Mathematics and religion

Summary: The connection between religion and mathematics is intricate, spanning cultures and centuries, with mathematics itself sometimes manifesting religion-like features.

Mathematical knowledge has been intertwined with spiritual or religious contemplation since humans began to develop numerical, spatial, and symbolic reasoning in order to understand the world and humanity’s place within it. Both practical and abstract knowledge have been significant to cosmological and theological considerations. Another way that mathematics is linked to religion is by those who suggest that mathematics is a religion.

Mathematics provides tools that underpin computation, prognostication, organization, and design. Consequently, mathematical knowledge—as constituted by practical arithmetical (computational), algebraic (numerical problem solving), and geometric (spatial) knowledge—has been an essential ingredient in divination as well as in ritual constructions and practices. The influences of mathematical knowledge, broadly construed, on cosmology can be found in different times, places, and cultures. They are evident in a variety of contexts that include Pythagorean, Judaic, and Chinese number mysticism; Vedic rituals; Islamic trigonometry; and pattern drawings that some South Pacific Islanders believe are essential to entering the land of the dead.

Beyond skill-based practicality, mathematics as a way of obtaining infallible knowledge of transcendental objects engendered and strengthened spiritual considerations that became more closely aligned with doctrine. It did so to such an extent that the development of new mathematical knowledge often instigated immediate responses from religious authorities. Such symbiotic yet ever-evolving relationships between mathematical epistemology and theological contemplation are a central feature of the Christian tradition across the ages.

Implicit Practices, Divination, and Pattern Drawing

In the oldest cultures it is difficult to separate mathematical and ritual practices. Shamans and priests, from ancient Babylonia to Mesoamerica, used arithmetical and geometrical knowledge as part of their efforts to organize time and space so as to facilitate particular observances. In some cultures, the drawing of geometric patterns was integral to storytelling that conveyed origin myths as well as aspects of the afterlife. For both ancient and contemporary peoples, mathematics is not identifiable as a constituent of an explicitly distinctive knowledge. Rather, mathematics as it is recognized today is seen as implicitly embedded within customs of cultural significance that included spiritual well-being.

Divination, as practiced in various times and places, typically involves both randomness and structure. The objects required for the foretelling of events, while specific to custom, are subjected to a process that produces a random outcome. The diviner’s skill comes into play when interpreting the result. Doing so involves adhering to rules that apply to the particular procedure. Consequently, divination often involves strictures that can be resolved into numerical or logical systems, systems that often reflect binary considerations. Such can be found today in the methods of divination practiced by the Caroline Islanders of the South Pacific (knot divination), the Yoruba people of Africa (Ifa), and the Malagasy (Sikidy).

Pattern drawing has often accompanied cultural narratives regarding both ancestors and the afterlife. Such traditions continue into the modern era with the Tshokwe people of Angola and the Malekula of Vanuatu. In each case, intricate patterns are drawn in a continuous, uninterrupted fashion. While modern mathematics conceives of such in terms of graph theory and Eulerian circuits, there is little evidence to suggest that the cultures discussed here have an explicit or external framework within which such patterns are considered. Indeed, Tshokwe have relatively few patterns that accompany their origin myths, and knowledge of their production is limited. The cultural situation for the Malekula is considerably different. Their patterns number in the hundreds and all require that the tracing begin and end at the same point without repetition of any edge. Knowing how such patterns are produced, which constitutes a form of implicit mathematical training insofar as it recognizes various systematic elements within the drawings, is part of what men pass on to their sons. The ability to reconstruct a pattern correctly earns one access to the land of the dead.

Like the Tshokwe and Malekula, Tamil women in southern India draw patterns as a way of marking passages or transitions. The ritual designs produced by them, which are known as kolam, are used to decorate the entrance to a house. They vary according to the events being marked, many of which relate to life- or worship-cycles. Recently kolam have attracted the attention of computer scientists who are interested in the formulation and formalization of picture languages.

