Michael V. Berry, a physicist at the University of Bristol, publishes in 1984 "Quantal Phase Factors Accompanying Adiabatic Changes", a paper revealing that the adiabatic theorem of quantum mechanics — which describes how a quantum system evolves when the parameters of its Hamiltonian change very slowly — was incomplete. Berry shows that, in addition to the usual dynamical phase, a quantum system transported adiabatically around a closed circuit in parameter space acquires an additional phase that depends exclusively on the geometry of the circuit traversed, not on the speed or dynamical details of the path. This "geometric phase", today universally known as the Berry phase, turns out to be a generalization of the 1959 Aharonov-Bohm effect: Berry himself points out that this effect can be reinterpreted as a particular case of his geometric phase. The concept becomes ubiquitous in theoretical and experimental physics: it explains phenomena in optics (electron-beam holography), in molecular physics (the vibrational Aharonov-Bohm effect), in condensed-matter physics (flux quantization, spontaneous polarization in ferroelectrics), and, foundationally, in the topological understanding of the quantum Hall effect, where the Berry phase integrated over the Brillouin zone gives rise to the Chern number that explains the robust quantization of Hall conductance. Just months before Berry's formal publication, mathematical physicist Barry Simon shows in December 1983 that this geometric phase is mathematically identical to the holonomy of a Hermitian line bundle, establishing the formal bridge between Berry's work and the topological invariant that Thouless, Kohmoto, Nightingale, and den Nijs had introduced in 1982 to explain the quantum Hall effect.