I speculate that ^ is used for xor in many languages for psychological compatibility with C, which is a very old language.

In SageMath, which uses a lightweight preparser on top of Python, I made it automatically convert ^ to , since otherwise mathematicians, who are used to LaTeX, would be very confused (I remember realizing this during a tutorial at Pycon in 2005).

C doesn't have an exponentiation operator, and instead uses `^` to mean XOR. Other languages have copied that meaning of `^` and hence need to use something different for exponentiation.

However, Lua is one language that does use `^` for exponentiation (its XOR operator is `~`).

Yes, it's often used for a XOR operation (bitwise exclusive or).