In mathematics, in combinatorics, the Li Shanlan identity (also called Li Shanlan's summation formula) is a certain combinatorial identity attributed to the nineteenth century Chinese mathematician Li Shanlan.[1] Since Li Shanlan is also known as Li Renshu (his courtesy name), this identity is also referred to as the Li Renshu identity.[2] This identity appears in the third chapter of Duoji bilei (垛积比类 / 垛積比類, meaning summing finite series), a mathematical text authored by Li Shanlan and published in 1867 as part of his collected works. A Czech mathematician Josef Kaucky published an elementary proof of the identity along with a history of the identity in 1964.[3] Kaucky attributed the identity to a certain Li Jen-Shu. From the account of the history of the identity, it has been ascertained that Li Jen-Shu is in fact Li Shanlan.[1] Western scholars had been studying Chinese mathematics for its historical value; but the attribution of this identity to a nineteenth century Chinese mathematician sparked a rethink on the mathematical value of the writings of Chinese mathematicians.[2]