I'm a mathematician. It's kind of a strange statement since, if we are talking about a matrix, it has two indices not one. Even if we do flatten the matrix to a vector, rows then columns are an almost universal ordering of those two indices and the natural lexicographic ordering would stride down the rows.

Yes. I think what all mathematicians can agree on is that the layout (and the starting index! :-) is like this:

  A[1,1] … A[1,n]
   …        …
  A[m,1] … A[m,n]