  This paper was presented on the occasion of an honorary doctoral degree for
Henryk Wozniakowski at Friedrich Schiller University in Jena, Germany on June
6, 2008. Information-based complexity (IBC) is the study of algorithms and
computational complexity of continuous problems. Examples of such problems
include partial differential equations (in particular, the Schrodinger
equation) very high dimensional integration, approximation, continuous
optimization, and path integration. Because the computer has only partial
information about the continuous mathematical problem adversary arguments at
the information level often lead to tight complexity bounds. This may be
contrasted with discrete problems where only conjectures that the complexity
hierarchy does not collapse are available. This paper discusses precursors to
IBC. It reports on the beginning of optimal iteration theory in the early 60s
which was published in Traub's 1964 monograph. In the 70s Traub and
Wozniakowski began to formulate the foundations of IBC leading to their 1980
monograph. The paper continues with the development of IBC to the present.
