This is a step-by-step guide into Heisenberg’s famous “Umdeutung paper” in which he created quantum mechanics in 1925. I include the experimental reason for the need of matrices, a deep dive into the four key ideas of Heisenberg’s paper, and a detailed worked-out example showing how zero-point energy naturally appears in Heisenberg’s theory thanks to an early draft of what years later would become Heisenberg’s uncertainty principle.