In the 3rd century BC, symbols of numbers appeared in India. From the year 200 to the year 1200, the ancient Indians knew the application of number symbols and zero symbols, which were very similar to the current numbers in some cases. Since then, Indian mathematics has introduced decimal numbers and established a digital position system, which greatly simplified the operation of numbers and made the notation clearer. For example, in ancient Babylon, the notation can represent both 1 and 1, while in India, the symbol 1 can only represent 1 unit. If it represents tens and hundreds, then 1 must be followed by the corresponding number of zeros, which is how modern people count.
Indians have long used negative numbers to indicate debt and movement in the opposite direction. They also accepted the concept of irrational number and applied the operation steps suitable for rational number to irrational number in practical calculation. They also solved the linear equation and quadratic equation.
Indian mathematics has made little progress in geometry, but it has made great contributions to trigonometry. This is a by-product of ancient Indians' keen interest in studying astronomy. For example, they used three trigonometric quantities in their calculation: one is equivalent to the current sine, one is equivalent to cosine, and the other is a positive vector, which is equal to 1-cosa, but it is no longer used. They already know some relations between trigonometric quantities. For example, sin2α+cos2α= 1, cos (90-α) = sinα, etc. The trigonometric values of some special angles are also calculated by using the half-angle expression.