Materialism has ceded to Idealism of late as our tool to root out the basic truth: we have come from the 19th century atomised reading of the runes of Thermodynamic phenomena (in the spirit of Democritus) to the 21st century program of applying Plato's Ideal (mathematical) forms to express those "tendencies" of material fundamental objects to decay and interact with each other as they do.

The indivisibility requirement of the fundamental atom precludes elementals from having spatial properties: being observable renders absurd the substantial elementariness of the electron in full view. Platonic (Idealistic-solid) forms rather characterise tendencies of the elements and their aggregates. Today's mathematical idealisations : the second quantised gauge, the string-membrane, knot, loop or twistor field are conceived in the spirit of Plato not of Democritus.

"[While Plato's symmetries were a far cry from conformal causality or isospin group invariance his insight was, that nature at its most fundamental (at least) is characterised] by mathematical symmetries." Heisenberg, The Debate between Plato and Democritus.

When CERN seeks to refine the (only, presumably) apparent indivisibility we observe to date by fixating on smaller scales we are just parsing out Platonic solid models. The tried and trusted way to test the truth-value of a mathematical theorem, historically has not been through validation against sensory evidence. Rather validation came from the inward experience: the determination or otherwise of the mental coherence of a train of logical propositions. That coherence, checked by the minds of other equally trained mathematicians never actively sought correspondence to the natural world for validation.

As such do we need to expand our definition of the scientific method (beyond physical sensory evidence) to embrace the mathematical method as:
" [...that involving] those knowledge-claims open to experiential validation or refutation." Wilder, Quantum Questions.