[kps]

No, it's the other way around; i, j, ... have a long history in mathematics as indices for matrices, summations, etc., with m, n likewise being traditional for the dimensions of a matrix.

In early FORTRAN, integers were present primarily to be used as array subscripts. The INteger mnemonic doesn't appear in any of the early papers or manuals.

As a side note, on the topic of features that would currently seem ‘strange’, some early languages that were intended to be programmed using teletypewriters rather than FORTRAN's Hollerith cards used half-line motions to write array subscripts as actual subscripts.