Why is the 1925 three-man paper by Born, Heisenberg, and Jordan important?

The 1925 work by Max Born, Werner Heisenberg, and Pascual Jordan, known as the "three-man paper" (Zur Quantenmechanik II), is considered the foundational document of modern quantum mechanics.1

This paper was significant because it formalized the revolutionary approach Heisenberg introduced earlier that year, which insisted that physical theory should be based solely on observable quantities. While Heisenberg’s initial work utilized a unique form of noncommutative multiplication, Born and Jordan recognized that this mathematical structure could be expressed through matrix algebra. By synthesizing these concepts, the three-man paper established the rigorous mathematical framework that defined the new field of quantum mechanics, moving physics away from classical descriptions toward a system based on matrix mechanics.1