Lambert is best known, however, for his work on π. Euler had already established in 1737 that e and e2 are both irrational . However Lambert was the first to give a rigorous proof that π is irrational.
Lambert ay pinakamahusay na kilala, gayunpaman, para sa kanyang trabaho sa π. Euler nagkaroon na itinatag sa 1737 na e at e 2 ay parehong labag sa katwiran. Subalit Lambert ay ang unang na bigyan ng isang mahigpit na patunay na π ay hindi makatwiran.