The curious fact that matter can exhibit wave-like properties (or should this rather be waves acting like particles?) is now referred to as the wave particle duality. In old times it was often believed that there was some magic in giving something a name, and that it will take some of the christened's power. Here is to hoping that there may be some truth to this, as this obvious incompatibility has claimed at least one prominent life.
It was Einstein who first made this two-faced character of matter explicit when publishing on the photo electric effect, assigning particle-like characteristics to light that up to this point was firmly understood to be an electromagnetic wave phenomenon.
But just like the question of the true nature of reality, the source of this dychotomy is almost as old as science itself, and arguably already inherent in the very idea of atomism as the other extrem of an all encompassing holism. The latter is often regarded as the philosophical consequence of Schroedinger's wave mechanics, since a wave phenomenon has no sharp and clear boundaries, and in this sense is often presented as connecting the entirety of the material world. Taken to the extreme, this holistic view finds its perfect expression in Everett's universal wavefunction (an interpretation happily embraced by Quantum Hippies of all ages) which gave rise to the now quite popular many worlds interpretation of quantum mechanics.
While atomism proved to be extremely fruitful in the development of physics, it was never popular with religious authorities. You can find echoes of this to this day if you look up this term at the Catholic Encyclopaedia:
Scholastic philosophy finds nothing in the scientific theory of atomism which it cannot harmonize with its principles, though it must reject the mechanical explanation, often proposed in the name of science, ...
Or at this site of religious physicists:
Atomism is incompatible with Judeo-Christian principles because atomism views matter as independent of God, ...
Religion of course really doesn't have a choice in the matter as it can hardly maintain doctrine without some holistic principle. It is no coincidence that physics only progressed after the cultural revolution of the Renaissance loosened the church's dominance over the sheeple's minds. But history never moves in a straight line. For instance, with Romanticism the pendulum swung back with a vengeance. It was at the height of this period that Ludwig Boltzmann achieved the greatest scientific breakthrough of atomism when developing statistical mechanics as the proper foundation of thermodynamics. It was not received well. With James Clerk Maxwell having seemingly established a holistic ether that explained all radiation as a wave phenomenon, atomism had thoroughly fallen out of favour. Boltzmann vigorously defended his work and was no stranger to polemic exchanges to make his point, yet he was beset by clinical depression and feared in the end that his life's work was for naught. He committed suicide while on a summer retreat that was supposed to help his ailing health.
He must have missed the significance of Einstein's publication on Brownian Motion just a year early. It is the least famous of his Annus Mirabelis papers, but it lay the foundation for experimentalists to once and for all settle the debate in Boltzmann's favor, just a few years after his tragic death.
Thermodynamics made no sense to me before I learned statistical mechanics, and it is befitting that his most elegant equation for the entropy of a system graces the memorial at his grave site (the k denoting the Boltzmann constant).