It has been recognized in the literature of the calculus of variations that the classical statement of the principle of least action (Hamilton's principle for conservative systems) is not strictly correct. Recently, mathematical proofs have been offered for what is claimed to be a more precise statement of Hamilton's principle for conservative systems. According to a widely publicized version of this more precise statement, the action integral for conservative systems is a minimum for discrete systems for small time intervals only (...) and is never minimum for continuous systems. In this paper, two contradictions to this “more precise” statement are demonstrated, one for a discrete system and one for a continuous system. (shrink)