i has been the default variable for sum notation in mathematics long before FORTRAN. Here's an example dating from 1838: https://www.numdam.org/item/JMPA_1838_1_3__508_0.pdf
Where in that doc, sorry? I thought I spotted something then realized it may have been a ‘1’.
It might actually be the other way round: Fortran adopted the convention that i,j,k are integer variables because that was the standard in maths.