As I mentioned in my earlier review of Naming Infinity by Loren Graham and Jean-Michel Kantor, the standard view among professional mathematicians today is that mathematics is an essentially secular discipline, in the sense that while mathematicians’ religious beliefs might have some influence on their professional conduct, they have no absolutely no relevance to the mathematical content of their research. I have become so accustomed to this conventional view that I was quite surprised to learn that, according to Daniel Cohen’s historical study Equations from God, the prevailing attitude in the U.S. and the U.K. during the early Victorian era was precisely the opposite—namely, many prominent Victorian mathematicians viewed mathematics as being divine, and potentially of enormous value in the search for divine knowledge.
Cohen begins his study with a chapter that summarizes the history of the idea of the kinship between mathematics and divinity, starting with Plato and continuing through Proclus and later thinkers such as John Dee, John Norris, and John Wallis. Since mathematics involves reasoning about abstractions that are free from the imperfections of the material world, it is a natural idea that mathematics should be an excellent training ground for reasoning about Platonic Forms, and these thinkers have developed this idea in detail. Cohen also mentions several precursors of modern mathematical logic, notably the symbolic systems of Ramon Llull, Thomas Harriet, and John Wilkins. A significant part of the motivation for these systems was a desire to place all logical reasoning—not just about strictly mathematical matters but also about religious truths—on a secure foundation. To round off the chapter, Cohen describes the idealist views of Romantic poets such as Samuel Taylor Coleridge and William Wordsworth. I was amazed to learn of a little-known work by Coleridge entitled Logic that contains three full chapters on mathematics and its value in leading the human intellect towards divine truth.
The central portion of the book focuses on three famous Victorian mathematicians, Benjamin Peirce, George Boole, and Augustus De Morgan. According to Cohen, Peirce was a vocal advocate of the divine nature of mathematics.
Peirce thus agreed with Plato and Galileo that God wrote the universe in the language of mathematics, a divine dialect waiting to be discovered by the highest faculty of the human mind. Remarkably, no inscribed stone tablets were needed to understand this language—it could pass directly from the mind of God to the mind of man. In this way mathematics was uniquely suited to guide society to a higher level of understanding and a higher sense of faith. This grander religion would come, Peirce believed, because mathematics was not associated with mere liturgy or ecclesiastical structures; it was a pure language from the heavenly realm. “The loftiest conceptions of transcendental mathematics have been outwardly formed, in their complete expression and manifestation, in some region or other of the physical world…They are the reflections of the divine image of man’s spirit from the clear surface of the eternal fountain of truth,” he concluded with an idealistic flourish. Mathematical symbols were clearly heavenly, rather than earthly, symbols.Boole is well known to modern mathematicians for his development of what are now called Boolean logic and Boolean algebra. Though these subjects are nowadays taught in a purely technical fashion, Boole’s original intent was to develop a system for reasoning accurately about religious matters. He hoped thereby to expose fallacious reasoning and transcend the sectarian strife, particularly between Catholics and Protestants, that surrounded him and plagued him all his life. Boole’s Laws of Thought contains many analyses of what he regarded as flawed philosophical reasoning by famous thinkers. Such analyses would be almost unthinkable in a modern mathematics textbook.
De Morgan is perhaps the most interesting case study in the book, because of the shift that took place in his views over the course of his life. Like Boole, De Morgan is best known for his work in logic, and he initially had a similar view that mathematical logic would be valuable for transcending sectarian divisions and arriving at pure, divine truth. However, Cohen recounts how during the course of De Morgan’s life, mathematicians (like many other academics) felt pressure to professionalize in order to cement their status in society. The process of professionalization drove mathematicians to distance themselves firmly from amateurs (whose illogical claims to have solved unsolvable problems such as squaring the circle were an embarrassment to the profession) and from clergymen (who were quick to use mathematical arguments to bolster specific dogmas that ecumenically-minded mathematicians such as Boole and De Morgan found objectionable). By the end of his career, De Morgan was firmly opposed to the use of mathematics for theological purposes.
What I found most fascinating about the book was the implicit suggestion that the secularization of mathematics was driven in large part by the desire to carve out a comfortable social niche for professional mathematicians. To what extent are our own attitudes towards the divinity (or otherwise) of mathematics driven by economic and social expediency? Though Cohen does not raise this question himself, it is one of the most valuable insights that I gained from reading the book.