The formula for combinations (nCr)
AI-drafted · awaiting admin review
Mahavira's Ganitasarasangraha (c. 850 CE) gives the general formula for the number of ways to choose r things from n, centuries before it appears in Europe.
India first (well documented)Mathematics & astronomy
Indian claim
The combinations formula used in every school today was first written by the Jain mathematician Mahaviracharya.
Evidence for the Indian claim
- Mahavira's Ganitasarasangraha, written about 850 CE in the court of the Rashtrakuta king Amoghavarsha, states the rule as a product of descending numbers divided by a product of ascending numbers.
- Earlier Indian texts already counted combinations: Pingala for metres, the Sushruta Samhita for 63 combinations of six tastes, and Varahamihira for mixtures of perfumes.
Commonly credited to
European textbooks credit combinatorics to writers such as Levi ben Gershon (1321), Hérigone (1634) and Pascal.
Evidence for the other claim
- Levi ben Gershon in France (1321) proved the formula; the editor of Mahavira's text notes that the formula appeared in Europe with Hérigone in 1634.
What historians and scientists say
The general combinations formula is documented first in India. Historians of combinatorics regularly cite Mahavira.