India's mathematical heritage
From the geometry of the Sulba Sutras to zero, the decimal system, infinite series and Ramanujan.
c. 800–500 BCE
The Sulba Sutras of Baudhayana, Apastamba and Katyayana give exact constructions for fire altars, including the rule for the diagonal of a rectangle (later called the Pythagorean theorem) and a value of √2 correct to five decimal places.
c. 3rd–2nd century BCE
Pingala's Chandahshastra counts poetic metres with a method that resembles binary numbers and arranges results in the Meru-prastara (later known in Europe as Pascal's triangle).
499 CE
Aryabhata's Aryabhatiya uses place value, gives π ≈ 3.1416, a table of sines, and explains the rotation of the Earth.
628 CE
Brahmagupta's Brahmasphutasiddhanta gives the rules of arithmetic with zero and negative numbers, and formulas for cyclic quadrilaterals.
c. 825 CE
Al-Khwarizmi writes on calculation with the Hindu numerals; through the Arab world, the Indian decimal system with zero reaches Europe.
1150 CE
Bhaskaracharya (Bhaskara II) writes Lilavati and Bijaganita. The chakravala method solves equations that Europe tackled only centuries later.
c. 1340–1425
Madhava of Sangamagrama founds the Kerala school, finding infinite series for π, sine and cosine about 250 years before they appeared in Europe.
1887–1920
Srinivasa Ramanujan transforms number theory and infinite series. India celebrates his birthday, 22 December, as National Mathematics Day.