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Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity (Belknap Press) Hardcover – April 30, 2009

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Editorial Reviews

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*Starred Review* How did a country wracked by civil war, devastated by famine, and overshadowed by tyranny incubate a major breakthrough in modern mathematics? In the origins of descriptive set theory, Graham and Kantor (both self-described secular rationalists) confront the puzzling cultural dynamics that converted religious mysticism into mathematical insight. The authors particularly probe the surprising way that a religious heresy (Name Worshipping) emboldened the Russian mathematicians who finally surmounted the theoretical difficulties that had overwhelmed earlier pioneers in set theory. Though readers unschooled in higher mathematics may stumble over some concepts (such as denumberable subsets or the hierarchy of alephs), the authors generally succeed in translating principles into a nonspecialist’s vocabulary. Readers thus share in both the perplexities of the French rationalists defeated by the mysteries of infinite sets and the triumphs of the Russian scholars who penetrated those mysteries by deploying strategies strangely similar to devotional practices for naming the Divine. But the authors illuminate more than the psychology of a mathematical revolution; their narrative also exposes the tangle of ideological ambitions and sexual passions that transformed some brilliant researchers into treacherous tools of Soviet inquisitors and doomed others as their victims. A candid and searching analysis, restoring human drama to seemingly sterile formulas.


The intellectual drama will attract readers who are interested in mystical religion and the foundations of mathematics. The personal drama will attract readers who are interested in a human tragedy with characters who met their fates with exceptional courage. (Freeman Dyson)

At the end of the nineteenth century, three young French mathematicians--Émile Borel, René Baire and Henri Lebesgue--built on the work of Georg Cantor to conceive a new theory of functions that in a few years transformed mathematical analysis. When their work met with skepticism, they began to doubt it and abandoned further investigation. In Russia, under the leadership of Dmitry Egorov, a group of Moscow mathematicians picked up the torch. Animated by a mystical tradition known as Name Worshipping, they found the creativity to name the new objects of the French theory of functions. And they changed the face of the mathematical world. (Bernard Bru, emeritus, University of Paris V)

A passionate confluence of mathematical creation and mystical practices is at the center of this extraordinary account of the emergence of set theory in Russia in the early twentieth century. The starkly drawn contrast with mathematical developments in France illuminates the story, and the book is electric with portraits of the great mathematicians involved: the tragic, the unfortunate, the villainous, the truly admirable. The authors offer an account of Infinity that is brief, deft, serious, and accessible to non-mathematicians, and their evocation of the mathematical circles of the period is so intimately written that one feels as if one had lived, worked, and suffered alongside the protagonists. Graham and Kantor have given us an amazing piece of mathematical history. (Barry Mazur, Harvard University)

Last week I read one of the most interesting books I've encountered so far this year, Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity, by Loren Graham and Jean-Michel Kantor, just published by Harvard University Press. I'll be writing more about this book, but in the meantime I wanted to let you know about it. Many books in the science-and-religion conversation tediously cover the same ground. This book comes from a fresh angle--the world of mathematics and the world of "science" are not the same, but they overlap--and it tells a fascinating story. I found it absolutely riveting. And it's encouraging to see two secular scholars doing their best to be scrupulously fair in representing religious thinkers whose worldview is very different from their own. (John Wilson Books & Culture 2009-03-10)

It is a story of the persistence of intellectual life against the wrecking tide of history. (Jascha Hoffman Nature 2009-04-23)

In the early 20th century, mathematicians grappled with the concept of infinity, relying heavily on set theory to prove and define it. The French mathematicians, rationalists not fond of abstraction (particularly abstractions with spiritual overtones), went head-to-head with the Russians, who had always linked mathematics to philosophy, religion and ideology. Name Worshipping played a key role in bringing the two closer together. Graham and Kantor do a beautiful job of fleshing out the key players in this gripping drama--nothing less than a struggle to prove the existence of God. (Susan Salter Reynolds Los Angeles Times 2009-03-22)

