Since then, about 1000 years, due to the lack of reliable historical materials, little is known about the development of mathematics.
The 5th-12nd century witnessed the rapid development of mathematics in India, and its achievements played an important role in the history of mathematics in the world. During this period, some famous scholars appeared, such as Riyabuta in the 6th century, who wrote the Book of aryabhata. In the 7th century, Brahma Gupta wrote Brahma-Huta-Sidenta, which contained mathematics chapters such as Lecture Notes on Arithmetic and Lecture Notes on Indefinite Equations. Mahvera in the 9th century; /kloc-Bhaskara (the second one) in the 20th century wrote Siddh nta iromani, and the important parts of mathematics are Lil vati and V jaganita.
In India, the decimal notation of integers appeared before the 6th century. With nine numbers and a small circle representing zero, any number can be written with the help of a numerical system. They therefore established arithmetic operations, including four arithmetic rules of integers and fractions; Square root and publisher's rules, etc. For "zero", they not only regard it as "nothing" or vacancy, but also take it as a number to participate in the operation, which is a great contribution of Indian arithmetic.
This set of numbers and position symbols created by Indians was introduced into the Islamic world in the 8th century, and was adopted and improved by Arabs. At the beginning of the 3rd century, 65438 spread to Europe through Fibonacci's abacus book, and gradually evolved into 1, 2, 3, 4, … etc., which is still in use today and is called Indo-Arabic numerals.
India has made great contributions to algebra. They use symbols to represent algebraic operations and abbreviations to represent unknowns. They recognized negative numbers and irrational numbers, described four algorithms of negative numbers in detail, and realized that quadratic equations with real solutions have two forms of roots. Indians have shown outstanding ability in indefinite analysis. They are not satisfied with understanding only one indefinite equation, but are committed to finding all possible integer solutions. Indians have also calculated the sum of arithmetic series and geometric series, and solved business problems such as simple interest and compound interest, discount and partnership.
Indian geometry is based on experience. They don't pursue logical rigorous proof, but only focus on developing practical methods, which are generally related to measurement and pay attention to the calculation of area and volume. Their contribution is far less than their contribution in arithmetic and algebra. In trigonometry, Indians use half-chords (sine) instead of Greek full chords, make sine tables, prove some simple trigonometric identities and so on. Their research in trigonometry is very important.