A. A. Markov's constructive mathematics: some reflections. A review of constructive
mathematics in the Markovian sense is presented, with particular attention to constructive analysis. An
account is given of the basic methodological principles of constructive mathematics and of expectations
connected with them. A number of results of constructive mathematical analysis, including basic facts
of constructive continuum theory and functions on the constructive continuum are presented. Additional
questions of constructive analysis, including problems of topology and functional analysis, are considered
as well. It is pointed out that although the initial revolutionary intentions are, perhaps, behind us
now, the constructive direction still provides a valuable experience of development of mathematics on a
purely syntactic and effectivist basis. The last two circumstances are of special importance in the light
of recent developments in computer science.