Fr. Pavel Florensky and Mathematics

Fr. Pavel Florensky was born in 1882 to an educated, rather secular family in Azerbaijan, then part of the Russian Empire. He was educated in Tbilisi and later at Moscow. His non-religious parents gave him appreciation of science (from his father, an engineer) and of the arts (from his mother). But, starting from his teen years, he began to see that this was not everything after suffering spiritual crises and having mystical experiences. Like St. Augustine, his parents had helped given him a desire to become a well-educated man with a decent career, but again like Augustine, his religious experiences changed this: “Suddenly, all empty hope for my career lost its appeal; and I was left with an unbelievable fire in my heart, desiring the deathless qualities of Wisdom, and I made a start to rise up and return to Thee” (Confessions, 3.4.7).

The Russian world which Florensky was born into was experiencing a religious revival, centered around the Philokalia (in Russian, the Dobrotolubiye), which emphasized above all mysticism and the end of prayer as union with God. Such a world is attested to by the popularity in Russia of The Way of a Pilgrim, a lovely book about a pilgrim who learns unceasing prayer and from this experiences the “sweetness of God’s love,” “inner peace,” and a “joyous bubbling in the heart” (p. 32). Many Russian writers, such as Solov’ev, wrote about how this contradicted the West’s rationalism and individualism, which, unlike the Russian focus on community, divided and analyzed endlessly. Yet the Russian Empire also had great respect for mathematics and science, as Florensky’s parents show. Even a conservative religious writer like St. John of Kronstadt could mention proudly his scientific learning in his diary (My Life in Christ, p. 1).

Although Florensky initially left for university in Moscow to study mathematics, he was well aware by this time that physics did not cover the whole of reality. He would soon also apply to and join the Moscow Spiritual Academy to study theology. Studying mathematics and theology simultaneously, Florensky was not a man for whom faith and science were two closed off “non-overlapping magisteria.” Rather, like Solov’ev, he sought unity in reality, and like the River Forest Thomists, thought not only that science did not contradict religious truth, but was harmonious with it and that each could inform the other.

An example of such an approach to faith and reason can be given. In early 20th century France, Georg Cantor’s set theory, due to some of the seeming contradictions it implied, was not well-received. It was commonly described by the French mathematicians as “philosophy” rather than mathematics, an accusation that presupposes the notion, common among Western scientists, that philosophy is confused, whereas mathematics and the natural sciences were precise. This was partly because of some of the difficulties and contradictions associated with it. The influence of Descartes, with his emphasis on the need for “clear and distinct ideas,” can be seen here. However, Russia’s more religious spirit lead to greater acceptance of set theory. Unlike the French, Florensky saw a connection between mathematics and philosophy. What was so dearly held about functions by the French, that they were continuous, he saw as a falsehood that lead to the determinism of modern philosophy which excluded many features of reality the existence of which were obvious to him, such as the spiritual world and free will. The existence of non-continuous functions, functions whose graphs have gaps, holes, or jump at points, allowed these back into consideration. Naturally, then, set theory appealed to Florensky, since continuous functions were only one possible set among others. But the religious influence of Florensky’s beliefs about set theory go in fact beyond merely this. In 1906, a friend of Florensky’s and mathematician, Nikolai Luzin, would write to him: “…I cannot be satisfied any more with the analytic functions and Taylor series … To see the misery of people, to see the torment of life … this is an unbearable sight … I cannot live by science alone…”. In response, Florensky, who at a younger age experienced a similar crisis of faith in science, helped lead his friend into a worldview where mathematics harmonized with answers to Luzin’s urgent religious needs. Florensky’s religious relationship with Luzin, as well as with their mutual mathematician-friend Dmitri Egorov, lead to the formation of the Moscow School of Mathematics, which had great influence in 20th century mathematics. This so-called School was influenced by religious mystical ideas. Egorov and Florensky clearly had an interest in the “Name Worshippers,” Russian monks who controversially thought the name of God was God, and tried to relate it to mathematics. This may have led to impressive results: the emphasis on names led them to argue that by naming sets, one could create them – one did not need to define them to know that they existed, as the French thought. The existence of the confusing notion of ‘transfinite numbers,’ so important to Cantor, earned far more easily acceptance in the mystical minds of the Russians than in the positivist minds of the French. It is clear, then, that the nature of mathematical objects was important in evaluating set theory, and that the Moscow mathematicians’ highly religious understanding put them in a different position regarding the existence of mathematical objects than their more rationalist counterparts, which led them to novel insights into set theory and analysis.

A genius polymath, Fr. Pavel Florensky’s contribution here to mathematics is one of many accomplishments, alongside his great number of contributions to physics, philosophy, and engineering. But it shows what can happen when religious and philosophical considerations are allowed to influence scientific considerations. This is not a legitimate endeavor for all, but to a man like Florensky, for whom the unity of reality was key, it is simply obvious.

Modern Sources
Graham, L., & Kantor, J-M. (2006). A comparison of two cultural approaches to mathematics: France and Russia, 1890–1930. Isis, 97(1), 56-74. http://www.journals.uchicago.edu/toc/isis/current. Most of the information in the second-to-last paragraph, about the Russians and set theory, is taken from this article.

Louth, A. (2015). Modern Orthodox thinkers: From the Philokalia to the present. Downers Grove, IL: InterVarsity. Much of the information above are taken from here, especially about Russia’s background, including the importance of the Philokalia and Solov’ev’s stress on unity, as well as some details about Florensky’s life.

The way of a pilgrim and the pilgrim continues his way. (2001). (O. Savin, Trans.). Boston, MA: Shambhala.

Sergieff, J. I. (St. John of Kronstadt). (1897). My life in Christ. (E.E. Goulaeff, Trans.). London: Cassell and Company. It is available online in its entirety here.

Yermakova, A. (2011). Mathematical foundation in Pavel Florensky’s
philosophical worldview.
(Master’s thesis, University of Oxford). Retrieved from http://www.anyayermakova.com/links/words/Florensky_AY.pdf

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