As far as I have been able to find, the first language to use
^ for exponentiation was BASIC, in 1964. Earlier languages, such as Fortran, used other symbols such as
** for exponentiation (although in Fortran's case this was likely influenced by its limited character set compared with later languages).
My question is, why did BASIC choose to use
^ for exponentiation? It is not a case of simply using existing mathematical notation (unlike
-), since the
^ symbol was not initially used in math to mean exponentiation (e.g. TeX usage is more recent than BASIC).
I am looking for an objective answer backed up with a proper source.
As pointed out in the accepted answer, the original 1964 Basic used
↑ (up-arrow) for exponentiation (as can be found in the original manual, page 5). ASCII did not even include a
^ until 1965. Later versions of Basic did, however, use
^ for exponentiation.