While peering across the internet this morning for the increasingly unlikely wisp of white smoke over Oxford I stumbled on the lengthy exchange sparked a few days ago by Jordan Ellenberg’s tweet on Piper Harron’s Princeton thesis, and then read the new Ph.D.s guest appearance on the mathbabe blog. She is alienated by the phallogocentrism of conventional mathematical discourse and she is not afraid to say so. The thesis begins with what could almost be called a manifesto.

Respected research math is dominated by men of a certain attitude. Even allowing for individual variation, there is still a tendency towards an oppressive atmosphere, which is carefully maintained and even championed by those who find it conducive to success. As any good grad student would do, I tried to fit in, mathematically. I absorbed the atmosphere and took attitudes to heart. I was miserable, and on the verge of failure. The problem was not individuals, but a system of self-preservation that, from the outside, feels like a long string of betrayals, some big, some small, perpetrated by your only support system. When I physically removed myself from the situation, I did not know where I was or what to do. First thought: FREEDOM!!!! Second thought: but what about the others like me, who don’t do math the “right way” but could still greatly contribute to the community? I combined those two thoughts and started from zero on my thesis. What resulted was a thesis written for those who do not feel that they are encouraged to be themselves.…

I’m unwilling to pretend that all manner of ways of thinking are equally encouraged, or that there aren’t very real issues of lack of diversity. It is not my place to make the system comfortable with itself. This may be challenging for happy mathematicians to read through; my only hope is that the challenge is accepted.

To judge by the enthusiastic reactions, PH’s challenge —

my goal is to write something that I can understand and remember and talk about with my non-puppeteer friends and family, which will allow me to speak my own language to the puppeteers —

is not only welcome, it appears to be long overdue. Is this a revolution?

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StaffanLet’s hope! More ways of presenting mathematics can only be a good thing, since which kinds of presentation tell one the most tends to vary from person to person.

I’m not sure that “phallogocentrism” is a very good name for what is attacked though, but rather a kind of “purity fetishism”, which requires purging published mathematics of everything except what is needed for the logical structure of proofs. Gone is all of the context, which contains motivations, alternative intuitive ways of picturing things, possible mistakes that one may risk making, and also personal attitudes to the proofs and things proved themselves.

After having looked through Harron’s thesis (very) quickly, it seems to me that what is different about it is that she adds those things back in. It isn’t an attack on logic: the mathematical argument is as rigorous as anyone else’s, and the role of logic (qua correct argumentation) is not questioned. But she (like me, and I would guess many other wannabe mathematicians) has trouble grasping the “pure” logical structure of the maths without the surrounding context.

I’m also not sure that it is an explicitly “feminist” thing to do… unless one somehow falls into the trap of connecting logic to possession of a phallos. As someone who works in the former and has been cursed with the latter, I can report that their connection is usually not a supporting one, but rather the opposite. I think that some people simply have an easier time understanding maths when it is presented in a rich context, rather than without one, and I don’t know if that is correlated with gender.

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mathematicswithoutapologiesPost authorTo be honest, I’m not sure I am using the word in its authorized sense, but I think it’s consistent with the deconstructive spirit. On p. 313 of the

Encyclopedia of Postmodernism, you can read thatIt becomes

phallogocentrismwhen the authorizing presence is identified with the (paternal) phallus as in Lacan’s psychoanalysis. At least that’s what it meant the first time around, with Derrida; the word has evolved in the intervening decades.I chose the word because PH’s gesture is (a) clearly aimed at the perception of an oppressive “authorizing presence” which (b) she identifies with “men of a certain attitude,” because (c) it takes the form of “liberated” writing, and because it expresses these three features in a single lexeme. Please feel free to suggest alternatives. I have not had a chance to consult one of the local deconstructionists to authorize my interpretation (but if they are consistent, they would say “what, me authorize?”).

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StaffanActually, I wasn’t even aware of Derrida’s use, but rather interpreted the word as your own creation! By its construction, It invites a reader to interpret it herself, even though I mistakenly took the “logo” to refer to logic, rather than to language.

I agree of course that Harron’s thesis is a revolt against the mathematical “establishment”, which does indeed mainly consist of “men of a certain attitude”. But this is mostly because it doesn’t look like PhD theses usually look. Seen from the actual way she presents her material, I think that the most significant positive aspect of it is the inclusion of lots of context, much of which is usually considered non-mathematical. In particular, she very much refuses to exorcise traces of the context of discovery.

So perhaps I would call it an attack on “context-free mathematics”? It doesn’t have the same elegance as “phallogocentrism”, though…

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