Werner Heisenberg, barely twenty-three years old and while recovering from a severe allergy on the island of Helgoland, formulates in 1925 the first mathematically complete version of quantum mechanics. Heisenberg deliberately abandons the idea of electron "orbits" from the Bohr model — which he considers unobservable and therefore metaphysical rather than physical — and builds a theory based exclusively on directly measurable quantities, such as the frequencies and intensities of spectral lines. Max Born, his supervisor at the University of Göttingen, recognizes that the calculation rules Heisenberg has developed intuitively correspond exactly to matrix algebra — then an abstract branch of mathematics virtually unknown to physicists — and, together with Pascual Jordan, formalizes the theory as "matrix mechanics". Heisenberg also formulates in 1927 the uncertainty principle, which establishes a fundamental and irreducible limit — not a product of technical measurement limitations, but of the very nature of quantum reality — on the precision with which the position and momentum of a particle can simultaneously be known. Heisenberg's matrix mechanics would turn out to be mathematically equivalent to the wave mechanics that Erwin Schrödinger would formulate independently months later, two distinct paths to the same complete physical theory.