Classical and Judeo-Christian Traditions

The mathematics of Greek antiquity marked a distinctive break with the implicitly integrated practices associated with various cultures across time. Moreover, it laid the foundation for more explicitly considered connections between the mathematical and the spiritual. The perspective held during the earliest portion of the Pythagorean-Platonic period is often simply characterized as follows: number is religion and religion is number. That is, numbers provided the lens through which the Pythagoreans viewed the cosmos. In this way mathematics links the mundane and the sacred in ways exemplified in different ages and cultures. Mathematical reasoning, which at this time might more closely have aligned with numerology or number mysticism, provided a means of bringing order and harmony to the universe.

The realization that certain numbers are irrational (that is, that some measures are incommensurable) represented a serious challenge to Pythagoreans, for it contradicted the assumption of a cosmic harmony. While the need to resolve paradoxes instigated monumental discoveries, it soon became apparent, as it would again in the years to come, that using mathematics as a means of demystifying the world could engender new and even greater mysteries.

According to Plato, arithmetic and geometry constituted areas of study essential to higher education, and thus they became part of the quadrivium of Western education, which included astronomy and music. That philosophical discussions found in his dialogues turn to and on mathematical reasoning underscores the significance of mathematics to Platonic conceptions of the good and true. It represented an “a priori,” if for many a latent, body of knowledge through which one accessed eternal and perfect forms rather than transient and imperfect perceptions of these.

While he maintained a distinction between the physical and the otherworldly, Aristotle differed from those who believed that mathematics provided a special conduit to transcendental realms. Rather, his perspective of mathematics as abstraction based on physical reality reverses the mystical point of view. Aristotelian thinking underpins a more humanistic and, in later ages, secular understanding of mathematics. Underscoring the difference between process and object, classical Greek mathematics attempted to distinguish between the potential and the actual when discussing infinity. Powerful analytic arguments and famous paradoxes hinged on the process of infinite subdivision that gave rise to infinitesimal considerations. Amid this conceptual ambiguity, Aristotle maintained that the actual infinite—the infinite as a completed object—is unknowable.

Euclid’sElements is especially significant among classical texts that helped to solidify, as well as perpetuate, connections between mathematical and metaphysical reasoning. As a compendium of geometric knowledge of its day, Elements is most significant for its presentation of timeless and unassailable conclusions rigorously deduced from self-evident truths. It speaks to absolute certainty and provides geometry as a model for attaining such. Consequently, the influences of the Elements on mathematics and Christian theology echo across the centuries.

Aurelius Augustinius (354–430), or Saint Augustine, helped to begin the process of transforming Pythagorean–Platonic conceptions into Christian doctrines during the Middle Ages (fifth through twelfth centuries). His contributions, among many things, served to imbue Christian symbolism, including the Ark of the Covenant with its divinely prescribed dimensions, with numerical and geometric significance. Such symbolism was considered necessary for analogizing and simulating the majesty of God’s power in ways comprehensible to a faithful laity. Following classical traditions, numbers represented an ideal conduit for transcendental contemplation. Shapes, on the other hand, could both signify the sacred and convey divine wisdom. The successful adaptation of Hellenistic mathematical cosmology to Christian theology owes much to Saint Augustine and others.

Scholastic theologians of the Early Modern period (twelfth through sixteenth centuries) built upon the connections between mathematics and Christian faith promoted by Saint Augustine. Setting the tone for the age, Giovanni di Fidanza (1221–1274), or Saint Bonaventure, extended Aristotle’s prohibition against attempting to understand the infinite by claiming that it existed in God only. Even so, one could aspire to a better appreciation of the divine. To this end Nicholas Cusanus (1401–1464), or de Cusa, believed that mathematics emulates the creative power of God insofar as it is a manifestation of humankind’s ability to create knowledge and to completely understand this creation. By virtue of this manifestation, mathematics served as an essential and mutually beneficial component of Cusanus’s theology. Specifically, practicing mathematics is a way by which humankind can become closer to the divine. Whereas the platonic dialogues use mathematics to underpin conceptions of the Good, the Neoplatonic theology of Cusanus redirects mathematical attention toward conceptions of the divine.

