The metonymy and metaphor functions in ‘The Instance of the Letter’ are a turning point in Lacan's thought. While he had sought to transform psychoanalysis into a science by providing formalizations laying out unconscious operative procedures in his works until the mid-1950s, this is no longer the case in ‘The Instance of the Letter’. Yet Lacan insists we take the formulas literally, that is, as mathematical functions. This essay argues that taking Lacan's request seriously leads to a necessary breakdown in (...) understanding that forces us to go through the split subject's disrupted constitutive process of metonymy and metaphor. Taking the language functions literally engenders the effect they merely seem to signify. Disruption is a catalyst for the split subject's constitutive, self-formalizing process, and its role is crucial for understanding how Lacan reconceptualized the relation between psychoanalysis and science. Lacan does not provide a formalism for us to master, but puts it into operation. The language functions are mathemes avant la lettre. (shrink)