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The two approaches are complementary, since both are attempts to describe formal systems with precise rules, and both demonstrate the power of the [[signifier]].
Although there is a general shift in [[Lacan]]'s work from the [[linguistic]] approach which predominates in the 1950s to a mathematical approach which predominates in the 1970s, there are traces of the mathematical approach as early as the 1940s (such as Lacan's analysis of a logical puzzle in Lacan, 1945; see his 1956 chain that "the laws of intersubjectivity are mathematical" in ).<ref>{{Ec, }} p.472).</ref>
The branches of [[mathematics]] which [[Lacan]] uses most are [[algebra]] and [[topology]], although there are also incursions into set theory and number theory (e.g<ref>{{E}} p. E, 316-18).</ref>
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[[Lacan]]'s use of [[mathematics]] represents an attempt to formalize [[psychoanalytic theory]], in keeping with his view that [[psychoanalytic theory]] should aspire to the formalization proper to [[science]].
"Mathematical formalization is our goal, our ideal." (<ref>{{S20, }} p.108)</ref>
[[Mathematics]] serves [[Lacan]] as a paradigm of modern scientific discourse, which "emerged from the little letters of mathematics." (<ref>{{S7, }} p.236)</ref>
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Also, by using mathematics Lacan attempts to prevent all attempts at imaginary intuitive understanding of [[psychoanalysis]].
