“In some cases, the reaction to Cantor’s theory broke along national lines. French mathematicians, on the whole, were wary of its metaphysical aura. Henri Poincaré (who rivaled Germany’s Hilbert as the greatest mathematician of the era) observed that higher infinities “have a whiff of form without matter, which is repugnant to the French spirit.” Russian mathematicians, by contrast, enthusiastically embraced the newly revealed hierarchy of infinities. Why the contrary French and Russian reactions? Some observers have chalked it up to French rationalism versus Russian mysticism. That is the explanation proffered, for example, by Loren Graham, an American historian of science retired from MIT, and Jean-Michel Kantor, a mathematician at the Institut de Mathématiques de Jussieu in Paris, in their book Naming Infinity (2009). And it was the Russian mystics who better served the cause of mathematical progress—so argue Graham and Kantor. The intellectual milieu of the French mathematicians, they observe, was dominated by Descartes, for whom clarity and distinctness were warrants of truth, and by Auguste Comte, who insisted that science be purged of metaphysical speculation. Cantor’s vision of a never-ending hierarchy of infinities seemed to offend against both. The Russians, by contrast, warmed to the spiritual nimbus of Cantor’s theory. In fact, the founding figures of the most influential school of twentieth-century Russian mathematics were adepts of a heretical religious sect called the Name Worshippers. Members of the sect believed that by repetitively chanting God’s name, they could achieve fusion with the divine. Name Worshipping, traceable to fourth-century Christian hermits in the deserts of Palestine, was revived in the modern era by a Russian monk called Ilarion. In 1907, Ilarion published On the Mountains of the Caucasus, a book that described the ecstatic experiences he induced in himself while chanting the names of Christ and God over and over again until his breathing and heartbeat were in tune with the words.”
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Jim Holt,
When Einstein Walked with Gödel: Excursions to the Edge of Thought