Born was born on December 11, 1882 into a Jewish family in Breslau (now Wrocław, Poland), which at Born's birth was in the Prussian Province of Silesia in the German Empire. He was one of two children born to Gustav Born, (b. 22 April 1850, Kempen, d. 6 July 1900, Breslau), an anatomist and embryologist, and Margarete Kauffmann (b. 22 January 1856, Tannhausen, d. 29 August 1886, Breslau), from a Silesian family of industrialists. Gustav and Margarethe married on 7 May 1881. Max Born had a sister called Käthe (b. 5 March 1884), and a half-brother called Wolfgang (b. 21 October 1892), from his father's second marriage (m. 13 September 1891) with Bertha Lipstein. His mother died when Max Born was four years old.

Initially educated at the König-Wilhelm-Gymnasium, Born went on to study at the University of Breslau followed by Heidelberg University and the University of Zurich. During study for his Ph.D. and Habilitation at the University of Göttingen, he came into contact with many prominent scientists and mathematicians including Klein, Hilbert, Minkowski, Runge, Schwarzschild, and Voigt. In 1908 - 1909 he studied at Gonville and Caius College, Cambridge.

When Born arrived in Göttingen in 1904, Klein, Hilbert, and Minkowski were the high priests of mathematics and were known as the “mandarins.” Very quickly after his arrival, Born formed close ties to the latter two men. From the first class he took with Hilbert, Hilbert identified Born as having exceptional abilities and selected him as the lecture scribe, whose function was to write up the class notes for the students’ mathematics reading room at the University of Göttingen. Being class scribe put Born into regular, invaluable contact with Hilbert, during which time Hilbert’s intellectual largesse benefited Born’s fertile mind. Hilbert became Born’s mentor and Hilbert eventually selected him to be the first to hold the unpaid, semi-official position of Hilbert’s assistant. Born’s introduction to Minkowski came through Born’s stepmother, Bertha, as she knew Minkowski from dancing classes in Königsberg. The introduction netted Born invitations to the Minkowski household for Sunday dinners. In addition, while performing his duties as scribe and assistant, Born often saw Minkowski at Hilbert’s house. Born’s outstanding work on elasticity - a subject near and dear to Klein - became the core of his magna cum laude Ph.D. thesis, in spite of some of Born’s irrationalities in dealing with Klein.

Born married Hedwig, née Ehrenberg, who was also of Jewish descent (although a practising Christian), on 2 August 1913, and converted to the Lutheran faith soon thereafter; the marriage produced three children including G.V.R. Born. His daughter Irene was the mother of British-born Australian singer and actress Olivia Newton-John.

After Born’s Habilitation in 1909, he settled in as a young academic at Göttingen as a Privatdozent (Associate Professor). In Göttingen, Born stayed at a boarding house run by Sister Annie at Dahlmannstraße 17, known as El BoKaReBo The name was derived from the first letters of the last names of its boarders: “El” for Ella Philipson (a medical student), “Bo” for Born and Hans Bolza (a physics student), “Ka” for Theodore von Kármán (a Privatdozent), and “Re” for Albrecht Renner (a medical student). A frequent visitor to the boarding house was Paul Peter Ewald, a doctoral student of Arnold Sommerfeld on loan to David Hilbert at Göttingen as a special assistant for physics. Richard Courant, a mathematician and Privatdozent, called these people the “in group.”

From 1915 to 1919, except for a period in the German army, Born was extraordinarius professor of theoretical physics at the University of Berlin, where he formed a life-long friendship with Albert Einstein. In 1919, he became ordinarius professor on the science faculty at the University of Frankfurt am Main. While there, the University of Göttingen was looking for a replacement for Peter Debye, and the Philosophy Faculty had Born at the top of their list. In negotiating for the position with the education ministry, Born arranged for another chair at Göttingen and for his long-time friend and colleague James Franck to fill it. In 1921, Born became ordinarius professor of theoretical physics and Director of the new Institute of Theoretical Physics at Göttingen. While there, he formulated the now-standard interpretation of the probability density function for ψ*ψ in the Schrödinger equation of quantum mechanics, published in July 1926 and for which he was awarded the Nobel Prize in Physics in 1954, some three decades later.

