toward a “divine plane where all knowledge converged into God's Truth” (105). Boole was a transitional figure who shared in the traditional belief that mathematics was a divine language but realigned it with Kantian philosophy. The first two chapters of Cohen's book are about the history of this mathematical idealism, and how it was robustly exemplified in the life and work of the Harvard Unitarian Benjamin Peirce (1808–1880). In Equations from God, Pierce stands looking backward; Boole takes a step forward to a more stripped-down, austere future; and Augustus De Morgan strives further forward out of religious zeal into a situation where it behooves him to couch his mathematical idealism in humble rhetoric.

De Morgan was the principal founder of the London Mathematical Society, a society that strove to separate professional mathematicians from amateurs and “arrogant metaphysicians” (107). De Morgan promoted a new rhetoric of humility for professional mathematicians as a means of separating themselves from amateurs and metaphysicians who waxed eloquent about mathematics as the language of God. On the other hand, De Morgan had his own high hopes for mathematics in religion.

De Morgan, like Boole, thought mathematics could help purify religion of its sectarian small-mindedness and lay a foundation for ecumenical universality. De Morgan was a great proponent of spiritualism and the use of mathematics to strengthen and clarify evidence for clairvoyance, telepathy, miracles, and the existence of spirits. De Morgan believed that the rise in spiritualism was being driven by human experience and substantial evidence, not by abstractions or authorities in theology, philosophy, or metaphysics. Cohen points out that this antagonism to abstraction and authority encouraged De Morgan to ratchet down the rhetoric of mathematical idealism. If mathematicians could stop being bound to theological, philosophical, and metaphysical systems, then mathematics could be free to find and support truth—especially truths such as communication with spirits.

Cohen shines a light into one of the more shadowy corners of how the history of modern science and modern religion work together. If we entwine Cohen's story with the history of Darwinism, we see that Benjamin Peirce was a close supporter of Louis Agassiz. De Morgan, on the other hand, found a compatriot in Alfred Wallace. None of these four wants to strip religion out of science or even have science lead religion. The differences between them are that the former were gripped by old metaphysical traditions and high theological concepts. The latter wanted religion and science to be driven by openness to practical experience and the intellectual freedom to follow evidence where evidence leads. De Morgan wanted to reform the conservative intellectual establishment that dismissed miracles and spiritualism by advocating a new, more austere professionalism that would recognize and support evidence no matter what the evidence pointed toward.

In the last chapter of the book, De Morgan's advocacy of purposefully humble rhetoric is taken up by other professionals who want to use it to separate mathematics fully from religious implications. John Venn in The Logic of Chance (London: MacMillan, 1866) wrote against the use of mathematics in debates about miracles. Irreconcilable differences in opposing viewpoints made the mathematics meaningless in the debate. Bertram Russell found comfort in praising the value of mathematics as a purely mental exercise separated from metaphysics and physical science.

Daniel Cohen has done what historians of science do best: make complex a story that has been told too simplistically and triumphantly. The pressure on mathematics to strip itself of religion was not irreligious. The standard story of moving from messy old traditions to clean scientific methods is not very accurate. Messy old traditions yield messy new traditions. One of these messy new traditions is the awkward rhetorical posturing of mental independence evident in G. H. Hardy's A Mathematician's Apology (Cambridge: Canto, 1992 [1940]): “The ‘real’ mathematics of ‘real’ mathematicians, the mathematics of Fermat and Euler and Gauss and Abel and Reimann, is almost wholly ‘useless’” (119).