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Born was the son of an embryologist, a professor of anatomy at the University of Breslau (now Wrocław) in Poland. He was educated at the university in his native city of Breslau, and at the universities of Heidelberg, Zurich, and Göttingen, where he obtained his PhD in 1907. From 1909 until 1933 he taught at Göttingen, being appointed professor of physics in 1921. With the rise of Hitler he moved to Britain, and from 1936 served as professor of natural philosophy at the University of Edinburgh, returning to Germany on his retirement in 1953.

Born's early work was on crystals, particularly the vibrations of atoms in crystal lattices. The Born–Haber cycle is a theoretical cycle of reactions and changes by which it is possible to calculate the lattice energy of ionic crystals. He is noted for his role in the development of the new quantum theory. Together with Pascual Jordan, he developed (1925) the matrix mechanics introduced by Werner Heisenberg. He also showed how to interpret the theoretical results of Louis de Broglie and the experiments of such people as Clinton J. Davisson, which showed that particles have wavelike behavior.

At the time, it was known that in some circumstances light, electrons, etc., behaved as waves whereas in others they acted like particles. (William Bragg once suggested using the corpuscular (particle) theory on Monday, Wednesday, and Friday, and the undulatory (wave) theory on Tuesday, Thursday, and Saturday.) Mathematical treatments could be used to predict behavior, but there was a problem in finding some accepted physical picture of how electrons, for instance, could act in this way. Erwin Schrödinger, who developed wave mechanics, interpreted particles as ‘wave packets’, but this was unsatisfactory because such packets would dissipate in time. Born's interpretation was that the particles exist but are ‘guided’ by a wave. At any point, the amplitude (actually the square of the amplitude) indicates the probability of finding a particle there.

An essential part of this idea of electrons, atoms, etc., is that it depends on probability – there is no predetermined way in which absolute predictions can be made, as in classical physics. A similar result is embodied in the uncertainty principle of Werner Heisenberg. Einstein, amongst others, could never accept this and Born corresponded with him on the subject (the Born–Einstein letters were published in 1971).

Born shared (with Walter Bothe) the 1954 Nobel Prize for physics. He is buried in Göttingen, where his tombstone displays his fundamental equation of matrix mechanics: pq – qp = h/2πi