Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity
The possibility of fostering a relationship between religious faith and disciplinary forms of learning is now a common cultural feature of many Christian colleges and universities. What began at Reformed institutions as the movement to integrate faith and learning has now spread in various forms to a number of institutions. In addition, the promise of secularity has now even subsided from many campuses for which their religious heritage has long since passed into the pages of their respective histories. More and more scholars at these institutions are also beginning to pose questions concerning what relationship faith and learning should share. The answers to such questions appear to come more readily in the humanities than the social and behavioral sciences. Continuing along this continuum, the natural sciences and, mathematics in particular, appear to be among the most difficult to strike a relationship in some fashion or another with religious faith. Risking oversimplification, disciplines such as mathematics appear to be invested so heavily in mechanistic forms of rationality that any presence of religious faith seems difficult to fathom.
In an attempt to challenge such ways of thinking, Loren Graham and Jean-Michel Kantoroffer Naming Infinity: A True Story of Religious Mysticism and Mathematical Concern. In simple terms, this book is a history of the Moscow School of Mathematics – a group of diverse yet imaginative mathematicians who in some way or another were related to the study of mathematics at Moscow University in the early portion of the 20th century. In more complex terms, this book is an exploration of how a particular mystical practice (and one deemed heretical by the Russian Orthodox Church) known as “Name Worshipping” facilitated an imaginative capacity. The presence of this imaginative capacity among these mathematicians led to some direct challenges to the mechanistic forms of rationality that had become so pervasive in mathematics. Graham and Kantor thus contend that “a religious heresy was instrumental in helping the birth of a new field of modern mathematics” (5). In the end, they also argue that “religious belief can, at least in some instances, facilitate scientific creativity” (197). The ironic dimension of this story is that it stands as the product of two scholars who also claim to “trust rational thought more than mystical inspiration” (191).
Graham, an historian of science and an emeritus faculty member at the Massachusetts Institute of Technology, and Kantor, a mathematician and an historian of mathematics at the Institut de Mathématiques de Jussieu in Paris, are both to be commended for not only their willingness to enter into this history but also the manner in which they do so. In essence, the power of this drama is one that can capture the attention of even someone with little to no formal training in mathematics. One strand of their story begins in 1913 with a standoff between the Russian military and a group of monks at the Monastery of St. Pantaleimon. The monks believed that “by naming God and Christ, and also by praying through different techniques, the believer could attain a union with God, or get as close to the divine as is humanly possible” (191). The challenge to orthodoxy that such a practice was believed to pose is that the name of God would become identified with God’s very being and thus become an idol. The influence of this practice and the threat various officials believed it posed to the Russian Orthodox Church and Russia itself propelled Tsar Nicholas II to order the storming of the monastery.
A second strand of Graham’s and Kantor ’s story begins with Georg Waldemar Cantor and his efforts during the late 1800s to establish what became known in mathematics as “set theory.” Drawing on the philosophical insights of Baruch Spinoza, Cantor believed “mathematical concepts have an ‘immanent reality,’ based on well-definedness and non-contradiction, and a ‘transsubjective or transient’ reality depending on representation in the external world” (28). In essence, both kinds of existence correspond to each other. Cantor ’s theory faced varying responses across Europe. Some rejected it. Others embraced it but could not face the great unknown of infinity inherent in Cantor ’s work. The fullest embrace came from three Russian mathematicians, Dmitri Egorov, Nicolai Luzin, and Pavel Florensky. The foundation for this embrace was established by the ways these mathematicians also embraced the practice of Name Worshipping. The relationship they struck between Name Worshipping and the legacy of Cantor’s work proved to be the very foundation upon which the Moscow School of Mathematics rested.
The majority of the book then follows the rise and fall of Egorov, Luzin, and Forensky and the school of thought they worked to establish. While their mathematical insights are significant on their own, part of what makes this story so powerful is the fact that these insights were developed during the Russian Revolution and the eventual establishment of the Soviet Union. While religious mysticism proved to be essential to the receptivity these mathematicians offered to Cantor’s work and thus the establishment of a new school of thought, the rise of the Soviet Union brought with it a greater emphasis upon materialism and even religious persecution. Graham and Kantor do an extraordinary job retelling this drama – a drama that not only includes triumphs that changed the face of mathematics but also the tortured lives of each one of these individuals. The price that all three of these men paid for their convictions and for their contributions to mathematics is extraordinary. In a culture whose singular emphasis was on the finite or the material, the price that was paid for the establishment of windows to the infinite or the immaterial proved excruciating.
Pouring forth from the pages of this drama is the realization that the academic disciplines are unstable categories that, when practiced under the guise of powerful imaginations, can serve as windows to the infinite. To simply reduce our efforts to a singular disciplinary silo, even if that silo is theology, rarely constitutes a command of the created order grand enough to capture a glimpse of its creator. In contrast, the practice of Name Worshipping brought Egorov, Luzin, and Florensky to the threshold of the infinite. Graham andKantor argue that “mathematicians usually do mathematics without thinking about the origins of their thoughts” (188). However, the very nature of the Moscow School was defined by a “mixing of mathematical, philosophical, and religious ideas which not only provided an opportunity for questions on the foundations of mathematics to be debated, but sometimes even forced such debate” (188). Matters of orthodoxy are certainly essential to the fabric of the Christian faith. Perhaps, however, the future of Christian scholarship is defined, in part, by the willingness of scholars to cultivate certain practices that allow them to transgress disciplinary boundaries once thought to be impermeable.
Despite this book’s overwhelming strengths, Graham and Kantor do find themselves susceptible at times to dualistic forms of thinking reflective of the high modernism they seek to limit. Toward the end of the book they identify the efforts made by the members of the Moscow School as expressions of subjectivism. First, Graham and Kantor view subjectivism and objectivism as philosophical poles fixed in history. To this end, they contend that “from the time of Pythagoras to the present, there have been periods of waxing and waning of the elements of rationalism and mysticism, or, perhaps more accurately, rationalism and subjectivism” (200). Second, they believe that these poles will also be firmly in place in the future. The only question that remains is when and to what extent intellectual efforts will gravitate to one pole or the other. However, perhaps these poles are not fixed as firmly as Graham and Kantor think. If so, how then are we to explain the efforts of the members of the Moscow School among countless others?
Regardless, Loren Graham’s and Jean-Michel Kantor ’s Naming Infinity is a work of immeasurable benefit to not only historians of mathematics but also anyone interested in the role religion can play in any number of disciplines. While often mathematics is thought of as a discipline that continues to prove impermeable to influences such as religious faith, the members of the Moscow School serve as examples of the kind of creativity that can lead one to identify windows to the infinite. As a result, Graham and Kantor are to be applauded for their ability to do justice to what is both a compelling and instructive account.