This absorbing book tells astonishing stories about some of the most important developments in mathematics of the past century...Perhaps the most moving section of the book is that dealing with the famous Moscow School of Mathematics in Soviet times. Its origins are traced to the Lusitania seminar established by Egorov and Luzin (the source of the name "Lusitania" is obscure). The enthusiasm that these teachers inspired in their students is clearly conveyed, as is the atmosphere of intellectual excitement, despite the freezing lecture rooms (the rule that lectures could not take place if the room temperature fell below -5C was ignored)...This is a remarkable book, illuminating the history of 20th-century mathematics and its practitioners. The stories it tells are important and too little known. It is clearly a labor of love and deserves a wide audience: it is an outstanding portrayal of mathematics as a fundamentally human activity and mathematicians as human beings. (Tony Mann Times Higher Education 2009-04-30)

The most unusual book I have read this year. (Alex Beam Boston Globe 2009-06-16)

Fifty years ago, C. P. Snow gave a soon-to-be famous lecture on the "Two Cultures" of modern society, the culture of the humanities and the culture of science, and the need to bridge the gap between them. Today we are more likely to hear debates about the alleged gulf between science and religion. Both divides are bridged in this superb book, which takes us from French rationalism at the turn of the 20th century to a thriving center of world-class mathematics in Moscow, where the presiding figures were also devout Russian Orthodox believers of a mystical bent. (John Wilson Christianity Today 2009-07-01)

Naming Infinity is a short, accessible book about mathematical imagination...Naming Infinity is a straightforward, kinetic, and seductive read...In describing the life trajectories of their subjects, the authors are unafraid to take sides, show their sympathies, even judge. There is something refreshingly honest in their striving to be fair to their real-life characters without feigned impartiality. This considered generosity and the passion that shows itself in the copious quantities of documentary and anecdotal evidence gathered by Loren Graham in Russia, make the book a fascinating read...Just as a stimulating conversation, even when left incomplete, opens the mind to new ideas, Naming Infinity suggests new ways of thinking about mathematical creativity and intellectual excellence. (Anna Razumnaya 2010-01-10)

This is not only a readable book, but a most worthwhile one, insofar as it offers a series of anecdotal life-stories of remarkable people, little known save to specialists, together with valuable insights into the Soviet Union of the 1930s. (Robin Milner-Gulland Times Literary Supplement 2010-04-23)

As Naming Infinity so sensitively shows, escaping the world we live in, and the exacting parameters of reason, can sometimes lead to surprising results. As powerful as the gift of rationalism may be, there is still more in heaven and earth. (Oren Harman New Republic 2010-08-12)

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Product Details

  • Series: Belknap Press
  • Hardcover: 256 pages
  • Publisher: Belknap Press; 1 edition (March 31, 2009)
  • Language: English
  • ISBN-10: 0674032934
  • ISBN-13: 978-0674032934
  • Product Dimensions: 8.3 x 5.8 x 1.1 inches
  • Shipping Weight: 15.2 ounces (View shipping rates and policies)
  • Average Customer Review: 3.5 out of 5 stars  See all reviews (19 customer reviews)
  • Amazon Best Sellers Rank: #179,079 in Books (See Top 100 in Books)

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32 of 38 people found the following review helpful By Barley on July 23, 2009
Format: Hardcover
I purchased this book thinking that it may just be a perfect read for me. I'm interested in infinity, in religious mysticism and in mathematical creativity. Well, it sure didn't fulfill the desire promised by the title.

This is more or less a biographical history of several early 20th Century Russian and French mathematicians. If that's your main interest in the book, then you might find some appeal in these arguably fascinating lives. The little math that the book does cover is not handled with any particular clarity. The writing is so imprecise as to appear self-contradictory at times.

