Also, geometric algebra is gross.

I wouldn't try to sell it to mathematicians but Hestenes reboot of Clifford's, Grassman's ideas for physics, engineering math extends how far can be gotten in one system before Tensors are needed

Gibbs/Heaviside Vector Algebra is pretty lame in that context, even if a practical improvement over Hamilton's Quaternions which Maxwell rewrote his initial "Cartesian Triples" ~20 equations E&M in

Gibbs himself introduced Dyadics less than a decade after "Vector Algebra", wrote about "multiple algebras", late in life endorsed Grassman/Clifford ideas as the better approach