First, it's useful to point out an interpretation of QM that brings it closer to classical mechanics; and this is the Bohmian Model in which particles move in a random walk; this is directly comparable to the Lucretian view that particles move randomly in themselves and not due to impacts ie the clinamen.
In Euclid one recalls that his definition of a point is
that which has no parts
Which directly recalls the notion of an atom as that which has no parts; parts meaning being seperable; but not distinguishable.
For Euclid, a line is not made up of points as we understand it; it is a synthetic object. Points mark the ends of a line or where one line crosses another; they are markers of position.
Hence, one can feasibly say that the first synthesis of lines and points is to conceive lines as points.
Now a particle is simply a point in motion; and a wave is a line in motion.
Concieved as points, a wave is just particles moving up and down; this might conceivably called the first synthesis of particles and waves.
But what about QM? After QM, physics began to posit extended objects - vortices, strings and branes; one might say they began to explore the possibility that conceiving particles as points was the basic mistake - a mistake that can be traced to The Euclidean definition of a point.
The first atomists were clear that their atoms had extension since they were modelled as Platonic solids; so, in a sense we've returned to an older tradition.
So yes; the point is, that points aren't simply points; that they don't have extension or parts; but that they have extension.
Aristotle pointed out that the actual infinite could not physically exist; but he did admit infinite divisibility; but this isn't the infinitely small; and the contrary appears to be true; that the infinitely small does not either in any aspect, be it space, time, matter or energy, exist; doing so leads to errors.