In 1925, while at Copenhagen, Heisenberg published his first paper laying the groundwork for his quantum mechanics. On receiving a copy of the paper, Max Born almost immediately saw that Heisenberg's multiplication of amplitudes involved a rule used in matrix multiplication–an area of mathematics to which few scientists were exposed. Months later, Born, Heisenberg, and Jordan coauthored the paper that established matrix mechanics, but their work was soon rivaled by a new approach developed by Erwin Schrödinger. Schrödinger treated the matter as waves rather than particles, and he was able to derive the same results with wave mechanics as Heisenberg had with matrix mechanics. Heisenberg acknowledged the mathematical advancement that Schrödinger's work contributed, but he refused to accept the completely different picture of the atom that the work entailed.
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