Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity, by Loren Graham and Jean-Michel Kantor. Strongly recommended.

*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,restor ing 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 DysonAt 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 VA 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 UniversityThis book is a wonderful and gripping account of a very important chapter in the history of 20th-century mathematics. Graham and Kantor challenge many “common wisdoms” and common myths about mathematics, religion, and mathematicians. It reminds us that the story behind the mathematics is often much more exciting than mathematics itself.

— D.Zeilberger (Rutgers University ).

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Naming Infinity « A Sentimental Journeyon June 10, 2009at 3:13 pm

I just finished reading “Naming Infinity”, wherein a truly gripping story is told.

Although the authors are of a rationalist bent they comment near the end:

“In contrast to the French leaders in set theory, the Russians were much bolder in embracing such concepts as non-denumerable transfinite numbers. While the French were constrained by their rationalism, the Russians were energized by their mystical faith. Just as the Russian Name Worshippers could “name God,” they could also “name infinities,” and they saw a strong analogy in the ways in which both operations were accomplished. A comparison of the predominant French and Russian attitudes toward set theory illustrates an interesting aspect of science: if science becomes too cut-and-dried, too rationalistic, this can slow down it adherents, impeding imaginative leaps.” (p. 190)

I wonder whether a visual mysticism of some sort might have a role to play today in promoting visual thinking in mathematics.

By:

dennison January 31, 2010at 5:38 pm

The End of the Luzin Affair

“One of the hopes of any book publisher, especially a University Press, is that its books will have an impact out in the world. And there’s no single metric for that. Sometimes books find a wide audience, sometimes they revolutionize a discipline, sometimes they win awards, or sometimes they become mainstays of college courses. At HUP we’re fortunate to have grown familiar with our books having these kinds of impact, but we recently learned of a real-world effect that’s almost certainly the first of its kind for an HUP publication: a large Russian bureaucracy has officially changed its position in large part because of an HUP book…”:

http://harvardpress.typepad.com/hup_publicity/2012/03/the-end-of-the-luzin-affair.html

By:

Thomason March 13, 2012at 7:41 pm