This paper introduces a mathematical model of a hint as a body of imprecise and uncertain information. Hints are used to judge hypotheses: the degree to which a hint supports a hypothesis and the degree to which a hypothesis appears as plausible in the light of a hint are defined. This leads in turn to support- and plausibility functions. Those functions are characterized as set functions which are normalized and monotone or alternating of order ∞. This relates the present work to G. Shafer’s mathematical theory of evidence. However, whereas Shafer starts out with an axiomatic definition of belief functions, the notion of a hint is considered here as the basic element of the theory. It is shown that a hint contains more information than is conveyed by its support function alone. Also hints allow for a straightforward and logical derivation of Dempster’s rule for combining independent and dependent bodies of information. This paper presents the mathematical theory of evidence for general, infinite frames of discernment from the point of view of a theory of hints.