This is a curious book. Purporting to show that faith can be a stimulus to progress in the exact sciences, it takes as its exemplars of belief the Russian mathematician Dmitri Egarov, his pupil Nikolai Luzin and the prolific theologian Pavel Florensky, whose teachings were embraced with enthusiasm by the young Luzin. Egarov and Luzin made important contributions to the discipline called set theory, which was engendered by the researches of George Cantor, himself of Russian origin though France now claims him. In Cantor's work, the paradox that infinity may exceed another – the set of all positive integers, for example, seems to contain the set of all even positive integers, though there is no last term in either – became amenable to mathematical analysis. The theory as he states it entails a distinction between continuous and discontinuous infinities, and it was to the elucidation of the latter that Egarov and Luzin addressed themselves, developing and amending the work of a trio of French precursors. Luzin became an object of suspicion in the Soviet era because his studies implied that mathematics has other functions than the measurement or denumeration of material entities. His life was spared, since he was a lukewarm churchman from whom profitable service could be expected; Egarov, an obstreperous critic of Marxism who persistently refused to comply with the mandates of the party, was put to death. The two were associated (though on the evidence of this book we can hardly say more) with a proscribed sect called the Name-worshippers, who not only made continual use of the Jesus Prayer – ‘Lord, Jesus Christ, son of God, have mercy on me a sinner’ – but identified the name of the Second Person in the Trinity with his hypostasis. The authors seem to be hinting at an analogy between this reification of an abstraction and the emancipation of mathematics from the material realm in the work of Egarov and Luzin. To substantiate this conjecture they can cite the observation of Florensky, himself a mathematician by training, that philosophy has concerned itself for too long with the continuum and ought to take more account of the discontinuous (p. 88). It would be easier to sift this argument if the theology of the Name-worshippers were more competently expounded; as it is, the reader is permitted to think that the Jesus prayer is itself the talisman of a nocturnal sect and that a priest who tried to suppress it on the grounds that the Son is not God in the same sense as the Father was a fair representative of orthodoxy (p.11). As a chapter in the history of mathematics, the book is more illuminating; at the same time, the reader who wishes to understand the refinements of set theory would be grateful for a few lines of algebraic reasoning, even if this entailed the deletion of the last thirty pages, in which mathematics is driven to the margins by the lives, amours and subterfuges of Luzin's epigoni.