Click below to visit the lecture on Caltech’s website. Frequently cited as one of the best and most logical explanations of the progression of math from simple concepts to the more complex.
Richard Feynman explains the progression from Algebra to Calculus in a beautiful lecture, easily accessible to anyone. From the last paragraph of the post:
When we began this chapter, armed only with the basic notions of integers and counting, we had little idea of the power of the processes of abstraction and generalization. Using the set of algebraic “laws,” or properties of numbers, Eq. (22.1), and the definitions of inverse operations (22.2), we have been able here, ourselves, to manufacture not only numbers but useful things like tables of logarithms, powers, and trigonometric functions (for these are what the imaginary powers of real numbers are), all merely by extracting ten successive square roots of ten!