John Bardeen, Leon Cooper, and John Robert Schrieffer, at the University of Illinois, published in 1957 'Theory of Superconductivity', the first complete microscopic explanation of superconductivity — a phenomenon observed by Heike Kamerlingh Onnes in 1911 but without a satisfactory theoretical explanation for 46 years. BCS theory (an acronym of the three surnames) shows that, below a critical temperature, the electrons in a superconducting material pair up — 'Cooper pairs' — through an attraction mediated by lattice vibrations (phonons), despite the natural electrostatic repulsion between like charges. These pairs condense into a single collective quantum state that moves without dissipating energy, completely eliminating electrical resistance. The theory solves one of the most persistent open problems of 20th-century condensed-matter physics and provides the conceptual framework underlying massive technological applications: the superconducting magnets of MRI machines, the electromagnets of particle accelerators such as CERN's LHC, magnetic-levitation trains, and the superconducting qubits used in quantum computing. Bardeen had already received the Nobel Prize in Physics in 1956 for inventing the transistor (1947, with Shockley and Brattain), making him, with the 1972 prize, the only person to be awarded the Nobel twice in the same category.