Irigaray is well-known as a psychoanalyst and feminist thinker. In the texts below, she tries to find ``sexist" bias in the discourse of modern science. She starts by saying that:
Every knowledge is produced by subjects in a given historical context. Even if it tries to be objective, even if its techniques want to be means of controlling it, science makes some choices, some exclusions, due, among other things, to the sex of the scientists. [Irigaray (1987)]
This is a very plausible statement. The problem comes when we look at her examples:
...As for Einstein, the main question that he raises, in my opinion, is that he does not leave us any other chance than his God, given his interest for accelerations without electromagnetic rebalancing ...But, for us, what does this general relativity represent, the one that is the law outside of the nuclear power plants and that questions our bodily inertia, vital necessary condition? [Irigaray (1987)]
This is quite remarkable: ``accelerations without electromagnetic rebalancing" is a pure invention of Irigaray. It simply does not make sense in physics and Einstein could not possibly have been interested in this nonexistent subject. Besides, general relativity has nothing to do with the nuclear power plants (she must confuse it with special relativity). How can one do a useful intellectual work on serious issues (like sexism in science) while being so ignorant?
Another work of Irigaray deals with sexism in fluid mechanics (Irigaray, 1985). An American feminist, Katherine Hayles, who is, in general, rather favorable to Irigaray summarizes her argument as follows:
The privileging of solid over fluid mechanics, and indeed the inability of science to deal with turbulent flow at all, she attributes to the association of fluidity with femininity. Whereas men have sex organs that protrude and become rigid, women have openings that leak menstrual blood and vaginal fluids. Although men, too, flow on occasion -- when semen is emitted, for example -- this aspect of their sexuality is not emphasized. It is the rigidity of the male organ that counts, not its complicity in fluid flow. These idealizations are reinscribed in mathematics, which conceives of fluids as laminated planes and other modified solid forms. In the same way that women are erased within masculinist theories and language, existing only as not-men, so fluids have been erased from science, existing only as not-solids. From this perspective it is no wonder that science has not been able to arrive at a successful model for turbulence. The problem of turbulent flow cannot be solved because the conceptions of fluids (and of women) have been formulated so as necessarily to leave unarticulated remainders. [Hayles (1992), p. 17]
But Hayles remarks that:
From talking with several applied mathematicians and fluid mechanicists about Irigaray's claim, I can testify that they unanimously conclude she does not know the first thing about their disciplines. In their view, her argument is not to be taken seriously. There is evidence to support this view. In a footnote to the chapter's first page, Irigaray airily advises the reader ``to consult some texts on solid and fluid mechanics'' without bothering to mention any. The lack of mathematical detail in her argument forces one to wonder whether she has followed this advice herself. Nowhere does she mention a name or date that would enable one to connect her argument with a specific theory of fluids, much less to trace debates between opposing theories. [Hayles (1992), p. 17]
Then, Hayles goes on to give her own arguments about sexism in fluid mechanics, which are also based on a rather deep misunderstanding of that science. But I shall leave that aside. I shall go back to Irigaray, and see what she writes about mathematics:
The mathematical sciences, in the theory of wholes [set theory], concern themselves with closed and open spaces ... They concern themselves very little with the question of the partially open, with wholes that are not clearly delineated [fuzzy sets], with any analysis of the problem of borders [boundaries]. [Irigaray (1982)]
Note again the sloppiness of the official translation (the correct translation from the French is in italics). Butof course, the problem of ``borders", i.e. of boundaries (e.g. for manifolds) is a big field of mathematics (except that it does not really make sense to speak of boundaries in pure set theory).
This would be an amusing confusion, but Sokal found, to his surprise, this sentence of Irigaray quoted by Suzanne Damarin, an American educator who writes high-school textbooks of mathematics, and who adds:
In the context provided by Irigaray we can see an opposition between the linear time of mathematics problems of related rates, distance formulas, and linear acceleration versus the dominant experiential cyclical time of the menstrual body. Is it obvious to the female mind-body that intervals have endpoints, that parabolas neatly divide the plane, and, indeed, that the linear mathematics of schooling describes the world of experience in intuitively obvious ways? [Damarin (1995).]
This is extraordinary: does anybody seriously think that women are unable to see that ``intervals have endpoints"? If this were true, it would be a very good argument against the access of women to the study of mathematics. Luckily, some of the best mathematics students nowadays are women and they would be very surprised indeed to learn that their ``menstrual body" prevents them from understanding such trivial facts. With friends such as Irigaray and Damarin, the feminist cause does not need enemies.