The discovery of high‐temperature superconductivity in lamellar copper oxide materials is one of the most dramatic and unexpected events in physics in the last several decades. In this paper, which is the text of the 48th Richtmyer Lecture, the basic physics of this new phenomenon is discussed and it is explained why the problem is proving to be so difficult in spite of the unprecedented assault on it by many thousands of physicists, chemists, and materials scientists.

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