In 1924 French physicist Louis De Broglie dared to ask the question if particles can exist as waves
It was known at this time that waves can exist as particles with Einstien’s theories in 1905 concerning the properties of light acting as photons.
De Broglie thought that if light can exist as both waves and particles, then why could not sub atomic particles exist as particles and waves.
Using Mathematical Equations derived from Einstien’s E=mc^2 equation De Broglie was able to describe what matter waves would look like if they existed.
In 1929 he won the nobel prize after the wavelike behavior of matter was experimentally determined in 1927.
So at this point in history it is known that matter can exhibit properties of both waves and particles.