The decimal number system and the binary number system in use today were first recorded in Indian mathematics. Indian mathematicians made early contributions to the study of the concept of zero as a number, concept of infinity, negative numbers, the modern positional notation numeral system, Floating point numbers (By Kerala school of astronomy and mathematics led by Madhavacharya), Number theory, Infinity (Yajur Veda), Transfinite numbers, Irrational numbers (Shulba Sutras), arithmetic, and algebra.
In addition, trigonometry was further advanced in India, and, in particular, the modern definitions of sine and cosine were developed here. From here only these concepts were transmitted to the Middle East, China, and Europe and led to further developments that now form the foundations of modern mathematics.
A later landmark in Indian mathematics was the development of the series expansions for trigonometric functions by mathematicians of Kerala in the 15th century CE.. Their remarkable work on calculas, completed two centuries before the invention of calculus in Europe, provided what is now considered the first example of a power series. They only first formulated the theorems known today as Rolls Theorem, Cauchy's integral theorem and Taylor's theorem.
