Who came up with the idea of using variables in mathematics to represent unknown numbers and other unknown entities? It must have been a big conceptual revolution, the idea of variables. Prior to that time, people could only think of specific numbers and equations, like for example the number 3, or the equation 2+3=5. But who was the first to come up with the idea of variables to represent unknown numbers and also make sweeping statement about all numbers? For example, the infinitely many facts that 1+0=0+1, 2+3=3+2, 4+7=7+4, etc. can be summarized by using variables to say: "For all x and y, x+y=y+x". But someone has to have been the first to come up the idea of variables. Who was that person, and do we even have a historical record of the writings of that person?

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    $\begingroup$ Are you asking specifically about the symbolic representation of variables and unknowns? For example, the Babylonians produced two types of mathematical texts - "table texts" and "problem texts". In problem texts the reader is asked to find some unknown, however this is all done in prose rather than symbolically. Also, mixing the terms "variable" and "unknown" is a bit confusing - variables vary over some domain while unknowns have precise values. $\endgroup$
    – nwr
    Commented Jun 4, 2022 at 3:46
  • $\begingroup$ Wikipedia has a decent section on the modern "x" notation: en.wikipedia.org/wiki/History_of_algebra#The_symbol_x $\endgroup$
    – ACR
    Commented Jun 4, 2022 at 4:09
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    $\begingroup$ Even if we had access to a lot more historical facts than we now do (from time machines, from immortal vampires, etc.), I think it would be nearly impossible to decide where to draw the line on what is meant by "variable usage in mathematics" when considering very ancient things like pebbles to keep track of how many objects there are of a certain type, scratches on a wall to mark the passage of days, fingers to do simple addition with, coins to represent the value of goods and services, etc. $\endgroup$ Commented Jun 4, 2022 at 20:33
  • $\begingroup$ See this post for Leibniz as well as this one for Descartes. $\endgroup$ Commented Jun 6, 2022 at 9:31
  • $\begingroup$ The concept of "arbitrary objects" as in "let ABC be an arbitrary triangle" in Euclid's writings have been extensively studied in the literature. This and related controversies are related to your question. $\endgroup$
    – A Mani
    Commented Jun 11, 2022 at 10:13


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