For the 12 years Born and Franck were at Göttingen (1921 – 1933), Born had a collaborator with shared views on basic scientific concepts — a distinct advantage for teaching and his research on the developing quantum theory. The approach of close collaboration between theoretical physicists and experimental physicists was also shared by Born at Göttingen and Arnold Sommerfeld at the University of Munich, who was ordinarius professor of theoretical physics and Director of the Institute of Theoretical Physics — also a prime mover in the development of quantum theory. Born and Sommerfeld not only shared their approach in using experimental physics to test and advance their theories, Sommerfeld, in 1922 when he was in the United States lecturing at the University of Wisconsin – Madison, sent his student Werner Heisenberg to be Born’s assistant. Heisenberg again returned to Göttingen in 1923 and completed his Habilitation under Born in 1924 and became a Privatdozent at Göttingen - the year before Heisenberg and Born published their first papers on matrix mechanics.

In 1925, Born and Werner Heisenberg formulated the matrix mechanics representation of quantum mechanics. On 9 July, Heisenberg gave Born a paper to review and submit for publication. In the paper, Heisenberg formulated quantum theory avoiding the concrete but unobservable representations of electron orbits by using parameters such as transition probabilities for quantum jumps, which necessitated using two indexes corresponding to the initial and final states. When Born read the paper, he recognized the formulation as one which could be transcribed and extended to the systematic language of matrices, which he had learned from his study under Jakob Rosanes at Breslau University. Born, with the help of his assistant and former student Pascual Jordan, began immediately to make the transcription and extension, and they submitted their results for publication; the paper was received for publication just 60 days after Heisenberg’s paper. A follow-on paper was submitted for publication before the end of the year by all three authors. (A brief review of Born’s role in the development of the matrix mechanics formulation of quantum mechanics along with a discussion of the key formula involving the non-commutativity of theprobability amplitudes can be found in an article by Jeremy Bernstein. A detailed historical and technical account can be found in Mehra and Rechenberg’s book The Historical Development of Quantum Theory. Volume 3. The Formulation of Matrix Mechanics and Its Modifications 1925 – 1926.)

Up until this time, matrices were seldom used by physicists; they were considered to belong to the realm of pure mathematics.Gustav Mie had used them in a paper on electrodynamics in 1912 and Born had used them in his work on the lattices theory of crystals in 1921. While matrices were used in these cases, the algebra of matrices with their multiplication did not enter the picture as they did in the matrix formulation of quantum mechanics. Born, however, had learned matrix algebra from Rosanes, as already noted, but Born had also learned Hilbert’s theory of integral equations and quadratic forms for an infinite number of variables as was apparent from a citation by Born of Hilbert’s work Grundzüge einer allgemeinen Theorie der Linearen Integralgleichungen published in 1912. Jordan, too was well equipped for the task. For a number of years, he had been an assistant to Richard Courant at Göttingen in the preparation of Courant and David Hilbert’s book Methoden der mathematischen Physik I, which was published in 1924. This book, fortuitously, contained a great many of the mathematical tools necessary for the continued development of quantum mechanics. In 1926, John von Neumann became assistant to David Hilbert, and he would coin the term Hilbert space to describe the algebra and analysis which were used in the development of quantum mechanics.

