This paper summarizes approaches to developing mathematics that can act as a language for immunogenetics. The need for this has been documented by showing inadequacies of the standard symbolism. Apparent distinctions in symbolizing and conceptualizing factors involved in immunogenetics are seen to disappear in the mathematical models presented here. One model, a three-fold Boolean matrix factorization, subsumes all approaches to the idea of specificity and yet is general enough to incorporate data beyond that found only in a reaction matrix. © 1983.