The nonrepresentability conjecture for almost all matroids

A matroid is representable over a field if it is represented by a matrix over that field in the usual matroidal sense.

Nonrepresentability conjecture. Asymptotically almost every matroid is not representable over any field.

This conjecture concerns the asymptotic scarcity of representable matroids among all matroids. The paper states that Nelson recently proved it.