The wave-particle duality of photons and other particles was indeed a surprising and revolutionary discovery in the early development of quantum mechanics. The classical physics of the 19th century primarily described particles as discrete, localized entities with definite positions and velocities, while waves were understood as continuous, spread-out disturbances in a medium, like sound waves or water waves.
However, in the early 20th century, experimental observations and theoretical developments challenged this classical view. It was discovered that phenomena like the photoelectric effect and the Compton scattering of X-rays could only be explained if light (composed of photons) exhibited particle-like behavior, while phenomena like diffraction and interference patterns could only be explained if light exhibited wave-like behavior.
The wave-particle duality implies that particles like photons can exhibit properties of both particles and waves depending on the experimental setup and the specific measurement being performed. This means that under certain circumstances, photons behave like discrete particles, interacting individually, while under other circumstances, they exhibit wave-like behavior, interfering with themselves.
It is important to note that when we say a particle exhibits wave-like behavior, it doesn't mean that the particle is "following" a wave pattern in the classical sense. Rather, the wave-like behavior is described by the mathematical formalism of quantum mechanics through the concept of a wavefunction. The wavefunction assigns a probability amplitude to each possible outcome of a measurement, and when squared, gives the probability of observing the particle in a particular state.
The wave-particle duality is a fundamental characteristic of quantum mechanics, and while it may seem counterintuitive from a classical perspective, it has been extensively verified through numerous experiments and is an essential aspect of our understanding of the microscopic world.