  Specialized intelligent systems can be found everywhere: finger print,
handwriting, speech, and face recognition, spam filtering, chess and other game
programs, robots, et al. This decade the first presumably complete mathematical
theory of artificial intelligence based on universal
induction-prediction-decision-action has been proposed. This
information-theoretic approach solidifies the foundations of inductive
inference and artificial intelligence. Getting the foundations right usually
marks a significant progress and maturing of a field. The theory provides a
gold standard and guidance for researchers working on intelligent algorithms.
The roots of universal induction have been laid exactly half-a-century ago and
the roots of universal intelligence exactly one decade ago. So it is timely to
take stock of what has been achieved and what remains to be done. Since there
are already good recent surveys, I describe the state-of-the-art only in
passing and refer the reader to the literature. This article concentrates on
the open problems in universal induction and its extension to universal
intelligence.
