Ne'eman, who was born at Tel Aviv, was educated at the Israel Institute of Technology (Haifa) where he graduated in engineering in 1945. His academic career was interrupted by service in the Israeli army in the post-World War II troubles of Palestine.

In 1948, with the formation of the independent Israeli state, Ne'eman was able to return to his studies, while still serving with the Israeli defense forces. He went to the Ecole de Guerre in Paris and, while serving as a military attaché at the Israeli embassy in London, gained his PhD in physics from the University of London in 1962.

In 1961 Ne'eman and the American Murray Gell-Mann, working independently, developed a mathematical representation for the classification of elementary particles. This was known as the SU(3) theory and it successfully predicted the mass of the omega-minus particle observed for the first time in 1964. The theory was consolidated in a book by the two men with the title The Eightfold Way (1964) and later formed the basis of a further significant theoretical development – the ‘quark' hypothesis.

From 1961 to 1963 Ne'eman was scientific director of the Saraq Research Establishment of the Israeli Atomic Energy Commission, and from 1963 was head of the physics department and an associate professor at Tel Aviv University. In 1964 he became a full professor and was also appointed vice-rector of the university.