Metaphysics of the Moscow mathematical school on the border of XIX–XX centuries

Abstract

The work deals with the topic of the formation of religious views among representatives of
the Moscow Mathematical School at the turn of the 19th - 20th centuries and the influence of
the world outlook on their scientific creativity. The main core of this group of scientists included
N.D. Brashman, N.V. Bugaev, P.A. Nekrasov, D.F. Yegorov, N.N. Luzin, P.A. Florensky.
The general tendency can be distinguished in the evolution of ideas of Moscow mathematicians-
thinkers of the 19th — early 20th centuries: they went all the way from Mathematics
to Philosophy and came back again to Mathematics. Moscow mathematical society
(N.D. Brashman, N.V. Bugaev etc.) cultivated Moscow Philosophical and Mathematical School
(N.V. Bugaev, P.A. Nekrasov, P.A. Florensky etc.) and the latter one gave an impulse to creating
Moscow School of Function Theory (D.F. Yegorov, N.N. Luzin etc.).
The work reveals philosophic sources of forming Moscow Mathematical School for the first
time. Philosophic preferences of representatives of this school are close to Slavophilism (negative
attitude to the development of Russia according to the Western patterns, the doctrine of spirit
integrity (which denies cognition only through reason or through senses not including spirit);
the doctrine of collegiality as obtaining freedom through the dissolution of the individual in the
church, society, state; Orthodox worldview; love to Motherland). These ideas also influenced
the nature of the mathematical creative work of Moscow mathematicians. It got some specific
features : 1) collective character, generating new directions in science and a strong wish to share
them with other scientists; 2) concentration on seeking general methods and regularities; 3) a
tendency to contemplation, a preference for theoretical research over practical (the sphere of
scientific interests included number theory, set theory, function theory etc.)