[joppy]

Mathematicians index the ith row and jth column of their n x m matrix as (i, j), which is nothing to do with row-major or column-major order. Those orderings are how a two-dimensional index is flattened to a one-dimensional index. Row-major makes it so that each row is stored one after the other: (i, j) goes to mi + j. Column-major uses i + nj instead.

[contravariant]

That's as may be but M[i][j] and Mij still refer to the same element.

[bee_rider]

This doesn't tell us anything about memory layout though.

If a mathematician actually has to write out their matrices, they do it on a piece of paper. Because it is a 2D medium, the each element can have two "neighbors" on in the next row, and one in the next column.

If they do their math on a computer, they have the same problem as the rest of us -- but, they probably just use BLAS, which is typically column major. Although, I think some of the more modern BLAS spinoffs accept a layout option:

https://www.intel.com/content/www/us/en/develop/documentatio...