Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity (Belknap Press) (Hardcover)

~ Loren Graham (Author), Jean-Michel Kantor (Author)

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.

Review

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 (20090423)

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 (20090322)

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 (20090430)

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 20090616)

It is a story of the persistence of intellectual life against the wrecking tide of history.
--Jascha Hoffman (Nature 20090701)

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 )

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 )

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

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 )

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Product Details

• Hardcover: 256 pages
• Publisher: Belknap Press of Harvard University Press; 1 edition (March 31, 2009)
• Language: English
• ISBN-10: 0674032934
• ISBN-13: 978-0674032934
• Product Dimensions: 8.6 x 5.9 x 1 inches
• Shipping Weight: 12.8 ounces (View shipping rates and policies)
• Average Customer Review: 3.8 out of 5 stars  See all reviews (6 customer reviews)
• Amazon.com Sales Rank: #63,264 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

4 of 4 people found the following review helpful:

2.0 out of 5 stars Doesn't live up to title's promise, July 23, 2009

By	Barley (City of Angels) - See all my reviews

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.

25 of 34 people found the following review helpful:

3.0 out of 5 stars Probably a great story, the book not so much, May 11, 2009

By	Harvey S. Liszt (Charlottesville, VA USA) - See all my reviews (REAL NAME)

Somebody must have told the authors that they would lose their audience if they tried to convey any insight into the math and the book is singularly devoid in this regard. The book also fails to provide much insight into the milieu in which Cantor or the French mathematicians (Borel, Lebesgue ... ) worked and its explanation for the supposed French failure to continue past a certain point is hollow. The story picks up somewhat when the focus moves to Russia but the book also fails to convey the character of the mathematical work done by the Moscow school or the deep nature of name-worshipping culture. After a somewhat superficial description of the Soviet-era politics which consumed two of the principal Russian figures it deteriorates into such things as an extended description of the homosexual amours of famous Russian mathematicians including (but not limited to) Alexandrov and Kolmogorov (a couple, actually). Yuck. What's up with that?

8 of 10 people found the following review helpful:

4.0 out of 5 stars The Mathematical Tower of Babel, June 5, 2009

By	Roger L. Cooke "Roger Cooke" (Burlington, Vermont USA) - See all my reviews (REAL NAME)

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. Alexandrov's tragic loss of his partner Uryson, who drowned in Brittany in 1924 is just one of them. (These two were known as "the PS's", because of their initials, Pavel Sergeevich Alexandrov and Pavel Samuilovich Urysohn. In Russian that is PSY, which means "the dogs", and Alexandrov once send a memo to Uryson headed "PSU ot PSA", that is, TO PSU FROM PSA. But in Russian the phrase can also be read "to a dog from a dog".) Alexandrov also figures prominently as one of Luzin's accusers in the tense hearing before a tribunal of the Academy of Sciences in 1936. At that trial he said, "I do not claim that Suslin named A-sets in my honor, because I never heard anything of the sort from him." Some 40 years later, that same Alexandrov wrote that "[Suslin] emphasized that he was naming the A-sets in my honor, in analogy with the B-sets [named for Borel]." Thus does memory play tricks on us all!

Read this book. You'll enjoy it if philsophical questions, political intrigue, or mathematics can interest you at all.