A matrix factorisation of a polynomial $f$ is an equation $AB = f \cdot {\rm I}_n$ where $A,B$ are $n \times n$ matrices with polynomial entries and ${\rm I}_n$ is the identity matrix. This question has been of interest for more than a century and has been studied by mathematicians like L.E. Dickson. I will discuss its relation with questions arising in algebraic geometry about the structure of subvarieties in projective hypersurfaces.