By Loren Graham, Jean-Michel Kantor
In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off clergymen engaged in a dangerously heretical perform referred to as identify Worshipping. Exiled to distant Russian outposts, the clergymen and their mystical circulation went underground. eventually, they stumbled on Russian intellectuals who embraced identify Worshipping—and who could in achieving one of many largest mathematical breakthroughs of the 20th century, going past contemporary French achievements.
Loren Graham and Jean-Michel Kantor take us on a thrilling mathematical secret journey as they resolve a strange story of political struggles, mental crises, sexual complexities, and moral dilemmas. on the middle of this publication is the competition among French and Russian mathematicians who sought new solutions to 1 of the oldest puzzles in math: the character of infinity. The French tuition chased rationalist strategies. The Russian mathematicians, significantly Dmitri Egorov and Nikolai Luzin—who based the well-known Moscow college of Mathematics—were encouraged by means of mystical insights attained in the course of identify Worshipping. Their spiritual perform seems to have opened to them visions into the infinite—and resulted in the founding of descriptive set idea.
the boys and girls of the top French and Russian mathematical faculties are valuable characters during this soaking up story which can now not learn earlier. Naming Infinity is a poignant human curiosity tale that increases provocative questions about technological know-how and faith, instinct and creativity.
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Extra info for Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity (Belknap Press)
When Borel began his work, the arithmetization of analysis was accepted by most mathematicians. ”6 Borel, however, at the time of his first research with Darboux had to consider the limits of points, and showed his creativity in using the theory of sets to do so. (Set theory had already been timidly introduced to France by Camille Jordan in a course at the École Polytechnique). Borel proved a key result concerning any covering of a fixed interval by an infinite sequence of small intervals (“Theorem of Heine-Â�Borel”).
Cantor gave infinity a mathematical defiÂ�niÂ�tion after 2500 years of unsuccessful efforts, and the ultimate result of his labors was to make set theory the lingua franca of mathematics. The evolution of cultural conceptions of infinity before and after Cantor reveals the sigÂ�nifiÂ�cance of his achievement. The first glimmer of a conception of infinity probably came at the birth of civilization. Is it possible to fathom the first non-Â�trivial thoughts of our ancestors millennia ago, watching the unbounded horizon, feeling time passing continuously from the past to an unknown and frightening future?
Such understanding, he thought, could only be achieved through a mystical, religious insight. An important further breakthrough was achieved by Bernard Bolzano (1781–1848), a Czech priest who made an in-Â�depth study of the speculative tradition of medieval philosophy. Bolzano was alarmed by the “antinomies” of infinity. In his book Paradoxien des Unendlichen (The Paradoxes of the Infinite), he tried to deal with various mathematical infinities in the same way as ordinary finite numbers. ” Furthermore, he stated explicitly that two infinities are the same if there is a law that assigns in a one-Â�to-Â�one way an element of the second set to each element of the first.