Lambert, the son of a poor tailor from Mulhouse (now in France), was largely self-educated. He spent the early part of his life in various occupations, including teaching and bookkeeping, and followed his scientific interests in his spare time. In 1764 he moved to Berlin where he attracted the notice of Frederick the Great and became a member of the Berlin Academy.

Lambert contributed to numerous branches of science and learning generally. His main mathematical achievement was to prove that ‘π’ is irrational. He did this by use of continued fractions and published the proof in 1768. He also studied the hyperbolic functions and introduced their use into trigonometry. Lambert did some remarkable work in non-Euclidean geometry, but this remained totally unknown until the end of the 19th century when it was published.

In addition to mathematics Lambert was an astronomer of note. The suggestion that there might be further galaxies beyond our own was first made by him and this was subsequently confirmed observationally by William Herschel. Lambert was the first to invent an accurate way of measuring light intensities and the lambert, a measurement of light intensity, was named for him.

In his philosophical ideas Lambert largely developed the ideas of the great German rationalist philosopher Gottfried Leibniz and his chief philosophical work, Neues Organon (New Organon), was published in 1764.