  Osvald Demuth (1936--1988) studied constructive analysis from the viewpoint
of the Russian school of constructive mathematics. In the course of his work he
introduced various notions of effective null set which, when phrased in
classical language, yield a number of major algorithmic randomness notions. In
addition, he proved several results connecting constructive analysis and
randomness that were rediscovered only much later.
  In this paper, we trace the path that took Demuth from his constructivist
roots to his deep and innovative work on the interactions between constructive
analysis, algorithmic randomness, and computability theory. We will focus
specifically on (i) Demuth's work on the differentiability of Markov computable
functions and his study of constructive versions of the Denjoy alternative,
(ii) Demuth's independent discovery of the main notions of algorithmic
randomness, as well as the development of Demuth randomness, and (iii) the
interactions of truth-table reducibility, algorithmic randomness, and
semigenericity in Demuth's work.
