The "Old Testament" and the Pauli matrices
Pauli's ability to describe complex relationships clearly was demonstrated after the publication of the "Encyclopaedia Article" in 1921 on the theory of relativity, and a second time in his chapter on Quantum Theory in the "Handbuch der Physik" of 1926. Physicists jokingly referred to it as the "Old Testament".
With Pauli working on this article during most of 1925, the "new quantum mechanics" came into being, introduced by Werner Heisenberg's fundamental work on matrix mechanics.
So Wolfgang Pauli was not initially involved in this new development. In January 1926, however, he published "Ueber das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik". Thus he had immediately recognised the importance of the new method and demonstrated its usefulness. As a result, Werner Heisenberg wrote to him on 3 November 1925: "I do not need to tell you how pleased I am with the new theory of hydrogen and how much I admire your having published this theory so quickly." In May 1927 Pauli published "Zur Quantenmechanik des magnetischen Elektrons", in which he introduced "Pauli matrices". This was a mathematical representation, still in use today, of "spin" in the physics of elementary particles and atoms.