Lambert, the son of a tailor, was largely self-educated and early in his life began geometric and astronomical investigations by means of instruments he designed and built himself. He worked for a time as a bookkeeper, secretary, and editor. As a private tutor in 1748, he gained access to a good library, which he used for self-improvement until 1759, when he resigned his post to settle in Augsburg. In 1764 he went to Berlin, where he received the patronage of Frederick the Great (Frederick II). His memoir containing the proof that π is irrational was published in 1768. In 1774 at Berlin he became editor of Astronomisches Jahrbuch oder Ephemeriden, an astronomical almanac.

Lambert made the first systematic development of hyperbolic functions. He is also responsible for many innovations in the study of heat and light. The lambert, a measurement of light intensity, was named in his honour. Among his most important works are Photometria (1760; “The Measurement of Light”); Die Theorie der Parallellinien (1766; “The Theory of Parallel Lines”), which contains results later included in non-Euclidean geometry; and Pyrometrie (1779; “The Measurement of Heat”). The Neues Organon (1764; “New Organon”), his principal philosophical work, contains an analysis of a great variety of questions, among them formal logic, probability (probability theory), and the principles of science (science, philosophy of). He also corresponded with Immanuel Kant (Kant, Immanuel), with whom he shares the honour of being among the first to recognize that spiral nebulae (nebula) are disk-shaped galaxies like the Milky Way (Milky Way Galaxy).