Louis de Broglie, in his doctoral thesis presented at the Sorbonne in 1924, formulates a radically symmetric hypothesis: if Einstein had shown that light — traditionally understood as a wave — also behaves as a particle (the photon), then perhaps matter — traditionally understood as a particle — should also behave as a wave. De Broglie derives a precise mathematical formula associating a wavelength with any particle with mass and velocity, including electrons, atoms, or, in principle, macroscopic objects — although for the latter the resulting wavelength is too small to be observable. The hypothesis, extraordinarily bold for its time and initially supported only by mathematical elegance and conceptual symmetry, is confirmed experimentally in 1927 when Clinton Davisson and Lester Germer observe diffraction patterns when passing electrons through a nickel crystal — an exclusively wave-like behavior that no classical particle model can explain. The wave-particle duality of matter becomes one of the conceptual pillars of quantum mechanics, and is the direct theoretical basis of technologies such as the electron microscope, which exploits the much shorter wavelength of electrons — compared to visible light — to achieve image resolutions impossible with conventional optical microscopes.