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.
The presidium of the Russian Academy of Sciences has passed a resolution clearing the name of the mathematician Nikolai Luzin, whom it had condemned in the 1930s because of his ideological views. Loren Graham and Jean-Michel Kantor, authors of Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity, have received word from the Academy that their book played a large part in the discussions that led to the passing of this resolution.
Naming Infinity, which we described on publication in 2009 as “an exciting mathematical mystery tour,” is about the founding of set theory, and a conflict between French and Russian mathematicians over the nature of infinity. The debate centered on the relation between math and mysticism, and we’ll take a stab at an explanation, though surely an oversimplified one.
Mathematicians deal in geometric perfection (like perfectly round circles and perfectly straight lines), but such things can’t actually be found in the natural, physical world. The same is also true of numbers, in that they must consist of perfectly equal units (speaking purely in mathematical terms, you cannot count two oranges if the two oranges you count are not exactly, perfectly similar). Okay, so if the objects studied by mathematicians don’t exist in this world then they must exist in another transcendent realm, one where perfection is possible. Or so said mathematicians.
The problem, though, was the question of how mathematicians gained knowledge of the objects in this other transcendent realm, or how anyone’s physical brain could grasp a non-physical reality. Now, you can basically get around this problem by using your imagination and a little common sense (you’ve experienced an orange, and you can pretend that the two you’re counting are identical). But the concept of infinity throws a roadblock on that shortcut, because we have no physical experience of the infinite. We cannot encounter a full infinity in the natural world. And, given the trouble conceptualizing a single infinity, wrapping one’s mind around the thought of an infinity of infinities, which calculus logically required, was nearly impossible. It presented such a complication that Aristotle actually banned infinity from Greek thought, but modern applied mathematics really couldn’t do without.
For French mathematicians, who were as advanced as any but still very much Descartes’ intellectual descendants, a phenomenon couldn’t be understood if it couldn’t be stated clearly. They resisted fuzziness, shunned metaphysics as theology. Not so for a group of Russian mathematicians who happened to be influenced by a heretical religious sect that practiced “Name Worshipping.” They believed that they could achieve union with the divine by chanting the name of God over and over; they believed, in other words, that Name Worshipping could connect them to another, transcendent realm. Just the sort of portal the concept of infinity seemingly required. So this sect of Russian mathematicians, Nikolai Luzin among them, “named” infinity. And this is one of the central arguments of Graham and Kantor’s book: that a religious heresy in the eyes of the Russian Orthodox Church (Name Worshipping), was actually instrumental in helping the birth of a new field of modern mathematics.
But remember the context. In the early years of the Soviet era mathematicians mostly were left alone, but Stalin’s ascendance brought a new scrutiny. Clearly, the metaphysical practices of the Name Worshipping mathematicians would clash with Marxist materialism. Several mathematicians were renounced as “reactionary supporters of religious beliefs” for their mixing of math and mysticism. One of those denounced was Luzin, who by then was influential enough to have inspired a group of young mathematicians at Moscow University to take the name “Lusitania.”
In 1936 there was an investigation into Luzin and his allegedly counter-revolutionary practices. He endured a humiliating public trial, during which he was accused of publishing his best work abroad while reserving only more pedestrian papers for domestic publication, and also of stealing the work of his students. The Commission of the Academy of Sciences endorsed all of the charges against Luzin, but for unclear reasons he was neither expelled from the Academy nor arrested.
Still, Luzin’s views had been condemned by the Academy, and his name bore official stain. Until, that is, Loren Graham and Jean-Michel Kantor wrote Naming Infinity, the Academy took note, and Luzin, though long dead, was politically rehabilitated. A new flavor of worldly impact of which a publisher can be proud.
Back in 2009 we spoke with Loren Graham for an episode of the HUP Podcast. You can listen or download via the player below.