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.
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.