In 1964, the year in which the present author obtained his doctorate, the highest known transition temperature Tc to the superconducting state was around 20 K. In that year, Professor Vitaly Ginzburg made a striking prediction; building on the work of Little [1], who had proposed a purely electronic mechanism to raise Tc, he predicted [2] that transition temperatures of the order of room temperature would indeed some day be achieved, and moreover that this was most likely to happen in a strongly layered (quasi-two-dimensional) system (rather than in the one-dimensional systems that Little had considered). As is well known, both these predictions were verified 22 years later, when transition temperatures over 90 K (subsequently raised to over 160 K) were realized in a class of cuprate materials whose most striking structural feature is indeed their metallic CuO2 planes separated by much less conducting materials. I would like, therefore, to devote this brief essay to the question: What is the role, in the genesis of high-temperature superconductivity in the cuprates, of the quasi-two-dimensionality of the CuO2 planes? In particular, I shall be interested in the question (which has, of course, already attracted much attention in the literature): why, in the various homologous cuprate series (T1, Hg, Bi, etc.) does Tc show a characteristic and reproducible dependence (see below) on the number n of CuO2 planes per multilayer? Let me start with a couple of remarks about the raw data. First, it seems to be a rather general observation, not confined to the cuprates, that compared to other materials in their general class, strongly layered materials have rather high transition tempera-
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