De Broglie's hypothesis suggests that particles, such as electrons, exhibit both wave-like and particle-like properties, similar to photons. The discussion emphasizes that while de Broglie was instrumental in proposing this duality, he did not "prove" it in the traditional sense. Instead, the behavior of particles as waves has been confirmed through various experiments, indicating that the focus should be on describing this behavior rather than seeking proof. The consensus is that the wave-particle duality is an established concept in quantum mechanics, rooted in empirical observations rather than theoretical proof.