In his book Quantum Theory of Solids (Oxford, 1955), Rudolf Peierls mathematically formalized the instability bearing his name: a one-dimensional linear chain of atoms with one electron per atom is thermodynamically unstable in a regular configuration. The system spontaneously distorts by alternating single and double bonds (dimerization), opening a band gap and turning the material into an insulator or semiconductor. This theoretical demonstration explained why linear conjugated polymers — like polyacetylene — should be insulators, and defined the conceptual barrier Heeger, MacDiarmid, and Shirakawa would have to overcome in 1977 via chemical doping. Peierls's original intuition dates to the 1930s (discussions with Landau on one-dimensional electron models in crystals), but the rigorous proof was published in 1955.