Numbers originated as a practical tool for tracking real quantities

Strogatz opens by grounding even basic counting in physical intuition, describing how numbers likely emerged from humans needing to track concrete things — sheep, days, trades — long before anyone conceived of numbers as abstract objects in their own right. Kindergarteners re-derive this history naturally, learning to count objects before they ever encounter an abstract numeral divorced from something tangible.

He uses this origin story to argue that mathematical abstraction, however sophisticated it eventually becomes, is always downstream of some concrete physical or practical need, and that reconnecting abstract concepts to that original concrete grounding is often the fastest way to make them intuitive again for adult learners who've lost the thread.

This framing sets up the book's overall method: rather than starting from formal definitions, Strogatz repeatedly returns to the everyday, physical situation that a mathematical idea was ultimately trying to capture, treating abstraction as a convenience built on top of ordinary experience rather than a replacement for it. Takeaway: even the most abstract math traces back to a concrete real-world problem, and finding that root often makes the abstraction click.