The connection to these new pictures of electrons and light from our more familiar view of an electron as a particle and light as a wave is provided by the relation which links the mass and speed of an electron to the wavelength of the associated wave, and by the relation which links the frequency of a light wave to the energy of the associated photon. Even so, they are unlike most mathematical statements, however, in the following sense. Implicit in this is the fact that both sides of the equation are referring to the same object, and so we have in mind one common picture of the object.
Questions then arise.
In this sense they are neither particles nor waves, in an absolute sense, but only exhibit wave or particle properties, depending on the experiment being performed. This philosophically challenging statement, which is at the heart of quantum theory, is still actively being debated and researched today.