The greatest fault that I find with the book, however, lay in its coverage of the religious mysticism involved. After the first chapter, the authors generally treat it with disdain, using words like "heretical" to describe the legitimate mystical practice of name-worshipping. Because they essentially choose to pooh-pooh this religious sect, they fail to make anything beyond a superficial connection between the religion and how it inspired its followers to important breakthroughs in mathematics. Just as Francis Crick claims that his inspiration for the double-helix came from a mystical encounter with entheogens, these brilliant thinkers found answers and inspiration through name-worshipping. That's the real story to be explored here, but you won't find much of it in this book.
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23 of 27 people found the following review helpful By Roger L. Cooke on June 5, 2009
Format: Hardcover
I had the pleasant assignment of reviewing this book for The Mathematical Intelligencer (my review is to appear in a few months). In that review, I invoked the image of the Tower of Babel as a metaphor for the efforts (ultimately vain) of N.N. Luzin to find an effective way of enumerating the countable ordinal numbers. It is more than a coincidence that Luzin was an adherent of a splinter group in the Orthodox Church that called itself "onomatodoxy" (imeslavie, in Russian), meaning "name-glorification" or "name-worshipping". This group attached supreme importance to getting names exactly right in religious matters. Luzin carried this zeal into mathematics as well, trying desperately to break everything into clear, unambiguous definitions. The Polish mathematician Sierpinski had horrified him with a list of results in analysis that can't be proved without invoking the axiom of choice, and he actually had insomnia over that for many nights. It is true that Henri Lebesgue, who shared none of Luzin's religious mysticism, also tried to deal only with functions that are "analytic," but he didn't make a fetish of it. Luzin invented the contrasting terms "effective" and "auswahlistic" to emphasize the true epistemological status of results in analysis. If they used the Auswahlprinzip (axiom of choice), they weren't "effective."

In order to make the book as widely accessible as possible, the authors do not go into any deep mathematical detail (there are no equations in the book), but they describe it in general terms well enough to give an adequate picture. In addition to the broad mathematical trends that are reflected in the book, there are gripping personal stories of individual mathematicians and their troubles.
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10 of 11 people found the following review helpful By Swifty on July 31, 2009
Format: Hardcover Verified Purchase
My abilities in mathematics are decidedly pre-Euclidean. A scientist friend of mine used the visual metaphor of an established tree to explain mathematics: arithmetic, geometry, algebra and trig are the roots, the many developments in modern math are the branches and leaves. The trunk connecting roots and branches and supporting the tree is the calculus. Given this metaphor, I'm still scrambling among the roots for acorns of understanding from the top of the tree, because I never climbed past calculus. This limited my capacity to understand the math concepts Graham and Kantor describe in "Naming Infinity". Other reviewers have commented on the book's lack of equations to demonstrate the math propositions discussed in it. I wish some simple clear definitions of the building blocks of set theory had been available in an appendix. Beyond the few figures which elucidate Cantor's discoveries in the second chapter, and a discussion of the conflict between Platonic and Aristotelian notions of mathematics and how these played out in both the French and Moscow Schools of math in the early XXth century, there are precious few tools to help the untutored reader develop a more profound comprehension of the subtleties of set theory and the mathematical continuum. It's also true that I sometimes wished for the authors to return to topics briefly discussed in earlier chapters: did the religious practices of the Name-Worshippers persist through the post-Stalin era, for example? What was Luzin's life like in his later years, after the discontinuity event of his pardon by Stalin? (Beyond his caustic insult to Kolmogorov, and his lover Bari's suicide after his death, there is precious little here about Luzin's twilight years.Read more ›
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6 of 7 people found the following review helpful By miriam1025 on April 21, 2010
Format: Hardcover
I concur with some of the other reviews. I too found the dust jacket description intriguing. I wanted to understand how religion influenced the Russian school of thought in relation to studies on mathematical infinity. In particular the unusual practice of Name Worshiping. Sadly the book quickly fizzled into little more than a series of uninsightful biographical sketches which one could easily find on wikipedia - with an overextended, bizarre obsession with who was sleeping with whom. A shame - because this is a fascinating subject. I wish they had focused more on the mathematics and the relation of the mysticism to its evolution.
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