© The Author . A mathematical matrix is usually defined as a two-dimensional array of scalars. And yet, as I explain, matrices are not in fact two-dimensional arrays. So are we to conclude that matrices do not exist? I show how to resolve the puzzle, for both contemporary and older mathematics. The solution generalises to the interpretation of all mathematical discourse. The paper as a whole attempts to reinforce mathematical structuralism by reflecting on how best to interpret mathematics.
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