‘Duality’ considers how the two different models of light—particle and wave—were reconciled. The dualism issue was partially resolved by William Rowan Hamilton in his ‘optical analogy’ following on from the work of Pierre de Fermat and Gottfried Wilhelm von Leibniz. But there were still unsolved puzzles: neither model could explain the colour of hot objects or the colour of different atoms in a flame. As a result of studies undertaken by Johannes Balmer, Max Planck, Niels Bohr, and Paul Dirac, the resolution of wave–particle duality is a new concept: the quantum field. Light particles—photons—are excitations of this field, which propagates according to quantum versions of Maxwell’s equations for light waves.