The triangle of binomial coefficients was used by Pingala (~200 BCE), al- Karaji (~1000 CE), Omar Khayyam (~1070 CE), Jia Xian (11th century), Yang Hui (1261), and Pascal (1665, published posthumously). At least four independent mathematical traditions discovered the same structure over 1,800 years. The name "Pascal's Triangle" forecloses the most interesting question in the philosophy of mathematics: why does this structure keep being discovered?
