the mathematics behind sine, cosine and arctangents (i.e. basic trig) were all developed in india in the 15th century, two hundred years before calculus - the first examples of a power series. mathematicians in india were the first to begin using the concept of zero, around the 4th century b.c. as well as fractions and powers of base 10, and the earliest usage of base 10 logarithms. india : cradle of modern mathematics.