Yakir Aharonov and David Bohm, at the University of Bristol, publish in 1959 "Significance of Electromagnetic Potentials in the Quantum Theory", a paper revealing one of the most counterintuitive consequences of quantum mechanics: an electron can be influenced by a magnetic field it is never physically exposed to. The authors propose a thought experiment in which an electron beam is split in two and passes on both sides of a long solenoid whose magnetic field is completely confined to its interior; outside the solenoid, the magnetic field is exactly zero at every point along the electrons' trajectory. Despite this, the quantum calculation predicts that the interference pattern observed on a screen beyond the solenoid depends on the current flowing through it, that is, on the enclosed magnetic flux. This result forces a revision of a classical idea established since the 19th century: that the electromagnetic vector potential is merely an auxiliary mathematical tool with no direct physical meaning, and that only the electric and magnetic fields have physical reality. Aharonov and Bohm show that in quantum mechanics the vector potential has measurable effects even in regions where the field is zero, revealing non-locality as a structural feature of quantum theory. The effect, experimentally confirmed by Akira Tonomura in 1986 via electron interferometry with unprecedented resolution, becomes a cornerstone of the physics of topological and geometric quantum phases, with applications ranging from mesoscopic physics (persistent currents in rings) to the topological understanding of the quantum Hall effect and the later development of the Berry phase.