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Naming Infinity A true story of religious mysticism and mathematical creativity
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 Naming Infinity A true story of religious mysticism and mathematical creativity
 English
 Tampakis, Kostas
 Mathematics
 2009
 Naming Infinity A true story of religious mysticism and mathematical creativity
 Naming Infinity : A true story of religious mysticism and mathematical creativity
 Mathematics  Name worshipping  Moscow School of Mathematics  Dimitri Egorov  Luzin, Nikolai  Florensky, Pavel


This book is one of the very few complete historical studies on how Orthodox Christianity, and specifically the brandedasheretical Name Worhsipping, influenced decisively scientific practice. As such, it is a rare example, not only on the subject of Orthodoxy and Science but generally in the field of Science and Religion. The book is obviously the labor of many decades of research, as it contains anecdotes and personal recollections going as far back as the 1970s. It is also part of a chain of papers from the two authors, which includes Graham’s 2011 paper ‘The power of names’, the 2006 article 'A comparison of two cultural approaches to mathematics France and Russia' and Kantor’s 2011 'Mathematics and Mysticism, Name Worshipping, Then and Now'. The central theme of the book is the work of the exemplary Moscow School of Mathematics, which appeared shortly before World War I and especially of its founding fathers Dimitri Egorov and Nikolai Luzin, as well as of the mathematician and priest Pavel Florensky. The book aims to show how the beliefs of this “Russian Trio” in Name Worshipping, a mystical approach of Orthodox communion with God, facilitated their radical approach to studying the mathematics of infinity. The first chapter of the book is devoted to a short description of Name Worshipping. Originally propagated by the monk Ilarion in a 1907 book, Name Worshipping established a strong presence in the Russian Orthodox Monastery of the Panteleimon in Mt Athos. The Russian government, with the help and blessings of Greece, send a detachment of marines to storm the monastery in 1913. By 1918, the official Russian Orthodox Church had reversed its initial mildly critical position on name Worshipping and had prohibited Name Worshippers from participating to the Orthodox services. However, many prominent Russian Christian scholars still continued to favor Name Worshipping. One of them was Pavel Florensky, who developed in defense of the practice a Neoplatonic interpretation of Name Worshipping, which combined deep intellectual traits with Orthodox mysticism. The second chapter of the book discusses how the 19th century saw the birth of modern Set Theory from Bolzano, Cantor, Hermite and du BoisReymond . The authors take the time to discuss the different approaches to mathematics, developed by Poincare and Hilbert respectively, as either a practical, connected to the world science versus a Kantian, abstract intellectual venture. It is a chapter that starts from Aristotle all the way up to the International Congress of Paris in 1900. The third chapter focuses on the French mathematicians, Émile Borel, Henri Lebesgue and René Baire –collectively called the French Trio who would go on to espouse the Hilbertian approach to mathematics and grapple the implications of Set Theory. However, they would later lose their nerve and succumb to the rationalistic approaches of their era, but not before tutoring the Russian Trio. The authors offer a detailed account of Borel’s climb to mathematical prominence and his encounter with the two bright students Lebesguw and Baire when he was teaching in the École Normale Supérieure. The book also offers a fascinating account of the mathematical dimension of the Dreyfus Affair that rocked France at the time, before going on to detail the development of Lebesgue’s and Baire’s career. The discovery of contradictions in Cantor’s theory of sets sparked a debate among prominent mathematicians, and also led to a cooling of the French Trio’s fervor for Set Theory. Later discussions about the Axiom of Choice and the Continuum Hypothesis only made matters worse.Kantor and Graham go on to highlight both the importance of these deadends for later mathematical developments (such as the Bourbaki School and the metamathematics approach) and the impact they made to the younger generation of Russian Mathematicians. The fourth chapter shifts the focus to the life stories of the Russian Trio of Dmitri Egorov, Nikolai Luzin, and Pavel Florensky. It starts by describing how late 19th century Russian mathematicians had a culture of integrating philosophy, religion and ideology in their work. They trace such views from Nikolai Bugaev, who thought that mathematical discontinuity proved free will to Pavel Florensky and later on to Nekrasov and Markov, whose work was influenced by spirituality and atheism respectively. Then, the chapter describes the lives of Egorov, Luzin and Florensky, showing how they influenced each other, and especially how Orthodox Christianity and especially Name Worshipping was a common, foundational belief. The sixth and seventh chapter form the core of the historiographical argument of the book. In many ways, the five preceding chapters set the stage for the discussion of the events highlighted in chapters six and seven. The authors offer an in depth historical analysis of the development of Luzin’s mysticism, from at least 1908 onwards, and through his connection with Florensky, of his induction to Name Worshipping. These focus on the importance of names was not unique to Luzin and his circle, but it acquired a special significance, as they saw naming as giving existence to an object, both in religion and in mathematics. The book then moves on to how Luzin and Egorov created around them an eager circle of students with the name Lusitania. The students themselves were very young, and their devotion to their teachers shaped the way they approached mathematics, both pedagogically and as a research subject. Luzin inaugurated a challenging, straighttothecuttingedge approach to teaching that captivated his students. His group formed bonds that extended into their social and cultural life. Thus, the group weathered the adverse material and political, for them, conditions of 1919, such as the severe weather, the food shortage, but also the educational reforms instituted by the new Communist government. Chapters seven and eight deal with the later history of the Russian Trio and the Lusitania. To protect their group, Luzin and Egorov retreated in the isolation of pure mathematical work. Set Theory’s abstract character could help them retain the norms and values of the old Russian Intelligentsia, at a time when they were at odds with that of the government. This led to the creation of the Moscow School of Mathematics. At first, they also secured the respect and patronage of some prominent revolutionariesmathematicians, such as Otto Schmidt. Later on, however, they earned the enmity of the fervent at the time Marxist mathematician Kol’man, who described Egorov as a dangerous reactionary. Egorov lost his position, which was offered to the loyal, but strongly moral, Nikolai Chebotaryov. He in turn turned it down, because he did not think himself better that Egorov. The 1929 and 1930 stalinist persecutions of believers found Egorov and Florensky arrested and exiled. The latter was arrested again in 1933, where he died under custody. Egorov soon followed. Luzin escaped prosecution largely because his view were far more moderate and private. Yet, Kol’man also attacked him and, with the help of some of his former students, prominent mathematicians in their own right who felt stifled by his leadership, Luzin faced serious charges. He narrowly escaped imprisonment by the intervention of Stalin himself. Finally, chapter eight deals with the later generations of the Moscow Mathematical School, which included mathematicians of the caliber of Kolmogorov, Alexandrov, Novikob and Lyusternik. The authors offer an account of how Kolmogorov’s and Alexandrov’s very intimate relationship could have led to been pressured to testify against Luzin. The final, ninth chapter is an historiographical reflection on the genesis of mathematical ideas and their relationship with the culture and ideology of the mathematicians that suggest them. The authors take a moderate stance, stating that factors such as religious convictions, ideological commitments and cultural and intellectual norms play a crucial, formative role, but they do not suffice as single causal factors. They create the way for mathematical ideas to emerge, but they are not the only such road possible. They offer the counterexamples of other French mathematicians who had similar ideas, but who started from very different cultural milieus. However, at the same time, they take great pains to show the intellectual and cultural legacy of the Russian school, as well as the importance of the milleu on the French Trio’s disillusionment with Set Theory. Thus, Graham’s and Kantor’s book constitutes the most exemplary historiographical work concerning the connection between Orthodoxy and Mathematics.
