Cooper's 1956 theorem: any attractive interaction, no matter how weak, causes the Fermi sea to be unstable against bound pairs of electrons with opposite momenta and spins (k↑, -k↓). The attraction is mediated by virtual phonons — electron 1 distorts the lattice, and electron 2 (arriving ~10⁻¹² s later when the distortion persists) is attracted to the positive ion wake. The BCS gap Δ = 2ℏω_D · exp(-1/N(0)V) opens at the Fermi energy, where N(0) is the density of states. The binding energy 2Δ is non-perturbative — cannot be reached by expanding in V. The coherence length ξ ∝ ℏv_F/Δ sets the Cooper pair size (typically 100–1000 nm, much larger than the lattice spacing).