Rendering perspective in painting by means of a vanishing point is one of the most important markers of Renaissance art. Anticipating the aesthetic significance of this development, Roger Bacon (1214–1294) encouraged the incorporation of geometric innovation in painting, believing it offered a way of better communicating God’s majesty through more powerful visual imagery. As such sentiments make clear, the connections between mathematics and religion could be both rendered and read visually, thereby making such concepts accessible to lay audiences who were not necessarily conversant with the particulars of either.

Alongside Neoplatonic scholasticism, the late Middle Ages saw a resurgence of interest in gematria, a practice by which one attempts to reveal and interpret divine secrets through the association of alphabetic characters with numbers. Truth seeking by means of numerically organized systems was not a new development; it has a long history in the Jewish religious tradition and is central to Kabbalism. Among the more shocking identifications established by Michael Stifel (1486–1567) through gematria was Pope Leo X with the Beast of the Apocalypse. Similar ideas underpin recent interest in topics such as the Bible Code.

While breaking with the intellectual traditions of the past, mathematicians associated with the Scientific Revolution (c. sixteenth through eighteenth centuries) and the Modern period (from c. eighteenth century) continued to connect the discipline’s reasoning and knowledge with theological concerns. René Descartes (1596–1650) promoted the individual’s power of reason through geometry. His rationalism was a reaction against the constraints of scholasticism and, therefore, many considered it a threat to religious authority. Nevertheless, and like others of the age, including Gottfried Leibniz (1646–1716), he used humankind’s ability to reason mathematically as the basis for discussions that ultimately asserted the existence of God.

Unlike some inclined to rationalism and deism, Blaise Pascal (1623–1662) believed that mathematical reasoning could not be applied to prove the existence of God. Another critic of mathematics’ influence on theology, George Berkeley (1685–1753) pointed out that accepting the mysterious notion of infinitesimal quantities so essential to the development of calculus was tantamount to an act of faith. Consequently, he contested deism by asserting that mathematical knowledge could not provide a more exact, or more acceptable, model for theological reasoning.

Immanuel Kant (1724–1804) asserted that geometry is a contentful, or synthetic, knowledge that adheres to a universal, “a priori” form of spatial intuition. He did not, however, use this to gird theological speculation. Indeed, he attacked proofs of God’s existence in his Critique of Pure Reason (1781) and Critique of Practical Reason (1788). Rather, Kant posited morality as a distinct form of intuition. The knowledge built upon this intuition leads to an understanding of the divine. Though independent forms of intuition, the geometric and the moral knowledge built upon these exemplified a common epistemological perspective.

The power of Kant’s argument is evident in responses to the development of non-Euclidean geometries in the nineteenth century. With this development, the absolute certainty long associated with geometric reasoning gave way to contingent knowledge. Along with more familiar paradigm shifts, most notably Darwinian evolution, new mathematical knowledge contributed significantly to the Victorian crisis in faith. Euclid’s Elements anchored mathematical and theological speculation for centuries; its promise of eternal and necessary truths was much in doubt.

Considerations outside geometry also exacerbated religious anxieties. Though obsessed with the notion of an all-encompassing infinite informed by the Ein Sof of the Jewish religious tradition, Georg Cantor (1845–1918) further destabilized relations between mathematics and spirituality with investigations that sought to establish the cardinality of the real continuum. Correspondences with Pope Leo XIII provide evidence that Cantor himself was concerned with the contentious potential of his work. The distinction between process and object so clearly delineated in antiquity meant that Christianity could safely adjudicate conceptions of the infinite as these pertained to the divine. Cantor’s identification of infinite sets as objects of mathematical interest represented a clear threat to this religious privilege.

Some claim that new and contingent perceptions of mathematical certainty evident from nineteenth-century innovations instigated a period of desecularization. Failure to secure mathematics on a firm epistemological foundation through Formalism, Logicism, and Constructivism suggested that its knowledge is the confirmation of intuitions and creative possibilities, even if such cannot be constrained by any particular formal systems. Reminiscent of relationships articulated by Aristotle and Cusanus centuries earlier, modern mathematical thinking provided a new model for theological contemplations attuned to divine immanence inherent in processes and potentialities as much as to transcendental conceptions.

