What I suspect he really means is that FORTRAN lays out its arrays column-major, whilst C choose row-major. Historically most math software was written in the former, including the de facto standard BLAS and LAPACK APIs used for most linear algebra. Mix-and-matching memory layouts is a recipe for confusion and bugs, so "mathematicians" (which I'll read as people writing a lot of non-ML matrix-related code) tend to prefer to stick with column major.

Of course things have moved on since then and a lot of software these days is written in languages that inherited their array ordering from C, leading to much fun and confusion.

The other gotcha with a lot of these APIs is of course 0 vs 1-based array numbering.