Abstract: Hadamard matrices were discovered in 1867 by a mathematician who coined the term "matrix" but who had no "Had" in his name. We discuss the theory behind these matrices and explore a simply-stated conjecture whose proof "has every appearance of difficulty", eluding mathematicians since at least the Great Depression. We also describe a few of the most fruitful methods for constructing these matrices a la Sylvester, Paley, and Williamson. Finally, we show how Hadamard matrices found their way to Mars in the last century and how they could find their way inside every computer in the next one.
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