Chinese, Indian, and Modern Esoteric Traditions

Chinese engagements with mathematics have long been intertwined with cosmological and spiritual concerns. Astrology and divination depended on computational abilities. Consequently, one finds strong associations between mathematical practices and number mysticism, relationships not unlike those found in antiquity and throughout Europe during the Middle Ages. Even so, the desire to predict astronomical and calendrical events inspired the need to solve systems of modular congruences. Such solutions date to the thirteenth century and form the basis of the Chinese Remainder Theorem.

Mathematical practices historically associated with the Indian subcontinent also evidence spiritual influences. Ancient Vedic observances required geometric knowledge in the construction of altars that were built in various shapes with fixed areas. Similar mathematical prescriptions eventually extended to the building of temples. Vedic literature also suggests the incorporation of a symbol for zero, which became part of the Hindu–Arabic system later adopted in Europe. The symbol emerged from the considerations of Brahma as universally divine and immanent even in nothingness.

Though distinct traditions, Hinduism and Jainism attended to numerical computations as a way of contemplating the complexity and extent of the universe, including the number of ways that things might be combined. One verse from the Jainaic sthananga sutra (c. 300 b.c.e.) identifies algebra, geometry, and combinatorics as constituents of mathematical expertise in a way that reflects the Platonic prescription of mathematics as an essential form of knowledge.

The emergence of modern theosophy in the nineteenth century was precipitated in part by the Victorian crisis in faith and obsession with orientalism. Mathematics occupied a special place in theosophy, particularly in the numerological interests of the ancients. More contemporary concerns, however, also commanded attention within this esoteric movement. The notion of higher dimensional space, which gained credibility and notoriety through the development of algebraic methodologies and non-Euclidean geometries, was a topic of considerable discussion among theosophists. Some appealed to it by way of analogy to support beliefs in a universal present that connected the past with the future. Others made claims of brotherhood based on the notion that all of humankind is the manifestation of a single universal being that could be accommodated in an expanded conception of space. Peter Ouspensky (1878–1947) provided one of the most fulsome accounts of such thinking in his Tertium Organum.

Islamic Tradition

Islamic mathematics incorporated and extended ancient Greek and Indian knowledge. More significantly Muslims transmitted this expanding body of knowledge widely during the period that saw their cultural and intellectual influence spread from the Middle East to Spain (c. 700–1500). As with other cultures, astronomical considerations focused attention on geometry and trigonometry. Further, requirements associated with daily prayers, one of the Five Pillars of Islam, served to connect religious and mathematical practices. Interest in accurately establishing the five daily prayer times, which are set according to the Sun’s position as determined by shadow length, provides one connection with the trigonometry of astronomical computations. Additionally, the problem of locating the direction of Mecca, toward which the faithful must face when praying, meant the Muslim mathematicians were equally concerned with the trigonometry of geography.

The significant relationships between the offering of prayers and trigonometry notwithstanding, discourses explicitly linking mathematical and theological concerns are not common features of Islamic texts dating from the Middle Ages. Patterns incorporated as architectural ornamentation may reflect natural observations rather than the realization of mathematical knowledge. However, some have suggested that the algorithmic pattern making so prevalent in Islamic architecture may reflect cosmological and theological contemplation. Specifically, it could provide a visual representation of creation that was understood in the context of number, especially in the generation of the many (numbers) from a singular unit (one). The use of multiple geometrical patterns, each integral yet distinct, may also serve a visual invitation to reflect on the parables of the Qur’an. While theological intentions might be difficult to document, mathematical expertise was certainly involved in rendering the elaborate spherical tessellations that adorn many of the domes found in Islamic architecture. Such knowledge is contained in Islamic texts such as Those Parts of Geometry Needed by Craftsmen (c. tenth century).

Bibliography

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

Rajagopal, Pinayur. “Indian Mathematics and the West.” In Knowledge Across Cultures: A Contribution to Dialogue Among Civilizations. Edited by Ruth Hayhoe and Julia Pan. Hong Kong: Comparative Education Research Center, 2001.