Alan Day’s Early Work: Congruence Identities

The death of R. Alan Day on November 26, 1990 was a great loss to the community of lattice theorists and universal algebraists. Alan was a hard working, hard playing man whose enthusiasm for mathematics and life will be greatly missed by all of us. This paper concentrates on congruence identities, i.e., lattice equations satisfied by the congruence lattices of all the algebras in a variety. Although this area represents only a small part of Alan’s mathematical work, this is a subject in which Alan was greatly interested and to which he made profound contributions. This paper surveys the struggles Alan and others of us made to understand this area. It also gives some of the recent results, including some of Alan’s, and lists several open problems.