Materials science has always balanced on the twin pillars of observation and abstraction—from the alchemists’ crude recipes to today’s AI‑driven materials design. In this talk, we begin by revisiting the pre‑quantum era, when early chemists grappled with the nature of elements and compounds, and examine how Mendeleev’s periodic table first imposed order on the chemical world. We then show that what underpins this table is the surprising power of integers and discrete mathematics—why you can’t “slip in” between whole numbers—and trace how that insight underlies quantum mechanics, blurring the boundary between chemistry and physics.