Unlike the geocentric doctrine of Ptolemy, which was widely read and inherited from Aristotle, according to which the Earth was immobile at the centre of the universe, Aryabhata argued that the Earth rotated. In the Aryabhatiya, he described the extraction algorithms of square roots and cube roots; he used a positional decimal system including graphs that is similar to our own and where the use of zero appeared implicitly. This short treatise on astronomy, published in 499, contains an overview of Indian mathematics and in particular 66 theorems of arithmetic, algebra, and plane and spherical trigonometry. The results of continued fractions, second-degree equations and series of powers are also described. To do this, Aryabhata invented a system of representation of numbers based on the consonants in the Indian alphabet, eventually followed by vowels for the large numbers. The Aryabhatiya contains exact formulas for the sum of n prime numbers, their squares or their cubes; it also includes a formula to calculate the area of a triangle or a circle as well as the approximate value 62 832/20 000 for the number π. The text also includes a systematic treatment of the position of planets in space, provides an excellent order of magnitude of the circumference of the Earth, and suggests that the apparent rotation of the skies due to the axial rotation of the Earth. The use of the decimal system is one of the vectors of development of Arabic mathematics in arithmetic and algebra. His fame has spanned centuries and in his honour, the first Indian satellite, launched April 19, 1975, and a lunar crater are named after him.
Aryabhata (476 – 550)