By Loren Graham, Jean-Michel Kantor
In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off priests engaged in a dangerously heretical perform referred to as identify Worshipping. Exiled to distant Russian outposts, the clergymen and their mystical circulate went underground. eventually, they came upon Russian intellectuals who embraced identify Worshipping—and who might in achieving one of many largest mathematical breakthroughs of the 20 th century, going past contemporary French achievements.
Loren Graham and Jean-Michel Kantor take us on an exhilarating mathematical secret journey as they get to the bottom of a strange story of political struggles, mental crises, sexual complexities, and moral dilemmas. on the center of this ebook is the competition among French and Russian mathematicians who sought new solutions to at least one of the oldest puzzles in math: the character of infinity. The French college chased rationalist recommendations. The Russian mathematicians, particularly Dmitri Egorov and Nikolai Luzin—who based the well-known Moscow university of Mathematics—were encouraged by means of mystical insights attained in the course of identify Worshipping. Their non secular perform appears to be like to have opened to them visions into the infinite—and resulted in the founding of descriptive set thought.
the lads and girls of the top French and Russian mathematical faculties are principal characters during this soaking up story which can now not learn in the past. 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 resources for Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity (Belknap Press)
Anti-Â�Semitism existed in both France and Russia, as well as in many other countries at the time. ] Henri Poincaré. Hadamard (a distant cousin of Dreyfus) that the army ofÂ�fiÂ�cer was inÂ� nocent. Another mathematician (and later famous politician), Paul Painlevé, drew up in 1898 a moderate petition (“appel à l’Â�union”) decrying the accusations against Dreyfus, but not all of his fellow mathematicians would sign it. Lebesgue, a kind of intellectual anÂ� archist who distrusted the power establishmentâ•›—â•›in this case, the armyâ•›—â•›readily signed, but Borel, a patriot, refused, still trusting the military authorities.
Dissimilarities between the French and Russian approaches would soon emerge. The crisis in mathematics was brought about by the birth and rise of set theory in Germany in the last deÂ�cades of the nineteenth century. ” This set obviously has a finite number of elements. By its description this set is different from the set of all flowers in your garden or all inÂ�habÂ�iÂ�tants of Cyprus, but in each case, the number of elements in these sets is finite. ) later denoted N, where the ellipses mean that one thinks of the entire series of integers as potentially never ending.
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.
Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity (Belknap Press) by Loren Graham, Jean-Michel Kantor