In 1928, Albert Einstein nominated Heisenberg, Born, and Jordan for the Nobel Prize in Physics, but it was not to be. The announcement of the Nobel Prize in Physics for 1932 was delayed until November 1933. It was at that time that it was announced Heisenberg had won the Prize for 1932 “for the creation of quantum mechanics, the application of which has led to the discovery of the allotropic forms of hydrogen” and Erwin Schrödinger and Paul Adrien Maurice Dirac shared the 1933 Prize "for the discovery of new productive forms of atomic theory". One can rightly ask why Born was not awarded the Prize in 1932 along with Heisenberg – Bernstein gives some speculations on this matter. One of them is related to Jordan joining the Nazi Party on 1 May 1933 and becoming a Storm Trooper. Hence, Jordan’s Party affiliations and Jordan’s links to Born may have affected Born’s chance at the Prize at that time. Bernstein also notes that when Born won the Prize in 1954, Jordan was still alive, and the Prize was awarded for the statistical interpretation of quantum mechanics, attributable alone to Born. Heisenberg’s reaction to Born for Heisenberg himself receiving the Prize for 1932 and Born receiving the Prize in 1954 is also instructive in evaluating whether Born should have shared the Prize with Heisenberg. On 25 November 1933 Born received a letter from Heisenberg in which he said he had been delayed in writing due to a “bad conscience” that he alone had received the Prize “for work done in Göttingen in collaboration — you, Jordan and I.” Heisenberg went on to say that Born and Jordan’s contribution to quantum mechanics cannot be changed by “a wrong decision from the outside.” In 1954, Heisenberg wrote an article honoring Max Planck for his insight in 1900. In the article, Heisenberg credited Born and Jordan for the final mathematical formulation of matrix mechanics and Heisenberg went on to stress how great their contributions were to quantum mechanics, which were not “adequately acknowledged in the public eye.”

Those who received their Ph.D. degrees under Born at Göttingen included Max Delbrück, Walter Elsasser, Friedrich Hund, Pascual Jordan, Maria Goeppert-Mayer, Lothar Wolfgang Nordheim, J. Robert Oppenheimer, and Victor Weisskopf. Born’s assistants at the University of Göttingen’s Institute for Theoretical Physics included Enrico Fermi, Werner Heisenberg, Gerhard Herzberg, Friedrich Hund, Pascual Jordan, Wolfgang Pauli, Léon Rosenfeld, Edward Teller, and Eugene Wigner. Walter Heitler became an assistant to Born in 1928 and under Born completed his Habilitation in 1929. Born not only recognized talent to work with him, but he let his “superstars stretch past him.” His Ph.D. student Delbrück, and six of his assistants (Fermi, Heisenberg, Goeppert-Mayer, Herzberg, Pauli, Wigner) went on to win Nobel Prizes.

In a letter to Born in 1926, Einstein made his famous remark regarding quantum mechanics, often paraphrased as "The Old One does not play dice."

In 1933 Born emigrated from Germany. He had strong and public pacifist opinions; moreover, though Born was a Lutheran, he was classified as a "Jew" by the Nazi racial laws due to his ancestry, and was thus stripped of his professorship. He took up a position as Stokes Lecturer at the University of Cambridge. From 1936 to 1953 he was Tait Professor of Natural Philosophy at the University of Edinburgh. He became a British subject and a Fellow of the Royal Society of London in 1939.

Born had a dislike for nuclear weapons research, but he still acknowledged “it might be the only way out.” Much of the theoretical power behind the development of the first atomic bomb was due to many of those surrounding him at Göttingen and working on atomic physics and quantum mechanics: three of his Ph.D. students (Maria Goeppert-Mayer, Oppenheimer and Weisskopf), three of his assistants (Fermi, Teller, and Wigner), the Director of the Second Institute for Experimental Physics (James Franck), and David Hilbert’s assistant (John von Neumann).

Max and Hedwig Born retired to Bad Pyrmont (10 km south of Hamelin) in West Germany, in 1954. Born was one of the 11 signatories to the Russell-Einstein Manifesto. Born is also the great-grandfather of the famous TV editor and percussionist Kip Thompson-Born. Born died in Göttingen, Germany. He is buried there in the same cemetery as Walther Nernst, Wilhelm Weber, Max von Laue, Max Planck, and David Hilbert. In memory of his important contributions, the Max Born prize was created by the German Physical Society and the British Institute of Physics. It is awarded annually.