proposed by Dirac is: where is the wave function for the electron of rest mass with spacetime coordinates . The are the components of the momentum, understood to be the momentum operator in the Schrödinger equation. Also, is the speed of light, and is the reduced Planck constant. These fundamental physical constants reflect special relativity and quantum mechanics, respectively. Dirac's purpose in casting this equation was to explain the behavior of the relativistically moving electron, and so to allow the atom to be treated in a manner consistent with relativity. His rather modest hope was that the corrections introduced this way might have a bearing on the problem of atomic spectra. Up until that time, attempts to make the old quantum theory of the atom compatible with the theory of relativity, which were based on discretizing the angular momentum stored in the electron's possibly non-circular orbit of the atomic nucleus, had failed – and the new quantum mechanics of Heisenberg, Pauli, Jordan, Schrödinger, and Dirac himself had not developed sufficiently to treat this problem. Although Dirac's original intentions were satisfied, his equation had far deeper implications for the structure of matter and introduced new mathematical classes of objects that are now essential elements of fundamental physics. The new elements in this equation are the four matrices , , and , and the four-component wave function . There are four components in because the evaluation of it at any given point in configuration space is a bispinor. It is interpreted as a superposition of a spin-up electron, a spin-down electron, a spin-up positron, and a spin-down positron. The matrices and are all Hermitian and are involutory: and they all mutually anticommute: These matrices and the form of the wave function have a deep mathematical significance. The algebraic structure represented by the gamma matrices had been created some 50 years earlier by the English mathematician W. K. Clifford. In turn, Clifford's ideas had emerged from the mid-19th-century work of the German mathematician Hermann Grassmann in his Lineare Ausdehnungslehre (Theory of Linear Extensions). The latter had been regarded as almost incomprehensible by most of his contemporaries. The appearance of something so seemingly abstract, at such a late date, and in such a direct physical manner, is one of the most remarkable chapters in the history of physics. The single symbolic equation thus unravels into four coupled linear first-order partial differential equations for the