This is a talk on heuristic aspects of Idempotent Mathematics in the spirit of current works of V.P. Maslov and his collaborators. Idempotent Mathematics can be treated as a result of a dequantizati- on of the traditional Mathematics as the Planck constant tends to zero taking pure imaginary values. For example, the field of real numbers can be treated as a quantum object whereas idempotent semi- rings can be examined as \"classical\"" or \""semiclassical\"" objects