Mathematics and theology, they have not always been the best of friends. They were often opponents, doomed to clash since they have their own approach to explain and understand men, nature and the cosmos. Did a god or gods design the universe and is men gradually uncovering the mathematical laws used in this design or is everything just mathematics as Max Tegmark claims in Our mathematical universe and are gods inventions of men? Mathematicians have published proofs or disproofs for the existence of god. Clerical authorities have banned and damned mathematicians for their theory. The history of mathematicians and their gods has been rich of tumultuous events. G.H. Hardy, an atheist, considered God as his personal enemy and tried to deceive Him. Paul Dirac, an atheist too, said that "God used beautiful mathematics in creating the world". Especially when we approach the boundaries of our knowledge and understanding, we start asking theological questions. "God does not play dice" is a well known quote from Albert Einstein and Stephen Hawking turned it into a question "Does God play dice?". Does not every mathematician, being human, have his own religious opinion? Some write explicitly about their own beliefs: e.g. Martin Gardner in his autobiography Undiluted Hocus-Pocus explains why he is a believer and Paul Nahin in Holy Sci-Fi! explores the boundaries between literature, science and religion, declaring himself an agnostic. And there are of course many more examples of published interactions, some of them even slipping into fluffy esoteric realms.
Religion and mathematics are not extreme opposites. There are conflicts but their interaction is much more subtle. This book is somewhat similar in content to Mario Livio's Is God a mathematician?. It has twelve essays on the interaction between mathematics, religion and theology, written by different experts, and that can be read independently. They are ordered more or less chronologically from the Greek origins till Gödel. They focus on the traditional Western Christian civilization deliberately excluding Asian and native American cultures. Even though the editors claim in their introduction that this book is not about history, it cannot be avoided and there are a lot of historical facts, but all this is needed to understand why or how things happened as they did in some personal or collective mathematical-religious melee.
Here is a brief survey of topics discussed in the twelve essays. First the Greeks are surveyed who had an almost religious relation with numbers and ratios that were supposed to rule all that exists. Although they did not have the proper concept of a number, since a number was a measure for something and a ratio was a proportion, not really a number, and both had a specific geometric meaning. Music was governed by ratios as well and Platonic solids were models of the cosmos. There is geometry in the humming of the strings ... there is music in the spacing of the spheres. Pythagoreans formed some kind of a sect, and mathematics was not their only occupation. Perhaps Pythagoras was someone mainly interested in the human soul after death who happened to have also contributed to mathematics.
To study the cosmos, optics and light are obviously essential. This thread of light is the rainbow used in another essay to span the period from the Greek to Newton. Optics were an important research subject in medieval times and with the microscope and telescope, one obtained instruments to study God's creation beyond what is observable with the naked eye. With Copernicus, Kepler, and Galileo we see the Earth loosing its central position, and the divine perfect circular trajectories of the planets deformed into ellipses, all culminating in the well known clash with the Catholic Church.
The Renaissance is represented with several chapters. The old Greek concept of numbers was restored and combinatorics emerged, originally developed to explore the mystical dimensions of religion (Ramond Lull 1232-1315), later developed further by Mersenne, Kircher and Leibniz. But besides this arithmology also hermeneutics which is the study of numbers in the bible and giving them a mystical meaning was popular. The demonic connotation of 666 dates from that period. John Napier (1550-1617), whom we know for his logarithms, analyzed the apocalypse on a mathematical-scientific basis, as did also Newton.
Maria Gaetana Agnesi (1718-1899) was the first female professor of mathematics in Milan but she devoted the last four years of her life to the study of theology, living as a nun and taking care of the poor. With the Freemasonry, geometry became important, an heritage from the original stone-cutting lodges. Gaspar Monge (1746-1818), who became a Freemason was inspired by stone-cutting to design descriptive geometry. Lewis Carroll (1832-1898), the author of Alice's Adventures in Wonderland was the alias of Charles Dodgson. He became an Anglican deacon and wrote books on logic as a mathematician.
The unseen universe (1875) by geophysicist Balfour Stewart and the mathematician P.G. Tait was originally published anonymously. This treatise rejects materialism on a scientific basis, proving that the soul survives after death, hence reconciling science and religion. It even proposes a theory of everything way ahead of time. John Tyndall (1820-1893) and his X-club on the other hand strongly opposed this reconciliation and defended Darwin's evolution theory. Yet another clash with the Roman clergy. Flatland by the theologian Edwin Abbott is a story of a two-dimensional world, but it is also a critique on Victorian society. His message: there is more "out there" that we cannot see in our world and Darwinism should be seen as a divine mechanism. Finally a discussion is devoted to Gödel's version of the ontological argument given by Anselm of Canterbury (c. 1033-1109) for the existence of God. Gödel never published this proof though.
Although the book is readable for a general public, it is a collection of serious essays that are not just written for the amusement of the reader. The different essays put the spotlight on some less known aspects of an historical book or person, and explain what could have been the deeper intentions, the origin of the ideas presented, or the circumstances that have triggered the ideas or what other people they have inspired on this slippery interface between science and religion. Although the different authors of these essays do not refer to each other, the whole gives a remarkable survey covering the last twenty centuries. Of course the topics discussed are exemplary since completeness is obviously impossible in just twelve chapters.