At school we learn to expand $(1+x)^2=1+2x+x^2$ and $(1+x)^3=1+3x+3x^2+x^3$. The coefficients come from the arithmetic triangle, which Pascal studied and which was known long before him. For positive whole-number exponents, the expansion always stops. In the winter of 1664–1665, still a student, Newton asked a question nobody had asked so boldly: what if the exponent were $\frac12$? Or $-1$? What would $(1+x)^{1/2}$, that is $\sqrt{1+x}$, look like as a sum of powers of $x$?