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I can understand how the Greek alphabet came to be prominent in mathematics as the Greeks had a huge influence in the math of today. Certain letters came to have certain implications about their meaning (i.e. $\theta$ is almost always an angle, never a function).

But why did $x$ and $y$ come to prominence? They seem like $2$ arbitrary letters for input and output, and I can't think why we began to use them instead of $a$ and $b$. Why did they become the de facto standard for Cartesian coordinates?

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    You can also see this MO question: http://mathoverflow.net/questions/30307/explanation-why-x-y-z-are-always-variables2010-08-21
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    Sorry, didn't see you'd already linked to it when I posted my answer. Hope you don't mind me leaving my response up though, as it does answer the question.2010-08-21
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    So you have never heard of theta functions?2010-08-21
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    GEdgar: On the other hand, I more often see $\vartheta$ for theta functions, and $\theta$ for angle-related things.2010-08-21
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    Probably because $a$ already has a role in English (e.g. a dog, a cat), so its just less confusing to use $x$ and $y$.2013-11-04

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