The mathematics, it is very known, causes the fright, in truth... .the passion. It is why the mathematical discourse is keying more than another to the dimension of Real. The history of the mathematics give us precisely the opportunity of following the sudden changes of fortune of the mathematicians subjects at grips whit the logic who raise at the Real. He is enough interesting of noting that the gait of Jacques LACAN, all to the long of its teaching, seems to follow the parade logic who goes of the geometric Greek science until to advanced most recent topologic researches. So, he conducts to the foundation of the command of the Real, but also to the location of its different fashions of circling. To more than a consideration, LACAN himself show geometer, at the classic sense of scientist in mathematics, particularly interested to work on the category of space in the conceptualization of the psychoanalysis.