Religious writings and mathematics

SUMMARY: Mathematics and religious thought have been driven by the same motive: the need to better understand the nature of life and the universe. 

In addition to its computational and problem-solving power, mathematics has long been joined to religious faith to form systems of mutual support. Evidence of the most productive relationships can be found in a variety of texts that call attention to mathematical concepts and knowledge as part of a religious or theological treatise. In other cases, the purported significance of mathematics to religion is a cause for antagonism and tension. Among the most persistent relationships evoked in writings that combine mathematics and religion is one that is understood to exist between their particular ways of knowing. Whether by way of analogy or more direct linkages, predominate characteristics of mathematical knowledge—its clarity, certainty, and timelessness—have often been called upon to serve theological contemplation. 

Plato

Several Platonic dialogues featured extended discussions of mathematical knowledge in relation to philosophical and cosmological considerations, most notably the Meno, the Timaeus, and the Republic. Coaxing a geometric argument from an unsuspecting slave boy in the Meno served as an epistemological lesson in humankind’s ability to access certain and timeless knowledge. In the Timaeus, the power of mathematics as a system that provided a way of comprehending the physical world legitimized adopting a cosmological perspective organized around identifiable characteristics, such as intelligence and goodness. The significance of mathematics to training philosopher-rulers as presented in the Republic was predicated on their need to reason effectively about ideal forms such as morality and justice. Although it would be incorrect to refer to them as “religious” in a strict sense, these Platonic dialogues established a crucial link between mathematical and metaphysical contemplation frequently reflected in later theological writing. 

Gregory of Rimini

Gregory of Rimini (c. 1300–1342) followed an Aristotelian mode of thinking, according to which abstract mathematical concepts exist only in the mind of mathematicians. Unlike their characterization within the Platonic tradition, mathematical entities have no existence independent of the objects that possessed them in terms of size, quantity, or other qualitative features. Even so, Gregory of Rimini’s compiled Lectures undertook discussions of the continuum that ultimately challenged Aristotle’s opinion on the impossibility of infinity as an actual or completed notion. This work intertwined discussions of divine omniscience, the temporal and spatial characteristics of angels, and the divisibility of the continuum, placing it squarely in a scholastic tradition that incorporated mathematical considerations within commentaries that focused primarily on religious subject matter. 

Nicholas Cusanus

Although the author of several texts dedicated to Classical problems, such as squaring the circle, the philosopher and theologian Nicholas Cusanus (1401–1464) explicitly elaborated on the connection between mathematics and religion in Learned Ignorance (c. 1440). The significance of mathematical reason to theological contemplation discussed in this text is founded upon its ability to provide reliable and infallible knowledge about objects that transcend direct human experience. For Casanus, relations that exist between all things meant that one was able to develop an appreciation of unknowable objects based on other, better-understood objects. Polygonal approximations to a circle underscore this relationship. At the same time, Cusanus was aware that obtaining knowledge in this way depended on using various symbols and symbolic relationships in consistent and correct ways. The study of mathematics employed immutable symbols that avoided interpretive ambiguity and, thus, appealed to Cusanus as an appropriate framework for working with them. 

Michael Stifel

In his 1532 Book of Arithmetic About the Antichrist, A Revelation in the Revelation, Michael Stifel (1468–1567) used computation skills and numerological inclinations to predict the end of the world. By doing so, he contributed to the fervor of the Reformation by associating the pope with the antichrist of the Book of Revelations. Indicative of his talents as a mathematician who pursued a lifelong fascination with numbers and their meaning, Stifel’s 1544 book, Arithmetica Integra , is considered his major achievement. In it, he explored and extended Pythagorean number theory, the construction of magic squares, the theory of irrationals, and the algebra of quadratic equations. 

Galileo Galilei

Galileo Galilei (1564–1642) articulated a connection between mathematics and the divine that many found problematic. Like others before him, much of his writing asserted the superiority of mathematical reasoning, acknowledging it as the most certain way to both read and describe truths pertaining to the natural world. However, his praise of mathematics went considerably further in some texts, including the 1632 book, Dialogues Concerning the Two Chief World Systems. Specifically, Galileo maintained that human knowledge was indistinguishable from divine knowledge regarding those areas of mathematics to which it turned its attention. Consequently, mathematical reasoning provided unmitigated and unparalleled access to God’s designs. As a threat to longstanding theological hierarchies, Galileo’s pronouncements on mathematics were part of the indictments brought against him by church inquisitors. 

René Descartes

A mathematical approach to reasoning is evident in the prescriptions set down by René Descartes (1596–1650) in his book, Discourse on the Method. Compelled by both skepticism and consistent criteria, he promoted a reductive framework for investigating problems that required breaking the analysis into pieces. Examining and understanding the simplest of the pieces would then lead to a solution. The first principle of this analytic approach allowed one to establish a simple truth by virtue of its evident nature. Using mathematics as an exemplar for all reasoning therefore demanded an assurance of certainty. Descartes addressed this requirement in his 1641 book, Mediations. In particular, this work contained proofs of the existence of a benevolent and non-deceiving God, by virtue of which humans are able to recognize eternal truths for themselves. Although not above philosophical criticism, Descartes’s work embraced mathematical and religious concerns of the time. 

