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It's my understanding that i,j are conventionally used in mathematics which carried over into programming, but specifically it comes from Fortran in which all integer variables start with "I" through "N" based on said mathematical convention
Yep, this is the answer. In Fortran, all variables are assumed to be floats, unless the variable starts with I, J, K, L, M or N. I’m sure they had a good reason, but it sounds so bizarre today!
In fact this goes all the way back to Hamilton when he invented quaternion, in which i,j,k are used as basis vectors (which are generalizations of the imaginary i). Later Gibbs dropped the scalar component and gave us the modern vector.
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