George Berkeley

George Berkeley (1685–1753) adopted a significantly antagonistic perspective on mathematics and theology. Some of his early writing evidences his affinity and appreciation for mathematics. However, later commentaries published while he served as the Bishop of Cloyne criticized mathematicians. Most notable among these are the 1732 book Alciphron, or the Minute Philosopher and the 1734 book, The Analyst, or a Discourse Addressed to an Infidel Mathematician. Berkeley asserted that mathematicians made unjust claims to exactness. His belief that the persuasive power of its problematic reasoning undermined the precepts of revealed religion only exacerbated this concern. Associating it with dogmatism and obscurantism, Berkeley was particularly hostile to the use of fluxions and infinitesimals, respectively, in the Newtonian and Leibnizian developments of calculus. One of his overarching objections pertained to the unacceptable admission of infinity in mathematics. Consequently, he attempted to establish the rule for computing the derivative of xn in the Analyst by avoiding the use of either fluxions or infinitesimals. 

Charles Babbage

Exemplary of natural theology in the nineteenth century, the Bridgewater Treatises were intended to provide commentary on modern scientific discoveries in relation to the Creation. In all, eight manuscripts were commissioned that discussed topics such as chemistry, geology, meteorology, and physiology. Mathematics was not one of the subjects included in the original commission, and Charles Babbage (1791–1871) took its omission as an opportunity to write his Ninth Bridgewater Treatise. Considered the father of modern mechanical computing, Babbage dedicated much of his life to designing the difference and analytic engines. His treatise highlighted this work by arguing that events appearing miraculous could be accounted for as part of a grand design. As consummate a promoter as he was a mathematician, Babbage publicly illustrated this point several times with a model of the difference engine. These demonstrations involved programming the machine to break an identifiable recursive pattern at a moment that defied explanation by his audience. 

Edwin Abbott

The enduringly popular 1884 book, Flatland: A Romance of Many Dimensions, introduced the concept of higher dimensional space to a wide readership. As its author, Edwin Abbott (1838–1926), drew upon his strengths as an educator, an expositor, and a theologian to convey multiple messages that related to mathematical imagination. Among these, scholarship focused attention on progressive theological imperatives that he developed elsewhere and subtly incorporated into Flatland. Specifically, Abbott was keen to promote a form of theology that would be able to respond positively to new scientific attitudes and investigations. Mathematical research provided an ideal vehicle for Abbott, as discussions of non-Euclidean geometries suggested a loss of certainty within the discipline concomitant with a loss of religious certainty. Though perhaps the best known, Abbott joined and influenced other writers who used new developments in geometry as the impetus for renewed spiritual reflection that continued into the twentieth century, including Charles Hinton, Arthur Schofield, Peter Ouspensky, and Claude Bragdon. 

Other Connections

There were other ways in which religion and mathematics were connected in writing. For example, mathematician Blaise Pascal produced many specifically religious writings, including Provincial Letters and the Pensées. Literary and religious scholars continued to study not only these works but also his mathematical and scientific writings to gain greater insight into his religious beliefs. A systematic study of the contributions of people from other cultures and religions to mathematics, such as Muslims or Hindus, or the geometric discussions in rabbinical writings also interested historians and mathematicians. Finally, while there were countless historical examples of mathematicians whose religious beliefs and mathematical work were philosophically intertwined, philosopher and mathematician Bertrand Russell’s 1927 lecture, and later essay, Why I Am Not a Christian, has been called “devastating in its use of cold logic” in critiquing religious beliefs. A book containing this and related essays was included in the New York Public Library’s list of the most influential books of the twentieth century. 

The Compatibility of Religion and the Natural Sciences

Many have suggested an “either or” approach to religious belief and the study of the natural sciences. This implied that an individual was limited to two options to base their understanding of how the natural world operatedo attribute their foundation to a divine being or instead to human “science” or “reason.” These approaches could be mutually incompatible. Humanists could minimize those of religious faith as superstitious, while conversely, the religious-minded commented that their counterparts had made science, reason, and human beings themselves, as their own deity of choice. This tendency was possibly best illustrated by the supporters and detractors of Charles Darwin and his Theory of Natural Selection. 

Other scientists, mathematicians, and biologists instead saw correlations and mutally supportive structures between religious belief and the natural sciences. These included Gregor Mendel, a Catholic friar and a scientist whose work became the foundation for the study of genetics. Another example was Georges Lemaître, again a Catholic priest but also a theoretical physicist and mathematician, who originated the ideas behind the Big Bang. This was the seminal event that, in both religious and scientific beliefs, ascribed the beginnings of the universe.  

Bibliography

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"Gregor Mendel." Biography, 21 May 2021, www.biography.com/scientists/gregor-mendel. Accessed 2 Oct. 2024.

Koetsier, T., and L. Bergmans, eds. Mathematics and the Divine: A Historical Study. Elsevier, 2005.

Swade, Doron. “‘It Will Not Slice a Pineapple:’ Babbage, Miracles and Machines.” In Cultural Babbage: Technology, Time and Invention. Edited by Francis Spufford and Jenny Uglow. Faber, 1996.

Valente, K. G. “Transgression and Transcendence: Flatland as a Response to ‘A New Philosophy.’” Nineteenth-Century Contexts, vol. 26, no. 1, 2007, https://doi.org/10.1080/08905490410001683309. Accessed 15, Oct. 2024.